Kurt Mehlhorn

Abstract New Constructions of (α, β)-Spanners and Purely Additive Spanners ∗ (2009)

Surender Baswana, Telikepalli Kavitha, Kurt Mehlhorn, Seth Pettie

An (α, β)-spanner of an unweighted graph G is a subgraph H that approximates distances in G in the following sense. For any two vertices u, v: δH(u, v) ≤ αδG(u, v) + β, where δG is the...

Boolean Operations on 3D Selective Nef ComplexesData Structure, Algorithms, and Implementation (2009)

Miguel Granados, Peter Hachenberger, Susan Hert, Lutz Kettner, Kurt Mehlhorn, Michael Seel

Abstract. We describe a data structure for three-dimensional Nef complexes, al-gorithms for boolean operations on them, and our implementation of data structure and algorithms. Nef polyhedra were...

Compaction on the (2009)

Kurt Mehlhorn, Wolfgang Rulling

Abstract-In this paper we introduce a general framework for com-paction on a torus. This problem comes up whenever an array of iden-tical cells has to be compacted. We instantiate our framework with...

Abstract Popular Matchings (2008)

David J. Abraham, Robert W. Irving, Telikepalli Kavitha, Kurt Mehlhorn

We consider the problem of matching a set of applicants to a set of posts, where each applicant has a preference list, ranking a non-empty subset of posts in order of preference, possibly involving...

der Universität des Saarlandes von (2008)

Andreas Crauser, Professor Dr, Kurt Mehlhorn, Mpi Für Informatik, Deutsche Kurzzusammenfassung

Die zu verarbeitenden Datenmengen sind in den letzten Jahren dramatisch gestiegen, so daß Externspeicher (in Form von Festplatten) eingesetzt wird, um die Datenmengen zu speichern. Algorithmen und...

Robert W. Irving Rank-Maximal Matchings (2008)

Telikepalli Kavitha, Kurt Mehlhorn, Dimitrios Michail, Katarzyna Paluch

Suppose that each member of a set ¡ of applicants ranks a subset of a set of posts in an order of preference, possibly involving ties. A matching is a set of (applicant, post) pairs such that each...

New Constructions of ¡ β ¢ α-Spanners and Purely Spanners£ Additive (2008)

Surender Baswana, Telikepalli Kavitha, Kurt Mehlhorn, Seth Pettie

An ¦ α § β ¨-spanner of an unweighted graph G is a subgraph H that approximates distances in G in the following sense. For any two vertices u § v: δH ¦ u § v¨� © αδG ¦ u § v¨� �...

Efficient Graphlet Kernels for Large Graph Comparison (2008)

Shervashidze, Nino, Vishwanathan, S.V.N., Petri, Tobias H., Mehlhorn, Kurt, Borgwardt, Karsten M.

State-of-the-art graph kernels do not scale to large graphs with hundreds of nodes and thousands of edges. In this article we attempt to rectify this situation. We compare graphs by counting common...

Efficient Graphlet Kernels for Large Graph Comparison (2008)

Shervashidze, Nino, Vishwanathan, S V N, Petri, Tobias, Mehlhorn, Kurt, Borgwardt, Karsten

State-of-the-art graph kernels do not scale to large graphs with hundreds of nodes and thousands of edges. In this article we propose to compare graphs by counting common {\it graphlets}, \ie...

An (O)over-tilde (m(2)n) Algorithm for Minimum Cycle Basis of Graphs (2008)

Kavitha, Telikepalli, Mehlhorn, Kurt, Michail, Dimitrios, Paluch, Katarzyna E

We consider the problem of computing a minimum cycle basis of an undirected non-negative edge-weighted graph G with m edges and n vertices. In this problem, a {0,1} incidence vector is associated...

Month: 12 (2008)

Stefan Funke, Christian Klein, Kurt Mehlhorn, Susanne Schmitt

Project co-funded by the European Commission within FP6 (2002–2006) under contract nr. IST-006413 Most geometric algorithms are idealistic in the sense that they are designed for the Real-RAM model...

Computer Algorithms. Addison-Wesley, 1974. (2008)

Milton Abramowitz, Irene A. Stegun, Leonard M. Adleman, Carl Pomerance, ...

numbers from composite numbers. Annals of Mathematics, 117:173–206, 1983. [4] Alok Aggarwal and Jeffrey Scott Vitter. The input/output complexity of sorting and related problems. Communications of...

Additive Spanners and (α, β)-Spanners ∗ (2008)

Surender Baswana, Telikepalli Kavitha, Kurt Mehlhorn, Seth Pettie

An (α, β)-spanner of an unweighted graph G is a subgraph H that distorts distances in G up to a multiplicative factor of α and an additive term β. It is well known that any graph contains a...

Project number IST-006413 ACS Algorithms for Complex Shapes with Certified Numerics and Topology Sweeping and Maintaining Two-dimensional Arrangements on Quadrics (2008)

Eric Berberich, Efi Fogel, Dan Halperin, Kurt Mehlhorn, Ron Wein

Project co-funded by the European Commission within FP6 (2002–2006) under contract nr. IST-006413 We show how to compute and maintain the two-dimensional arrangement on a quadric that is induced by...

Minimum Cycle Bases: Faster and Simpler (2008)

Kurt Mehlhorn, Dimitrios Michail

We consider the problem of computing exact or approximate minimum cycle bases of an undirected (or directed) edge-weighted graph G with m edges and n vertices. In this problem, a {0, 1} ({−1, 0,...

An Õ(m2 n) algorithm for Minimum Cycle Basis of graphs ∗ (2008)

Telikepalli Kavitha, Kurt Mehlhorn, Dimitrios Michail, Katarzyna E. Paluch

We consider the problem of computing a minimum cycle basis in a graph G with m edges and n vertices. The input to this problem is an undirected graph whose edges have non-negative weights. In this...

Approximability of Cycle Covers and Smoothed Analysis of Binary Search Trees (2008)

Bodo Manthey, Zur Erlangung Der, Bodo Manthey, Berichterstatter Prof, Dr. Rüdiger Reischuk, ...

the years. I also thank the current and former members of the Institut für Theoretische Informatik at the Universität zu Lübeck for many valuable discussions, not only about computer science. In...

Minimum Cycle Bases in Graphs Algorithms and Applications (2008)

Kurt Mehlhorn

A cycle basis of a graph is a family of cycles which spans all cycles of the graph. In an undirected graph, a cycle is simply a set of edges with respect to which every vertex has even degree. We...

ii Datum des Kolloquiums: 21.10.2002 (2008)

Ulrich Meyer, Dekan Prof, Gutachter Prof, Dr. Kurt Mehlhorn, Prof Dr, ...

Abstract. We study the performance of algorithms for the Single-Source Shortest-Paths (SSSP) problem on graphs with   nodes ¡ and edges with nonnegative random weights. All previously known SSSP...

Federal Republic of Germany (2008)

Helmut Alt, Rudolf Fleischer, Michael Kaufmann, Kurt Mehlhorn, Stefan Schirra, Christian Uhrig, ...

Abstract: We study rigid motions of a rectangle amidst polygonal obstacles. The best known algorithms for this problem have running time f~(n 2) where n is the number of obstacle corners. We...

Abstract Point Containment in the Integer Hull of a Polyhedron 1 (2008)

Ernst Althaus, Friedrich Eisenbrand, Stefan Funke, Kurt Mehlhorn

We show that the point containment problem in the integer hull of a polyhedron, which is defined by m inequalities, with coefficients of at most ϕ bits can be solved in time O(m + ϕ) in the...

158 Certifying Algorithms for Recognizing Interval Graphs and Permutation Graphs (2008)

Dieter Kratsch, Ross M. Mcconnell, Kurt Mehlhorn, Jeremy P. Spinrad

A certifying algorithm for a decision problem is an algorithm that provides a certificate with each answer that it produces. The certificate is a piece of evidence that proves that the answer has not...

Abstract: POLYNOMIAL AND ABSTRACT SUBRECURSIVE CLASSES* (2008)

Kurt Mehlhorn

We define polynomial time computable operator. Our definition generalizes Cook's definition to arbitrary function inputs. Polynomial classes are defined in terms of these operators; the...

der Universität des Saarlandes (2008)

Roman Dementiev, Prof Dr. -ing, Gerhard Weikum, Prof Dr. -ing, Gerhard Weikum, Prof Dr, ...

In recent years, the development of theoretically I/O-efficient algorithms and data structures has received considerable attention. However, much less has been done to evaluate their performance, in...

Smoothed Analysis of Three Combinatorial Problems ⋆ (2008)

Cyril B, René Beier, Kurt Mehlhorn

Abstract. Smoothed analysis combines elements over worst-case and average case analysis. For an instance x, the smoothed complexity is the average complexity of an instance obtained from x by a...

ii Datum des Kolloquiums: 21.10.2002 (2008)

Ulrich Meyer, Dekan Prof, Gutachter Prof, Dr. Kurt Mehlhorn, Prof Dr, ...

Abstract. We study the performance of algorithms for the Single-Source Shortest-Paths (SSSP) problem on graphs withÒnodes andÑedges with nonnegative random weights. All previously known SSSP...

AND (2008)

Kurt Mehlhorn, Athanasios Tsakalidis

Abstract. A new data structure called interpolation search tree (1ST) is presented which supports interpolation search and insertions and deletions. Amortized insertion and deletion cost is O(log n)....

LEDA A Library of Efficient Data Types and Algorithms * (2008)

Stefan Niiher, Kurt Mehlhorn

LEDA is a library of efficient data types and algorithms. At present, its strength is graph algorithms and related data structures. The computational geometry part is evolving. The main features of...

Minimum Cycle Bases: Faster and Simpler (2008)

Kurt Mehlhorn, Dimitrios Michail

We consider the problem of computing exact or approximate minimum cycle bases of an undirected (or directed) edge-weighted graph G with m edges and n vertices. In this problem, a {0, 1} ({−1, 0,...

Abstract Certifying and Repairing Solutions to Large LPs (2008)

Marcel Dhiflaoui, Stefan Funke, Kurt Mehlhorn, Michael Seel, Elmar Schömer, ...

State-of-the-art linear programming (LP) solvers give solutions without any warranty. Solutions are not guaranteed to be optimal or even close to optimal. Of course, it is generally believed that the...

On the All-Pairs Shortest Path Algorithm (2008)

Of Moffat, Kurt Mehlhorn, Volker Priebe

Abstract. We review how to solve the all-pairs shortest path problem in a non-negatively weighted digraph with n vertices in expected time O(n 2 log n). This bound is shown to hold with high...

Geometric Computing with CGAL and LEDA (2008)

Kurt Mehlhorn, Stefan Schirra

Abstract. LEDA and CGAL are platforms for combinatorial and geometric computing. We discuss the use of LEDA and CGAL for geometric computing and show that they provide a unique framework for exact,...

Universit~t des Saarlandes (2008)

Scott Huddleston, Kurt Mehlhorn

Robust balancing is a technique for maintaining generalized B-trees with a cumulative rebalancing cost that is asymptotically linear. It is especially significant in conjunction with fingers, which...

Certifying and Repairing Solutions to Large LPs - How Good are LP-solvers? (2008)

Marcel Dhiflaoui, Carsten Kwappik, Stefan Funke, Kurt Mehlhorn, Michael Seel, ...

State-of-the-art linear programming (LP) solvers give solutions without any warranty. Solutions are not guaranteed to be optimal or even close to optimal. Of course, it is generally believed that the...

External-Memory Breadth-First Search with Sublinear I/O (2008)

Kurt Mehlhorn, Ulrich Meyer

Breadth-first search (BFS) is a basic graph exploration technique. We give the first external memory algorithm for sparse undirected graphs with sublinear I/O. The best previous algorithm requires (n...

A Faster Deterministic Algorithm for Minimum Cycle Basis in Directed Graphs (2008)

Ramesh Hariharan, Telikepalli Kavitha, Kurt Mehlhorn, Kavitha Kurt Mehlhorn

We consider the problem of computing a minimum cycle basis in a directed graph. The input to this problem is a directed graph G whose edges have non-negative weights. A cycle in this graph is...

SCIL - Symbolic Constraints in Integer Linear Programming (2008)

Ernst Althaus, Alexander Bockmayr, Matthias Elf, Michael Jünger, Thomas Kasper, Kurt Mehlhorn

We describe a new software system SCIL that introduces symbolic constraints into branch-and-cut-and-price algorithms for integer linear programs. Symbolic constraints are known from constraint...

Classroom examples of robustness problems in geometric computations (2008)

Kettner, Lutz, Mehlhorn, Kurt, Pion, Sylvain, Schirra, Stefan, Yap, Chee

The algorithms of computational geometry are designed for a machine model with exact real arithmetic. Substituting floating-point arithmetic for the assumed real arithmetic may cause...

Classroom examples of robustness problems in geometric computations (2008)

Kettner, Lutz, Mehlhorn, Kurt, Pion, Sylvain, Schirra, Stefan, Yap, Chee

The algorithms of computational geometry are designed for a machine model with exact real arithmetic. Substituting floating-point arithmetic for the assumed real arithmetic may cause...

Faster Algorithms for Minimum Cycle Basis in Directed Graphs (2008)

Hariharan, Ramesh, Kavitha, Telikepalli, Mehlhorn, Kurt

We consider the problem of computing a minimum cycle basis in a directed graph. The input to this problem is a directed graph $G$ whose edges have nonnegative weights. A cycle in this graph is...

z Max-Planck-Institut (2007)

Lower Bounds, Martin Dietzfelbinger, Anna Karlin, Kurt Mehlhorn, Fur Informatik, ...

The dynamic dictionary problem is considered: provide an algorithm for storing a dynamic set, allowing the operations insert, delete, and lookup. A dynamic perfect hashing strategy is given: a...

X (2007)

Kurt Mehlhorn, Christian Uhrig

1. Min-cuts in undirected graphs. Let G = (V; E) be an undirected graph (self-loops and parallel edges are allowed) and let w: E!!0 be a non-negative weight function on the edges of G. A cut C of G...

Acknowledgements (2007)

Kurt Mehlhorn, Kurt Mehlhorn, Stefan Schirra, Stefan Schirra

Partially supported by ESPRIT project 28155 (GALIA). Work done while the second author was at Max-Planck-Institut fur Informatik. We prove a separation bound for a large class of algebraic...

DB log M=B (2007)

Sublinear I/o, Kurt Mehlhorn, Ulrich Meyer

Abstract. Breadth-first search (BFS) is a basic graph exploration technique. We give the first external memory algorithm for sparse undirected graphs with sublinear I/O. The best previous algorithm...

zur Erlangung des Grades (2007)

Volker Priebe, Dekan Prof, Dr. Rainer Schulze-pillot-ziemen, Gutachter Prof, Dr. Kurt Mehlhorn, ...

ii Abstract. We study both upper and lower bounds on the average-case complexity of shortest-paths algorithms. It is proved that the all-pairs shortest-paths problem on n-vertex networks can be...

An Ecient Algorithm for the Conguration Problem of Dominance Graphs (2007)

Ernst Althaus, Denys Duchier, Alexander Koller, Kurt Mehlhorn, Joachim Niehren, Sven Thiel

Dominance constraints are logical tree descriptions originating from automata theory that have multiple applications in computational linguistics. The satisability problem of dominance constraints is...

Alan Frieze (2007)

Colin Cooper, Kurt Mehlhorn, Volker Priebe

complexity of shortest-paths problems in the

Veri ed Result Checkers (2007)

Kurt Mehlhorn

The programs in LEDA have reached a very high level of reliability. In fact, I claim that all major algorithms and data structures are correct. We have reached the current level of reliability...

Certifying and Repairing Solutions to Large LPs - How Good are LP-solvers? (2007)

Marcel Dhiflaoui, Carsten Kwappik, Stefan Funke, Kurt Mehlhorn, Michael Seel, ...

State-of-the-art linear programming (LP) solvers give solutions without any warranty. Solutions are not guaranteed to be optimal or even close to optimal. Of course, it is generally believed that the...

Algorithms to Compute Minimum Cycle Basis in Directed Graphs (2007)

Kavitha, Telikepalli, Mehlhorn, Kurt

We consider the problem of computing a minimum cycle basis in a directed graph G with m arcs and n vertices. The arcs of G have non-negative weights assigned to them. In this problem a {-1,0,1}...

Algorithms to Compute Minimum Cycle Basis in Directed Graphs (2007)

Kavitha, Telikepalli, Mehlhorn, Kurt

We consider the problem of computing a minimum cycle basis in a directed graph G with m arcs and n vertices. The arcs of G have non-negative weights assigned to them. In this problem a {-1,0,1}...

Popular Matchings (2007)

Abraham, David J, Irving, Robert W, Kavitha, Telikepalli, Mehlhorn, Kurt

We consider the problem of matching a set of applicants to a set of posts, where each applicant has a preference list, ranking a nonempty subset of posts in order of preference, possibly involving...

Popular Matchings (2007)

Abraham, David J, Irving, Robert W, Kavitha, Telikepalli, Mehlhorn, Kurt

We consider the problem of matching a set of applicants to a set of posts, where each applicant has a preference list, ranking a nonempty subset of posts in order of preference, possibly involving...

Sweeping and maintaining two-dimensional arrangements on surfaces: A first step (2007)

Eric Berberich, Efi Fogel, Dan Halperin, Kurt Mehlhorn, Ron Wein

We introduce a general framework for processing a set of curves defined on a continuous two-dimensional parametric surface, while sweeping the parameter space. We can handle planes, cylinders,...

Acknowledgements (2007)

Pavel Emeliyanenko, Erstgutachter First Examiner, Prof Dr, Kurt Mehlhorn, Mpi Informatik Saarbrücken, ...

First of all I would like to thank Prof. Dr. Kurt Mehlhorn, my supervising professor at Saarland University, for offering me this stimulating topic as well as Algorithm Engineering course that...

Sweeping and maintaining two-dimensional arrangements on surfaces: A first step (2007)

Eric Berberich, Efi Fogel, Dan Halperin, Kurt Mehlhorn, Ron Wein

Abstract. We introduce a general framework for sweeping a set of curves embedded on a two-dimensional parametric surface. We can handle planes, cylinders, spheres, tori, and surfaces homeomorphic to...

New approximation algorithms for minimum cycle bases of graphs (2007)

Telikepalli Kavitha, Kurt Mehlhorn, Dimitrios Michail

We consider the problem of computing an approximate minimum cycle basis of an undirected non-negative edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also...

Engineering DFS-Based Graph Algorithms (2007)

Kurt Mehlhorn, Stefan Näher, Peter S

Depth-first search (DFS) is the basis for many efficient graph algorithms. We introduce general techniques for efficient implementations of DFS-based graph algorithms and exemplify them on three...

New approximation algorithms for minimum cycle bases of graphs (2007)

Telikepalli Kavitha, Kurt Mehlhorn, Dimitrios Michail

We consider the problem of computing an approximate minimum cycle basis of an undirected edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this...

Implementing Minimum Cycle Basis Algorithms (2007)

Mehlhorn, Kurt, Michail, Dimitrios

In this paper, we consider the problem of computing a minimum cycle basis of an undirected graph G = (V,E) with n vertices and m edges. We describe an efficient implementation of an O(m3...

New Approximation Algorithms for Minimum Cycle Bases of Graphs (2007)

Kavitha, Telikepalli, Mehlhorn, Kurt, Michail, Dimitrios

We consider the problem of computing an approximate minimum cycle basis of an undirected edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this...

A Faster Deterministic Algorithm for Minimum Cycle Bases in Directed Graphs (2006)

Hariharan, Ramesh, Kavitha, Telikepalli, Mehlhorn, Kurt

We consider the problem of computing a minimum cycle basis in a directed graph. The input to this problem is a directed graph G whose edges have non-negative weights. A cycle in this graph is...

A Faster Deterministic Algorithm for Minimum Cycle Bases in Directed Graphs (2006)

Hariharan, Ramesh, Kavitha, Telikepalli, Mehlhorn, Kurt

We consider the problem of computing a minimum cycle basis in a directed graph. The input to this problem is a directed graph G whose edges have non-negative weights. A cycle in this graph is...

Acknowledgements (2006)

Michael Kerber, Erstgutachter First Examiner, Prof Dr, Kurt Mehlhorn, Zweitgutachterin Second Examiner, ...

The following persons contributed to the success of this work. I want to thank them all for their support during the last year: Arno Eigenwillig provided great assistance in all respects, a special...

A faster deterministic algorithm for minimum cycle basis in directed graphs (2006)

Ramesh Hariharan, Telikepalli Kavitha, Kurt Mehlhorn

Abstract. We consider the problem of computing a minimum cycle basis in a directed graph. The input to this problem is a directed graph G whose edges have non-negative weights. A cycle in this graph...

Faster randomized and deterministic algorithms for minimum cycle bases in directed graphs. Preliminary versions of the results in this paper appeared in ICALP’05 and ICALP’06. submitted for publication (2006)

Ramesh Hariharan, Telikepalli Kavitha, Kurt Mehlhorn

We consider the problem of computing a minimum cycle basis in a directed graph. The input to this problem is a directed graph G whose edges have non-negative weights. A cycle in this graph is...

Reliable and efficient computational geometry via controlled perturbation (2006)

Kurt Mehlhorn, Ralf Osbild, Michael Sagraloff

Abstract. Most algorithms of computational geometry are designed for the Real-RAM and non-degenerate inputs. We call such algorithms idealistic. Executing an idealistic algorithm with floating point...

ii Datum des Kolloquiums: 14. 05. 2007 (2006)

Annamária Kovács, Dekan Prof, Dr. Thorsten Herfet, Vorsitzender Prof, Dr. Raimund Seidel, ...

iii Abstract. The thesis deals with problems from two distint areas of scheduling theory. In the first part we consider the preemptive Sum Multicoloring (pSMC) problem. In an instance of pSMC,...

Matching algorithms are fast in sparse random graphs (2006)

Holger Bast, Kurt Mehlhorn, Guido Schäfer, Hisao Tamaki

Abstract. We present an improved average case analysis of the maximum cardinality matching problem. We show that in a bipartite or general random graph on n vertices, with high probability every...

Matching algorithms are fast in sparse random graphs (2006)

Holger Bast, Kurt Mehlhorn, Guido Schäfer, Hisao Tamaki

We present an improved average case analysis of the maximum cardinality matching problem. We show that in a bipartite or general random graph on n vertices, with high probability every non-maximum...

Rank-Maximal Matchings (2006)

Irving, Robert W., Kavitha, Telikepalli, Mehlhorn, Kurt, Michail, Dimitrios, Paluch, Katarzyna

Suppose that each member of a set A of applicants ranks a subset of a set P of posts in an order of preference, possibly involving ties. A matching is a set of (applicant, post) pairs such that each...

New bounds for the Descartes method (2006)

Krandick, Werner, Mehlhorn, Kurt

We give a new bound for the number of recursive subdivisions in the Descartes method for polynomial real root isolation. Our proof uses Ostrowski’s theory of normal power series from 1950 which has...

Reply to "Backward Error Analysis ..." (2006)

Kettner, Lutz, Mehlhorn, Kurt, Pion, Sylvain, Schirra, Stefan, Yap, Chee, Gavrilova, Marina, ...

The algorithms of computational geometry are designed for a machine model with exact real arithmetic. Substituting floating-point arithmetic for the assumed real arithmetic may cause implementations...

Reliable and Efficient Computational Geometry Via Controlled Perturbation (2006)

Mehlhorn, Kurt, Osbild, Ralf, Sagraloff, Michael, Bugliesi, Michele, Preneel, Bart, Sassone, Vladimir, ...

Most algorithms of computational geometry are designed for the Real-RAM and non-degenerate input. We call such algorithms idealistic. Executing an idealistic algorithm with floating point arithmetic...

A Faster Deterministic Algorithm for Minimum Cycle Bases in Directed Graphs (2006)

Hariharan, Ramesh, Telikepalli, Kavitha, Mehlhorn, Kurt, Bugliesi, Michele, Preneel, Bart, Sassone, Vladimir, ...

We consider the problem of computing a minimum cycle basis in a directed graph. The input to this problem is a directed graph G whose edges have non-negative weights. A cycle in this graph is...

Reliable and Efficient Geometric Computing (2006)

Mehlhorn, Kurt, Calamoneri, Tiziana, Finocchi, Irene, Italiano, Giuseppe F.

Reliable implementation of geometric algorithms is a notoriously difficult task. Algorithms are usually designed for the Real-RAM, capable of computing with real numbers in the sense of mathematics,...

Implementing Minimum Cycle Basis Algorithms (2006)

Mehlhorn, Kurt, Michail, Dimitrios

In this paper, we consider the problem of computing a minimum cycle basis of an undirected graph G = (V,E) with n vertices and m edges. We describe an efficient implementation of an O(m3...

Polyline Fitting of Planar Points under Min-sum Criteria (2006)

Aronov, Boris, Asano, Tetsuo, Katoh, Naoki, Mehlhorn, Kurt, Tokuyama, Takeshi

Fitting a curve of a certain type to a given set of points in the plane is a basic problem in statistics and has numerous applications. We consider fitting a polyline with k joints under the min-sum...

Matching Algorithms are Fast in Sparse Random Graphs (2006)

Bast, Holger, Mehlhorn, Kurt, Schäfer, Guido, Tamaki, Hisao

We present an improved average case analysis of the maximum cardinality matching problem. We show that in a bipartite or general random graph on $n$ vertices, with high probability every non-maximum...

Certifying Algorithms for Recognizing Interval Graphs and Permutation Graphs (2006)

Kratsch, Dieter, McConnell, Ross, Mehlhorn, Kurt, Spinrad, Jeremy P.

A certifying algorithm for a problem is an algorithm that provides a certificate with each answer that it produces. The certificate is a piece of evidence that proves that the answer has not been...

A Descartes Algorithms for Polynomials with Bit-Stream Coefficients (2006)

Mehlhorn, Kurt, Eigenwillig, Arno, Kettner, Lutz, Krandick, Werner, Schmitt, Susanne, Wolpert, Nicola

The Descartes method is an algorithm for isolating the real roots of square-free polynomials with real coefficients. We assume that coefficients are given as (potentially infinite) bit-streams. In...

Polyline fitting of planar points under min-sum criteria (2006)

ARONOV, BORIS, ASANO, TETSUO, KATOH, NAOKI, MEHLHORN, KURT, TOKUYAMA, TAKESHI

Fitting a curve of a certain type to a given set of points in the plane is a basic problem in statistics and has numerous applications. We consider fitting a polyline with k joints under the min-sum...

A Polynomial Time Algorithm for Minimum Cycle Basis in Directed Graphs (2005)

Telikepalli Kavitha, Kurt Mehlhorn

Abstract. We consider the problem of computing a minimum cycle basis in a directed graph G with m arcs and n vertices. The arcs of G have non-negative weights assigned to them. We give an Õ(m4 n)...

Exacus: Efficient and exact algorithms for curves and surfaces (2005)

Eric Berberich, Arno Eigenwillig, Michael Hemmer, Susan Hert, Lutz Kettner, Kurt Mehlhorn, ...

Abstract. We present the first release of the EXACUS C++ libraries. We aim for systematic support of non-linear geometry in software libraries. Our goals are efficiency, correctness, completeness,...

A Descartes algorithm for polynomials with bit-stream coefficients (2005)

Arno Eigenwillig, Lutz Kettner, Werner Kr, Kurt Mehlhorn, Susanne Schmitt, Nicola Wolpert

Abstract. The Descartes method is an algorithm for isolating the real roots of square-free polynomials with real coefficients. We assume that coefficients are given as (potentially infinite)...

Exacus: Efficient and exact algorithms for curves and surfaces (2005)

Eric Berberich, Arno Eigenwillig, Michael Hemmer, Susan Hert, Lutz Kettner, Kurt Mehlhorn, ...

Abstract. We present the first release of the EXACUS C++ libraries. We aim for systematic support of non-linear geometry in software libraries. Our goals are efficiency, correctness, completeness,...

A Descartes algorithm for polynomials with bit-stream coefficients (2005)

Arno Eigenwillig, Lutz Kettner, Werner Kr, Kurt Mehlhorn, Susanne Schmitt, Nicola Wolpert

Abstract. The Descartes method is an algorithm for isolating the real roots of square-free polynomials with real coefficients. We assume that coefficients are given as (potentially infinite)...

Implementing Minimum Cycle Basis Algorithms (2005)

Kurt Mehlhorn, Dimitrios Michail

In this paper we consider the problem of computing a minimum cycle basis of an undirected graph G = (V, E) with n vertices and m edges. We describe an e#cient implementation of an O(m algorithm...

Network Problems with Non-Polynomial (2005)

Weights And Applications, Kurt Mehlhorn, Dimitrios Michail

The most e#cient algorithms for several network problems like minimum cost flow and the maximum weight matching problem follow the primal-dual paradigm. These algorithms perform arithmetic (additions...

EXACUS: Efficient and Exact Algorithms for Curves and Surfaces (2005)

Eric Berberich, Arno Eigenwillig, Michael Hemmer, Susan Hert, Lutz Kettner, Kurt Mehlhorn, ...

We present the first release of the EXACUS C++ libraries. We aim for systematic support of non-linear geometry in software libraries. Our goals are efficiency, correctness, completeness, clarity of...

Towards Optimal Multiple Selection (2005)

Kanela Kaligosi, Kurt Mehlhorn, J. Ian Munro, Peter Sanders, Peter S

The multiple selection problem asks for the elements of rank r1 , r2 , . . . , rk from a linearly ordered set of n elements. Let B denote the information theoretic lower bound on the number of...

A Descartes Algorithm for Polynomials with Bit-Stream Coefficients (2005)

Arno Eigenwillig, Lutz Kettner, Werner Krandick, Kurt Mehlhorn, Susanne Schmitt, Nicola Wolpert

The Descartes method is an algorithm for isolating the real roots of square-free polynomials with real coefficients. We assume that coefficients are given as (potentially infinite) bit-streams. In...

Algorithms to Compute Minimum Cycle Basis in Directed Graphs (2005)

Telikepalli Kavitha, Kurt Mehlhorn

We consider the problem of computing a minimum cycle basis in a directed graph G with m arcs and n vertices. The arcs of G have nonnegative weights assigned to them. In this problem a associated with...

Cycle Bases of Graphs and Sampled Manifolds (2005)

Craig Gotsman, Kanela Kaligosi, Kurt Mehlhorn, Dimitrios Michail, Evangelia Pyrga

... are the dominant output of a multitude of 3D scanning devices. The usefulness of these devices rests on being able to extract properties of the surface from the sample. We show that, under...

New constructions of (α, β)-spanners and purely additive spanners (2005)

Surender Baswana, Telikepalli Kavitha, Kurt Mehlhorn, Seth Pettie

An α�β-spanner of an unweighted graph G is a subgraph H that approximates distances in G in the following sense. For any two vertices u�v: δH u�v�αδG u�v β, where δG is the distance...

Cycle bases of graphs and sampled manifolds (2005)

Craig Gotsman, Kanela Kaligosi, Kurt Mehlhorn, Dimitrios Michail, Evangelia Pyrga

Point samples of a surface in R 3 are the dominant output of a multitude of 3D scanning devices. The usefulness of these devices rests on being able to extract properties of the surface from the...

Site: MPI Month: 36 (2005)

Eric Berberich, Arno Eigenwillig, Michael Hemmer, Susan Hert, Lutz Kettner, Kurt Mehlhorn, ...

Project funded by the European Community under the “Information Society Technologies” Programme (1998–2002)

Algorithms to compute Minimum Cycle Basis in Directed Graphs Full version submitted to special issue, preliminary version (2005)

Telikepalli Kavitha, Kurt Mehlhorn

We consider the problem of computing a minimum cycle basis in a directed graph G with m arcs and n vertices. The arcs of G have nonnegative weights assigned to them. In this problem a {−1,0,1}...

Implementing minimum cycle basis algorithms (2005)

Kurt Mehlhorn, Dimitrios Michail

In this paper, we consider the problem of computing a minimum cycle basis of an undirected graph G = (V,E) with n vertices and m edges. We describe an efficient implementation of an O(m3 + mn2 log n)...

Towards optimal multiple selection (2005)

Kanela Kaligosi, Kurt Mehlhorn, J. Ian Munro, Peter S

Abstract. The multiple selection problem asks for the elements of rank r1, r2,..., rk from a linearly ordered set of n elements. Let B denote the information theoretic lower bound on the number of...

Implementing minimum cycle basis algorithms (2005)

Kurt Mehlhorn, Dimitrios Michail

In this paper we consider the problem of computing a minimum cycle basis of an undirected graph G = (V, E) with n vertices and m edges. We describe an efficient implementation of an O(m 3 + mn 2 log...

Implementing Minimum Cycle Basis Algorithms (2005)

Mehlhorn, Kurt, Michail, Dimitrios, Nikoletseas, Sotiris

In this paper we consider the problem of computing a minimum cycle basis of an undirected graph $G = (V,E)$ with $n$ vertices and $m$ edges. We describe an efficient implementation of an $O(m^3 +...

Controlled Perturbation for Delaunay Triangulations (2005)

Funke, Stefan, Klein, Christian, Mehlhorn, Kurt, Schmitt, Susanne

Most geometric algorithms are idealistic in the sense that they are designed for the Real-RAM model of computation and for inputs in general position. Real inputs may be degenerate and floating point...

EXACUS: Efficient and exact algorithms for curves and surfaces (2005)

Berberich, Eric, Eigenwillig, Arno, Hemmer, Michael, Hert, Susan, Kettner, Lutz, Mehlhorn, Kurt, ...

We present the first open-source release of the C\texttt{++} libraries of the \textsc{Exacus} project of the Max-Planck-Institut f{\"u}r Informatik. Our software computes arrangements of curves and...

04301 Abstracts Collection -- Cache-Oblivious and Cache-Aware Algorithms (2005)

Arge, Lars, Bender, Michael A., Demaine, Erik, Leiserson, Charles, Mehlhorn, Kurt

The Dagstuhl Seminar 04301 ``Cache-Oblivious and Cache-Aware Algorithms'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl, from 18.07.2004 to 23.07.2004. During...

An efficient graph algorithm for dominance constraints (2004)

Althaus, Ernst, Duchier, Denys, Koller, Alexander, Mehlhorn, Kurt, Niehren, Joachim, Thiel, Sven

Dominance constraints are logical descriptions of trees that are widely used in computational linguistics. Their general satisfiability problem is known to be NP-complete. Here we identify normal...

Classroom Examples of Robustness Problems in Geometric Computations (2004)

Kettner,Lutz, Mehlhorn,Kurt, Pion,Sylvain, Schirra,Stefan, Yap,Chee

The algorithms of computational geometry are designed for a machine model with exact real arithmetic. Substituting floating point arithmetic for the assumed real arithmetic may cause implementations...

Point containment in the integer hull of a polyhedron (2004)

Althaus,Ernst, Eisenbrand,Friedrich, Funke,Stefan, Mehlhorn,Kurt

We show that the point containment problem in the integer hull of a polyhedron, which is defined by $m$ inequalities, with coefficients of at most $\varphi$ bits can be solved in time $O(m+\varphi)$...

A Faster Algorithm for Minimum Cycle Basis of Graphs (2004)

Mehlhorn,Kurt, Michail,Dimitrios, Telikepalli,Kavitha, Paluch,Katarzyna

In this paper we consider the problem of computing a minimum cycle basis in a graph $G$ with $m$ edges and $n$ vertices. The edges of $G$ have non-negative weights on them. The previous best result...

Matching Algorithms Are Fast in Sparse Random Graphs (2004)

Bast,Holger, Mehlhorn,Kurt, Schäfer,Guido, Tamaki,Hisao

We present an improved average case analysis of the maximum cardinality matching problem. We show that in a bipartite or general random graph on n vertices, with high probability every nonmaximum...

Point Containment in the Integer Hull of a Polyhedron (2004)

Althaus,Ernst, Eisenbrand,Friedrich, Funke,Stefan, Mehlhorn,Kurt

We show that the point containment problem in the integer hull of a polyhedron, which is defined by $m$ inequalities, with coefficients of at most $\varphi$ bits can be solved in time...

Point containment in the integer hull of a polyhedron (2004)

Althaus,Ernst, Eisenbrand,Friedrich, Funke,Stefan, Mehlhorn,Kurt

We show that the point containment problem in the integer hull of a polyhedron, which is defined by $m$ inequalities, with coefficients of at most $\varphi$ bits can be solved in time $O(m+\varphi)$...

Classroom Examples of Robustness Problems in Geometric Computations (2004)

Kettner, Lutz, Mehlhorn, Kurt, Pion, Sylvain, Schirra, Stefan, Yap, Chee, Albers, Susanne, ...

The algorithms of computational geometry are designed for a machine model with exact real arithmetic. Substituting floating point arithmetic for the assumed real arithmetic may cause implementations...

Point containment in the integer hull of a polyhedron (2004)

Althaus, Ernst, Eisenbrand, Friedrich, Funke, Stefan, Mehlhorn, Kurt

We show that the point containment problem in the integer hull of a polyhedron, which is defined by $m$ inequalities, with coefficients of at most $\varphi$ bits can be solved in time $O(m+\varphi)$...

A Faster Algorithm for Minimum Cycle Basis of Graphs (2004)

Mehlhorn, Kurt, Michail, Dimitrios, Telikepalli, Kavitha, Paluch, Katarzyna, Díaz, Josep, Karhumäki, Juhani, ...

In this paper we consider the problem of computing a minimum cycle basis in a graph $G$ with $m$ edges and $n$ vertices. The edges of $G$ have non-negative weights on them. The previous best result...

Matching Algorithms Are Fast in Sparse Random Graphs (2004)

Bast, Holger, Mehlhorn, Kurt, Schäfer, Guido, Tamaki, Hisao, Diekert, Volker, Habib, Michel

We present an improved average case analysis of the maximum cardinality matching problem. We show that in a bipartite or general random graph on n vertices, with high probability every nonmaximum...

Point Containment in the Integer Hull of a Polyhedron (2004)

Althaus, Ernst, Eisenbrand, Friedrich, Funke, Stefan, Mehlhorn, Kurt

We show that the point containment problem in the integer hull of a polyhedron, which is defined by $m$ inequalities, with coefficients of at most $\varphi$ bits can be solved in time...

Point containment in the integer hull of a polyhedron (2004)

Althaus, Ernst, Eisenbrand, Friedrich, Funke, Stefan, Mehlhorn, Kurt

We show that the point containment problem in the integer hull of a polyhedron, which is defined by $m$ inequalities, with coefficients of at most $\varphi$ bits can be solved in time $O(m+\varphi)$...

Classroom Examples of Robustness Problems in Geometric Computations (2004)

Kettner, Lutz, Mehlhorn, Kurt, Pion, Sylvain, Schirra, Stefan, Yap, Chee

The algorithms of computational geometry are designed for a machine model with exact real arithmetic. Substituting floating point arithmetic for the assumed real arithmetic may cause implementations...

Classroom Examples of Robustness Problems in Geometric Computations (2004)

Kettner, Lutz, Mehlhorn, Kurt, Pion, Sylvain, Schirra, Stefan, Yap, Chee

The algorithms of computational geometry are designed for a machine model with exact real arithmetic. Substituting floating point arithmetic for the assumed real arithmetic may cause implementations...

Pareto optimality in house allocation problems (2004)

David J. Abraham, Katarína Cechlárová, David F. Manlove, Kurt Mehlhorn

Abstract. We study Pareto optimal matchings in the context of house allocation problems. We present an O ( √ nm) algorithm, based on Gale’s Top Trading Cycles Method, for finding a maximum...

der Naturwissenschaftlich-Technischen Fakultäten (2004)

René Beier, Dekan Prof, Dr. Jörg Eschmeier, Vorsitzender Prof, Dr. Raimund Seidel, Erstgutachter Prof, ...

We investigate the performance of exact algorithms for hard optimization problems under random inputs. In particular, we prove various structural properties that lead to two general average-case...

Point containment in the integer hull of a polyhedron (2004)

Ernst Althaus, Friedrich Eisenbrand, Stefan Funke, Kurt Mehlhorn

We show that the point containment problem in the integer hull of a polyhedron, which is dened by m inequalities, with coecients of at most ' bits can be solved in time O(m + ') in the...

Classroom Examples of Robustness Problems In Geometric Computations (2004)

Lutz Kettner, Kurt Mehlhorn, Sylvain Pion, Stefan Schirra, Chee Yap

The algorithms of computational geometry are designed for a machine model with exact real arithmetic. Substituting floating point arithmetic for the assumed real arithmetic may cause implementations...

Rank-maximal matchings (2004)

David J. Abraham, Robert W. Irving, Telikepalli Kavitha, Kurt Mehlhorn

Abstract. We consider the problem of matching a set of applicants to a set of posts, where each applicant has a preference list, ranking a non-empty subset of posts in order of preference, possibly...

Rank-maximal matchings (2004)

David J. Abraham, Robert W. Irving, Telikepalli Kavitha, Kurt Mehlhorn

Abstract. We consider the problem of matching a set of applicants to a set of posts, where each applicant has a preference list, ranking a nonempty subset of posts in order of preference, possibly...

Classroom examples of robustness problems in geometric computations (2004)

Lutz Kettner, Kurt Mehlhorn, Sylvain Pion, Stefan Schirra, Chee Yap

The algorithms of computational geometry are designed for a machine model with exact real arithmetic. Substituting floating-point arithmetic for the assumed real arithmetic may cause implementations...

Rank-maximal matchings (2004)

Robert W. Irving, Telikepalli Kavitha, Kurt Mehlhorn, Dimitrios Michail, Katarzyna Paluch

Suppose that each member of a set�of applicants ranks a subset of a set Èof posts in an order of preference, possibly involving ties. A matching is a set of (applicant, post) pairs such that each...

Classroom examples of robustness problems in geometric computations (2004)

Lutz Kettner, Kurt Mehlhorn, Sylvain Pion, Stefan Schirra, Chee Yap, Inria Sophia

Abstract. The algorithms of computational geometry are designed for a machine model with exact real arithmetic. Substituting floating point arithmetic for the assumed real arithmetic may cause...

Rank-maximal matchings (2004)

David J. Abraham, Robert W. Irving, Telikepalli Kavitha, Kurt Mehlhorn

We consider the problem of matching a set of applicants to a set of posts, where each applicant ranks a non-empty subset of posts in an order of preference, possibly involving ties. We say that a...

A faster algorithm for minimum cycle basis of graphs (2004)

Telikepalli Kavitha, Kurt Mehlhorn, Dimitrios Michail

Abstract. In this paper we consider the problem of computing a minimum cycle basis in a graph G with m edges and n vertices. The edges of G have non-negative weights on them. The previous best result...

Pareto optimality in house allocation problems (2004)

David J. Abraham, Katarína Cechlárová, David F. Manlove, Kurt Mehlhorn

Abstract. We study Pareto optimal matchings in the context of house allocation problems. We present an O ( √ nm) algorithm, based on Gale’s Top Trading Cycles Method, for finding a maximum...

Point Containment in the Integer Hull of a Polyhedron (2004)

Althaus, Ernst, Eisenbrand, Friedrich, Funke, Stefan, Mehlhorn, Kurt

We show that the point containment problem in the integer hull of a polyhedron, which is defined by $m$ inequalities, with coefficients of at most $\varphi$ bits can be solved in time...

Matching Algorithms Are Fast in Sparse Random Graphs (2004)

Bast, Holger, Mehlhorn, Kurt, Schäfer, Guido, Tamaki, Hisao, Diekert, Volker, Habib, Michel

We present an improved average case analysis of the maximum cardinality matching problem. We show that in a bipartite or general random graph on n vertices, with high probability every nonmaximum...

Classroom Examples of Robustness Problems in Geometric Computations (2004)

Kettner, Lutz, Mehlhorn, Kurt, Pion, Sylvain, Schirra, Stefan, Yap, Chee, Albers, Susanne, ...

The algorithms of computational geometry are designed for a machine model with exact real arithmetic. Substituting floating point arithmetic for the assumed real arithmetic may cause implementations...

A Faster Algorithm for Minimum Cycle Basis of Graphs (2004)

Mehlhorn, Kurt, Michail, Dimitrios, Telikepalli, Kavitha, Paluch, Katarzyna, Díaz, Josep, Karhumäki, Juhani, ...

In this paper we consider the problem of computing a minimum cycle basis in a graph $G$ with $m$ edges and $n$ vertices. The edges of $G$ have non-negative weights on them. The previous best result...

An efficient graph algorithm for dominance constraints (2003)

Althaus, Ernst, Duchier, Denys, Koller, Alexander, Mehlhorn, Kurt, Niehren, Joachim, Thiel, Sven

Dominance constraints are logical descriptions of trees that are widely used in computational linguistics. Their general satisfiability problem is known to be NP-complete. Here we identify normal...

Boolean Operations on 3D Selective Nef Complexes: Data Structure, Algorithms, and Implementation (2003)

Granados,Miguel, Hachenberger,Peter, Hert,Susan, Kettner,Lutz, Mehlhorn,Kurt, Seel,Michael

We describe a data structure for three-dimensional Nef complexes, algorithms for boolean operations on them, and our implementation of data structure and algorithms. Nef polyhedra were introduced by...

A Heuristic for Dijkstra's Algorithm With Many Targets and its Use in Weighted Matching Algorithms (2003)

Bast,Holger, Mehlhorn,Kurt, Schäfer,Guido, Tamaki,Hisao

We consider the single-source many-targets shortest-path (SSMTSP) problem in directed graphs with non-negative edge weights. A source node $s$ and a target set $T$ is specified and the goal is to...

Smoothed Analysis of Three Combinatorial Problems (2003)

Banderier,Cyril, Beier,Rene, Mehlhorn,Kurt

Smoothed analysis combines elements over worst-case and average case analysis. For an instance $x$, the smoothed complexity is the average complexity of an instance obtained from $x$ by a...

Boolean Operations on 3D Selective Nef Complexes: Data Structure, Algorithms, and Implementation (2003)

Granados, Miguel, Hachenberger, Peter, Hert, Susan, Kettner, Lutz, Mehlhorn, Kurt, Seel, Michael, ...

We describe a data structure for three-dimensional Nef complexes, algorithms for boolean operations on them, and our implementation of data structure and algorithms. Nef polyhedra were introduced by...

A Heuristic for Dijkstra's Algorithm With Many Targets and its Use in Weighted Matching Algorithms (2003)

Bast, Holger, Mehlhorn, Kurt, Schäfer, Guido, Tamaki, Hisao

We consider the single-source many-targets shortest-path (SSMTSP) problem in directed graphs with non-negative edge weights. A source node $s$ and a target set $T$ is specified and the goal is to...

Smoothed Analysis of Three Combinatorial Problems (2003)

Banderier, Cyril, Beier, Rene, Mehlhorn, Kurt, Rovan, Branislav, Vojtáš, Peter

Smoothed analysis combines elements over worst-case and average case analysis. For an instance $x$, the smoothed complexity is the average complexity of an instance obtained from $x$ by a...

An Efficient Graph Algorithm for Dominance Constraints (2003)

Ernst Althaus, Denys Duchier, Alexander Koller, Kurt Mehlhorn, Joachim Niehren, Sven Thiel

Abstract. Dominance constraints are logical descriptions of trees that are widely used in computational linguistics. Their general satisfiability problem is known to be NP-complete. Here we identify...

Certifying algorithms for recognizing interval graphs and permutation graphs (2003)

Dieter Kratsch, Ross M. Mcconnell, Kurt Mehlhorn, Jeremy P. Spinrad

Abstract. A certifying algorithm for a problem is an algorithm that provides a certificate with each answer that it produces. The certificate is a piece of evidence that proves that the answer has...

The reliable algorithmic software challenge RASC : dedicated to Thomas Ottmann on the occassion of his 60th birthday (2003)

Kurt Mehlhorn

When I was asked to contribute to a volume dedicated to Thomas Ottmann’s sixtieth birthday, I

Smoothed analysis of three combinatorial problems (2003)

Cyril Banderier, Kurt Mehlhorn, Rene Beier

Smoothed analysis combines elements over worst-case and average case analysis. For an instance x the smoothed complexity is the average complexity of an instance obtained from x by a perturbation....

A Heuristic for Dijkstra's Algorithm with Many Targets and Its Use in Weighted Matching Algorithms (2003)

Kurt Mehlhorn

Abstract. We consider the single-source many-targets shortest-path (SSMTSP) problem in directed graphs with non-negative edge weights. A source node s and a target set T is specied and the goal is to...

An Efficient Graph Algorithm for Dominance Constraints (2003)

Ernst Althaus, Denys Duchier, Alexander Koller, Kurt Mehlhorn, Joachim Niehren, Sven Thiel

Dominance constraints are logical descriptions of trees that are widely used in computational linguistics. Their general satisfiability problem is known to be NP-complete. Here we identify normal...

Boolean Operations on 3D Selective Nef Complexes (2003)

Data Structure Algorithms, Miguel Granados, Peter Hachenberger, Susan Hert, Lutz Kettner, Kurt Mehlhorn, ...

this paper has been partially supported by the IST Programme of the EU as a Shared-cost RTD (FET Open) Project under Contract No IST-2000-26473 (ECG - Effective Computational Geometry for Curves and...

Strongly Stable Matchings in Time O(nm) (2003)

Telikepalli Kavitha, Kurt Mehlhorn, Dimitrios Michail, Katarzyna Paluch

An instance of the stable marriage problem is an undirected bipartite graph G = (X [W;E) with linearly ordered adjacency lists; ties are allowed. A matching M is a set of edges no two of which share...

Smoothed Analysis of Three Combinatorial Problems (2003)

Cyril Banderier, Cyril B, Rene Beier, Kurt Mehlhorn

Smoothed analysis combines elements over worst-case and average case analysis. For an instance x, the smoothed complexity is the average complexity of an instance obtained from x by a perturbation....

Certifying Algorithms for Recognizing Interval Graphs and Permutation (2003)

Graphs Dieter Kratsch, Dieter Kratsch, Ross M. Mcconnell, Kurt Mehlhorn, Jeremy P. Spinrad

A certifying algorithm for a problem is an algorithm that provides a certificate with each answer that it produces. The certificate is a piece of evidence that proves that the answer has not been...

An Efficient Graph Algorithm for Dominance Constraints (2003)

Ernst Althaus, Denys Duchier, Alexander Koller, Kurt Mehlhorn, Joachim Niehren, Sven Thiel

Dominance constraints are logical descriptions of trees that are widely used in computational linguistics. Their general satisfiability problem is known to be NPcomplete. Here we identify normal...

The reliable algorithmic software challenge RASC : dedicated to Thomas Ottmann on the occassion of his 60th birthday (2003)

Kurt Mehlhorn

When I was asked to contribute to a volume dedicated to Thomas Ottmann’s sixtieth birthday,

Boolean operations on 3D selective Nef complexes: Data structure, algorithms, and implementation (2003)

Peter Hachenberger, Lutz Kettner, Kurt Mehlhorn

Nef polyhedra in d-dimensional space are the closure of half-spaces under boolean set operations. In consequence, they can represent non-manifold situations, open and closed sets, mixed-dimensional...

Boolean operations on 3D selective Nef complexes: Data structure, algorithms, and implementation (2003)

Miguel Granados, Peter Hachenberger, Susan Hert, Lutz Kettner, Kurt Mehlhorn, Michael Seel

Abstract. We describe a data structure for three-dimensional Nef complexes, algorithms for boolean operations on them, and our implementation of data structure and algorithms. Nef polyhedra were...

External-Memory Breadth-First Search with Sublinear I/O (2002)

Mehlhorn,Kurt, Meyer,Ulrich

Breadth-first search (BFS) is a basic graph exploration technique. We give the first external-memory algorithm for sparse undirected graphs with sublinear I/O. The best previous algorithm requires O(...

A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons (2002)

Berberich,Eric, Eigenwillig,Arno, Hemmer,Michael, Hert,Susan, Mehlhorn,Kurt, Schömer,Elmar

We give an exact geometry kernel for conic arcs, algorithms for exact computation with low-degree algebraic numbers, and an algorithm for computing the arrangement of conic arcs that immediately...

SCIL - Symbolic Constraints in Integer Linear Programming. (2002)

Althaus,Ernst, Bockmayr,Alexander, Elf,Matthias, Kasper,Thomas, Jünger,Michael, Mehlhorn,Kurt

We describe a new software system SCIL that introduces symbolic constraints into branch-and-cut-and-price algorithms for integer linear programs. Symbolic constraints are known from constraint...

Implementation of $O(nm \log n)$ Weighted Matchings in General Graphs: The Power of Data Structures (2002)

Mehlhorn,Kurt, Schäfer,Guido

We describe the implementation of an algorithm which solves the weighted matching problem in general graphs with $n$ vertices and $m$ edges in time $O(nm \log n)$. Our algorithm is a variant of the...

Geometric Computing with CGAL and LEDA (2002)

Mehlhorn, Kurt, Schirra, Stefan

LEDA and CGAL are platforms for combinatorial and geometric computing. We discuss the use of LEDA and CGAL for geometric computing and show that they provide a unique framework for exact efficient...

External-Memory Breadth-First Search with Sublinear I/O (2002)

Mehlhorn, Kurt, Meyer, Ulrich, Möhring, Rolf, Raman, Rajeev

Breadth-first search (BFS) is a basic graph exploration technique. We give the first external-memory algorithm for sparse undirected graphs with sublinear I/O. The best previous algorithm requires O(...

A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons (2002)

Berberich, Eric, Eigenwillig, Arno, Hemmer, Michael, Hert, Susan, Mehlhorn, Kurt, Schömer, Elmar, ...

We give an exact geometry kernel for conic arcs, algorithms for exact computation with low-degree algebraic numbers, and an algorithm for computing the arrangement of conic arcs that immediately...

SCIL - Symbolic Constraints in Integer Linear Programming. (2002)

Althaus, Ernst, Bockmayr, Alexander, Elf, Matthias, Kasper, Thomas, Jünger, Michael, Mehlhorn, Kurt, ...

We describe a new software system SCIL that introduces symbolic constraints into branch-and-cut-and-price algorithms for integer linear programs. Symbolic constraints are known from constraint...

Implementation of $O(nm \log n)$ Weighted Matchings in General Graphs: The Power of Data Structures (2002)

Mehlhorn, Kurt, Schäfer, Guido

We describe the implementation of an algorithm which solves the weighted matching problem in general graphs with $n$ vertices and $m$ edges in time $O(nm \log n)$. Our algorithm is a variant of the...

External-memory breadth-first search with sublinear I/O (2002)

Kurt Mehlhorn, Ulrich Meyer

Abstract. Breadth-first search (BFS) is a basic graph exploration technique. We give the first external memory algorithm for sparse undirected graphs with sublinear I/O. The best previous algorithm...

SCIL -- Symbolic Constraints in Integer Linear Programming (2002)

Ernst Althaus, Thomas Kasper, Alexander Bockmayr, Michael Jünger, Matthias Elf, Kurt Mehlhorn

We describe SCIL. SCIL introduces symbolic constraints into branch-and-cut-and-price algorithms for integer linear programs. Symbolic constraints are known from constraint programming and contribute...

SCIP – symbolic constraints in integer linear programming (2002)

Ernst Althaus, Thomas Kasper, Alexander Bockmayr, Michael Junger, Kurt Mehlhorn

We describe SCIL. SCIL introduces symbolic constraints into branch-and-cut-and-price algorithms for integer linear programs. Symbolic constraints are known from constraint programming and contribute...

A computational basis for conic arcs and Boolean operations on conic polygons (2002)

Eric Berberich, Arno Eigenwillig, Michael Hemmer, Susan Hert, Kurt Mehlhorn, Elmar Schömer

Abstract. We give an exact geometry kernel for conic arcs, algorithms for exact computation with low-degree algebraic numbers, and an algorithm for computing the arrangement of conic arcs that...

A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons (2002)

Eric Berberich, Arno Eigenwillig, Michael Hemmer, Susan Hert, Kurt Mehlhorn, Elmar Schömer

We give an exact geometry kernel for conic arcs, algorithms for exact computation with low-degree algebraic numbers, and an algorithm for computing the arrangement of conic arcs that immediately...

All-pairs shortest-paths computation in the presence of negative cycles (2001)

Kurt Mehlhorn, Volker Priebe, Naveen Sivadasan

We present an algorithm that solves the all-pairs shortest-paths problem on a directed graph with n vertices and m arcs in time O(nm + n 2 log n), where the arcs are assigned real, possibly negative...

A separation bound for real algebraic expressions (2001)

Christoph Burnikel, Stefan Funke, Kurt Mehlhorn, Stefan Schirra, Susanne Schmitt

Real algebraic expressions are expressions whose leaves are integers and whose internal nodes are additions, subtractions, multiplications, divisions, k-th root operations for integral k, and taking...

A Separation Bound for Real Algebraic Expressions (2001)

Christoph Burnikel, Stefan Funke, Kurt Mehlhorn, Stefan Schirra, Susanne Schmitt

Real algebraic expressions are expressions whose leaves are integers and whose internal nodes are additions, subtractions, multiplications, divisions, k-th root operations for integral k, and taking...

Exact computation with leda real - theory and geometric applications (2001)

Kurt Mehlhorn, Stefan Schirra

The number type leda real provides exact computation for a subset of real algebraic numbers: Every integer is a leda real, and leda reals are closed under the basic arithmetic operations +, −, ∗,...

A separation bound for real algebraic expressions (2001)

Christoph Burnikel, Stefan Funke, Kurt Mehlhorn, Stefan Schirra, Susanne Schmitt

Real algebraic expressions are expressions whose leaves are integers and whose internal nodes are additions, subtractions, multiplications, divisions, k-th root operations for integral k, and taking...

Traveling salesman-based curve reconstruction in polynomial time (2001)

Ernst Althaus, Kurt Mehlhorn

Abstract. An instance of the curve reconstruction problem is a finite sample set V of an unknown collection of curves γ. The task is to connect the points in V in the order in which they lie on γ....

An Efficient Algorithm for the Configuration Problem of Dominance Graphs (2001)

Althaus, Ernst, Duchier, Denys, Koller, Alexander, Mehlhorn, Kurt, Niehren, Joachim, Thiel, Sven

Dominance constraints are logical tree descriptions originating from automata theory that have multiple applications in computational linguistics. The satisfiability problem of dominance constraints...

Traveling Salesman-Based Curve Reconstruction in Polynomial Time (2001)

Althaus, Ernst, Mehlhorn, Kurt

An instance of the curve reconstruction problem is a finite sample set $V$ of an unknown curve $\gamma$. The task is to connect the points in $V$ in the order in which they lie on $\gamma$....

CNOP - {A} Package for Constrained Network Optimization (2001)

Mehlhorn, Kurt, Ziegelmann, Mark, Buchsbaum, Adam L., Snoeyink, Jack

We present a generic package for resource constrained network optimization problems. We illustrate the flexibility and the use of our package by solving four applications: route planning, curve...

A Heuristic for Dijkstra's Algorithm With Many Targets and its Use in Weighted Matching Algorithms (2001)

Mehlhorn, Kurt, Schäfer, Guido

We consider the single-source many-targets shortest-path (SSMTSP) problem in directed graphs with non-negative edge weights. A source node $s$ and a target set $T$ is specified and the goal is to...

Scanning multiple sequences via cache memory (2000)

Kurt Mehlhorn, Peter Sanders

We consider the simple problem of scanning multiple sequences. There are k sequences of total length N which are to be scanned concurrently. One pointer into each sequence is maintained and an...

Faster Algorithms for Bound-Consistency of the Sortedness and the Alldifferent Constraint (2000)

Kurt Mehlhorn, Sven Thiel

Abstract. We present narrowing algorithms for the sortedness and the alldierent constraint which achieve bound-consistency. The algorithm for the sortedness constraint takes as input 2n intervals X1;...

Implementation of O(nmlogn) weighted matchings in general graphs: The power of data structures (2000)

Kurt Mehlhorn

Abstract. We describe the implementation of an O(nm log n) algorithm for weighted matchings in general graphs. The algorithm is a variant of the algorithm of Galil, Micali, and Gabow [GMG86] and...

TSP-Based Curve Reconstruction (2000)

Ernst Althaus, Kurt Mehlhorn, Stefan Schirra

An instance of the curve reconstruction problem is a nite sample V of an unknown curve . The task is to connect the points in V in the order in which they lie on . Several new algorithms for the...

Experiments on Curve Reconstruction (2000)

Ernst Althaus, Kurt Mehlhorn, Stefan Näher, Stefan Schirra

An instance of the curve reconstruction problem is a finite sample V of an unknown curve gamma...

TSP-Based Curve Reconstruction in Polynomial Time (2000)

Ernst Althaus, Kurt Mehlhorn

An instance of the curve reconstruction problem is a nite sample V of an unknown curve and the task is to connect the points in V in the order in which they lie on . Giesen [Gie99] showed recently...

A Polynomial-Time Fragment of Dominance Constraints (2000)

Alexander Koller, Kurt Mehlhorn, Joachim Niehren

Dominance constraints are a logical language for describing trees that is widely used in computational linguistics. Their general satis ability problem is known to be NP-complete. Here we identify...

LOOK - A Lazy Object-Oriented Kernel for Geometric Computation (2000)

Stefan Funke, Kurt Mehlhorn

In this paper we describe and discuss a new kernel design for geometric computation in the plane. It combines different kinds of floating-point filter techniques and a lazy evaluation scheme with the...

Average-Case Complexity of Shortest-Paths Problems in the Vertex-Potential Model (2000)

Colin Cooper Alan, Kurt Mehlhorn, Volker Priebe

We study the average-case complexity of shortest-paths problems in the vertex-potential model. The vertex-potential model is a family of probability distributions on complete directed graphs with...

Constraint Programming and Graph Algorithms (2000)

Kurt Mehlhorn

mming paradigm, that allows one to formulate computational problems at a very high level. A computational problem is formulated as a constraint. A constraint is simply a conjunction of formulae of...

Infimaximal Frames (2000)

Technique For Making, Kurt Mehlhorn, Michael Seel

Many geometric algorithms that are usually formulated for points and segments generalize easily to inputs also containing rays and lines. The sweep algorithm for segment intersection is a...

Resource Constrained Shortest Paths (2000)

Kurt Mehlhorn And, Kurt Mehlhorn

The resource constrained shortest path problem (CSP) asks for the computation of a least cost path obeying a set of resource constraints. The problem is NP-complete. We give theoretical and...

Faster Algorithms for Bound-Consistency of the Sortedness and the Alldifferent Constraint (2000)

Kurt Mehlhorn, Sven Thiel

Abstract. We present narrowing algorithms for the sortedness and the alldifferent constraint which achieve bound-consistency. The algorithm for the sortedness constraint takes as input 2n intervals...

www.elsevier.com/locate/comgeo LOOK: A Lazy Object-Oriented Kernel design for geometric computation (2000)

Stefan Funke, Kurt Mehlhorn

In this paper we describe and discuss a new kernel design for geometric computation in the plane. It combines different kinds of floating-point filter techniques and a lazy evaluation scheme with the...

Infimaximal frames: A technique for making lines look like segments (2000)

Kurt Mehlhorn, Michael Seel

Many geometric algorithms that are usually formulated for points and segments generalize easily to inputs also containing rays and lines. The sweep algorithm for segment intersection is a...

Author’s (2000)

Kurt Mehlhorn, Michael Seel

Many geometric algorithms that are usually formulated for points and segments generalize easily to inputs also containing rays and lines. The sweep algorithm for segment intersection is a...

Resource constrained shortest paths (2000)

Kurt Mehlhorn

Abstract. The resource constrained shortest path problem (CSP) asks for the computation of a least cost path obeying a set of resource constraints. The problem is NP-complete. We give theoretical and...

Average-Case Complexity of Shortest-Paths Problems in the Vertex-Potential Model (2000)

Cooper, Colin, Frieze, Alan M., Mehlhorn, Kurt, Priebe, Volker

We study the average-case complexity of shortest-paths problems in the vertex-potential model. The vertex-potential model is a family of probability distributions on complete directed graphs with...

TSP-Based Curve Reconstruction in Polynomial Time (2000)

Althaus, Ernst, Mehlhorn, Kurt

An instance of the curve reconstruction problem is a finite sample set $V$ of an unknown curve $\gamma$. The task is to connect the points in $V$ in the order in which they lie on $\gamma$....

A strong and easily computable separation bound for arithmetic expressions involving radicals (2000)

Burnikel, Christoph, Fleischer, Rudolf, Mehlhorn, Kurt, Schirra, Stefan

We consider arithmetic expressions over operators + , - , * , / , and $\sqrt[k]$ , with integer operands. For an expression E having value $\xi$ , a separation bound sep (E) is a positive real number...

Faster Algorithms for Bound-Consistency of the Sortedness and the Alldifferent Constraint (2000)

Mehlhorn, Kurt, Thiel, Sven, Dechter, Rina

We present narrowing algorithms for the sortedness and the alldifferent constraint which achieve bound-consistency. The algorithm for the sortedness constraint takes as input $2n$ intervals $X_1,...

Resource Constrained Shortest Paths (2000)

Mehlhorn, Kurt, Ziegelmann, Mark, Paterson, Mike

The resource constrained shortest path problem (CSP) asks for the computation of a least cost path obeying a set of resource constraints. The problem is NP-complete. We give theoretical and...

A Polynomial-Time Fragment of Dominance Constraints (2000)

Koller, Alexander, Mehlhorn, Kurt, Niehren, Joachim

Dominance constraints are a logical language for describing trees that is widely used in computational linguistics. Their general satisfiability problem is known to be NP-complete. Here we identify...

Implementation of $O(nm \log n)$ weighted matchings: The power of data structures (2000)

Mehlhorn, Kurt, Schäfer, Guido, Näher, Stefan, Wagner, Dorothea

We describe the implementation of an $O(nm \log n)$ algorithm for weighted matchings in general graphs. The algorithm is a variant of the algorithm of Galil, Micali, and Gabow and requires the use of...

Curve reconstruction: Connecting dots with good reason (2000)

Dey, Tamal K., Mehlhorn, Kurt, Ramos, Edgar A.

Curve reconstruction algorithms are supposed to reconstruct curves from point samples. Recent papers present algorithms that come with a guarantee: Given a sufficiently dense sample of a closed...

LEDA: A Platform for Combinatorial and Geometric Computing (1999)

Kurt Mehlhorn, Christian Uhrig

Abstract. We give an overview of the LEDA platform for combinatorial and geometric computing and an account of its development. We discuss our motivation for building LEDA and to what extent we have...

An analysis of the highest-level selection rule in the preflow-push max-flow algorithm (1999)

Joseph Cheriyan, Kurt Mehlhorn

Consider the problem of finding a maximum flow in a network. Goldberg and Tarjan introduced the preflow-push method for solving this problem. When this method is implemented with the highest-level...

Structural filtering: A paradigm for efficient and exact geometric programs (1999)

Stefan Funke, Kurt Mehlhorn, Stefan Näher

We introduce a new filtering technique that can be used in the implementation of geometric algorithms called "structural filtering". Using this filtering techniques we gain about 20 % when...

Structural Filtering - A Paradigm for Efficient and Exact Geometric Programs (1999)

Stefan Funke, Kurt Mehlhorn, Stefan Näher

We introduce a new and simple filtering technique that can be used in the implementation of geometric algorithms called "structural filtering". Using this filtering technique we gain about...

Curve Reconstruction: Connecting Dots with Good Reason (1999)

Tamal K. Dey, Kurt Mehlhorn, Edgar A. Ramos

Curve reconstruction algorithms are supposed to reconstruct curves from point samples. Recent papers present algorithms that come with a guarantee: Given a suciently dense sample of a closed smooth...

Curve Reconstruction: Connecting Dots with Good Reason (1999)

Tamal K. Dey, Kurt Mehlhorn, Edgar A. Ramos

Curve reconstruction algorithms are supposed to reconstruct curves from point samples. Recent papers present algorithms that come with a guarantee: Given a suÆciently dense sample of a closed smooth...

LEDA-SM - A Platform for Secondary Memory Computation (1999)

Andreas Crauser, Kurt Mehlhorn

Contents 1 Introduction 3 1.1 License Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . ....

On the expected depth of random circuits (1999)

Sunil Arya, Mordecai J. Golin, Kurt Mehlhorn

Abstract: In this paper we analyze the expected depth of random circuits of fixed fanin f. Such circuits are built a gate at a time, with the f inputs of each new gate being chosen randomly from...

An analysis of the highest-level selection rule in the preflow-push max-flow algorithm (1999)

Cheriyan, Joseph, Mehlhorn, Kurt

Consider the problem of finding a maximum flow in a network. Goldberg and Tarjan introduced the preflow-push method for solving this problem. When this method is implemented with the highest-level...

LEDA-SM : Extending LEDA to Secondary Memory (1999)

Crauser, Andreas, Mehlhorn, Kurt, Vitter, Jeffrey S., Zaroliagis, Christos D.

During the last years, many software libraries for \emph{in-core} computation have been developed. Most internal memory algorithms perform very badly when used in an \emph{external memory} setting....

Efficient exact geometric computation made easy (1999)

Burnikel, Christoph, Fleischer, Rudolf, Mehlhorn, Kurt, Schirra, Stefan

We show that the combination of the CGAL framework for geometric computation and the number type leda-real yields easy-to-write, correct and efficient geometric programs.

A correctness certificate for the Stoer-Wagner min-cut algorithm (1999)

Arikati, Srinivasa Rao, Mehlhorn, Kurt

The Stoer–Wagner algorithm computes a minimum cut in a weighted undirected graph. The algorithm works in n−1 phases, where n is the number of nodes of G. Each phase takes time O(m+nlogn), where m...

Curve reconstruction: Connecting dots with good reason (1999)

Dey, Tamal K., Mehlhorn, Kurt, Ramos, Edgar A.

Curve reconstruction algorithms are supposed to reconstruct curves from point samples. Recent papers present algorithms that come with a guarantee: Given a sufficiently dense sample of a closed...

LEDA: a platform for combinatorial and geometric computing (1999)

Mehlhorn, Kurt, Näher, Stefan

Contents Preface page xi 1 Introduction 1 1.1 Some Programs 1 1.2 The LEDA System 8 1.3 The LEDA Web-Site 10 1.4 Systems that Go Well with LEDA 11 1.5 Design Goals and Approach 11 1.6 History 13 2...

On the Expected Depth of Random Circuits (1999)

Arya, Sunil, Golin, Mordecai J., Mehlhorn, Kurt

In this paper we analyse the expected depth of random circuits of fixed fanin f . Such circuits are built a gate at a time, with the f inputs of each new gate being chosen randomly from among the...

Ten Years of LEDA Some Thoughts (Abstract) (1999)

Mehlhorn, Kurt, Vitter, Jeffrey S., Zaroliagis, Christos D.

Stefan Näher and I started the work on LEDA [LED] in the spring on 1989. Many collegues and students have contributed to the project since then. A first publication appeared in the fall of the same...

Faster Algorithms for the Shortest Path Problem, (1998)

Ahuja, Ravindra K., Mehlhorn, Kurt, Orlin, James B., Tarjan, Robert E.

This document investigates efficient implementations of Dijkstra's shortest path algorithm. The authors propose a new data structure, called the redistributive heap, for use in this algorithm. On a...

On the expected depth of random circuits (1998)

Arya, Sunil, Golin, Mordecai J., Mehlhorn, Kurt

In this paper we analyze the expected depth of random circuits of fixed fanin f. Such circuits are built a gate at a time, with the f inputs of each new gate being chosen randomly from among the...

Polyline fitting of planar points under min-sum criteria (1998)

Boris Aronov, Tetsuo Asano, Naoki Katoh, Kurt Mehlhorn, Takeshi Tokuyama

Fitting a curve of a certain type to a given set of points in the plane is a basic problem in statistics and has numerous applications. We consider fitting a polyline with k joints under the min-sum...

2nd Workshop on Algorithm Engineering WAE'98 - Proceedings (1998)

Kurt Mehlhorn (ed.), Kurt Mehlhorn, Kurt Mehlhorn

We consider a problem of reconstructing a discrete structure from unstructured numerical data. The problem arises in the computer-aided design of machines, motor vehicles, and other technical...

An Analysis of the Highest-Level Selection Rule in the Preflow-Push Max-Flow Algorithm (1998)

Joseph Cheriyan, Kurt Mehlhorn

Consider the problem of finding a maximum flow in a network. Goldberg and Tarjan introduced the preflow-push method for solving this problem. When this method is implemented with the highest-level...

From Algorithms to Working Programs On the Use of Program Checking in LEDA (1998)

Kurt Mehlhorn, Stefan Näher

. We report on the use of program checking in the LEDA library of efficient data types and algorithms. 1 Introduction LEDA [MN95,MNU97,MN98] is a collection of implementations of data structures and...

A Polyhedral Approach to Sequence Alignment Problems (1998)

John D. Kececioglu, Hans-peter Lenhof, Kurt Mehlhorn, Petra Mutzel, Knut Reinert, Martin Vingron

We study two new problems in sequence alignment both from a practical and a theoretical view, using tools from combinatorial optimization to develop branchand -cut algorithms. The Generalized Maximum...

Komplexitätstheorie: WS 98/99 (1998)

Kurt Mehlhorn, Laurant Porkolap

ent checkers. There could be a reason for that, namely that the problems have no checkers. Complexity theory could give the answer and so I hope that I learn something for my problem in the course. 4...

Convex Hulls in Higher-dimensional Space (1998)

Michael Müller, Joachim Ziegler, Kurt Mehlhorn, Michael Seel

We define and implement the data type chull . It maintains convex hulls in arbitrary dimensions and supports insertions of points and membership queries. The interior of the hull and the boundary of...

An Analysis of the Highest-Level Selection Rule in the Preflow-Push Max-Flow Algorithm (1998)

Joseph Cheriyan, Kurt Mehlhorn

Consider the problem of finding a maximum flow in a network. Goldberg and Tarjan introduced the preflow-push method for solving this problem. When this method is implemented with the highest-level...

On the Expected Depth of Random Circuits (1998)

Sunil Arya, Mordecai J. Golin, Kurt Mehlhorn

: In this paper we analyze the expected depth of random circuits of fixed fanin f: Such circuits are built a gate at a time, with the f inputs of each new gate being chosen randomly from among the...

Delaunay Triangulations in Higher-dimensional Space (1998)

Kurt Mehlhorn, Michael Seel

We define and implement the data type delaunay . It maintains Delaunay triangulations in arbitrary dimensions and supports insertions of points, lookup and location queries. The delaunay...

Polyline Fitting of Planar Points under Min-Sum (1998)

Criteria Boris Aronov, Boris Aronov, Tetsuo Asano, Naoki Katoh, Kurt Mehlhorn, Takeshi Tokuyama Polytechnic

Fitting a curve of a certain type to a given set of points in the plane is a basic problem in statistics and has numerous applications. We consider fitting a polyline with k joints under the min-sum...

Polyline Fitting of Planar Points under Min-Sum Criteria (1998)

Boris Aronov Tetsuo, Tetsuo Asano, Naoki Katoh, Kurt Mehlhorn, Takeshi Tokuyama

Fitting acurv e of a certain type to agiv en set of points in the plane is a basic problem in statistics and has numerous applications. We consider fitting a polyline with k joints under the min-sum...

Maximum Network Flow with Floating Point Arithmetic (1998)

Althaus, Ernst, Mehlhorn, Kurt

We discuss the implementation of network flow algorithms in floating point arithmetic. We give an example to illustrate the difficulties that may arise when floating point arithmetic is used without...

A Parallelization of Dijkstra's Shortest Path Algorithm (1998)

Crauser, Andreas, Mehlhorn, Kurt, Meyer, Ulrich, Sanders, Peter, Brim, Lubos, Gruska, Jozef, ...

The single source shortest path (SSSP) problem lacks parallel solutions which are fast and simultaneously work-efficient. We propose simple criteria which divide Dijkstra's sequential SSSP algorithm...

A Complete Roundness Classification Procedure (1997)

Kurt Mehlhorn, Thomas C. Shermer, Chee K. Yap

We describe a roundness classification procedure, that is, a procedure to determine if the roundness of a planar object I is within some ffl 0 from an ideal circle. The procedure consists of a...

A Robust and Efficient Implementation of a Sweep Line Algorithm for the Straight Line Segment Intersection Problem (1997)

Ulrike Bartuschka, Kurt Mehlhorn, Stefan Näher

We describe a robust and efficient implementation of the Bentley-Ottmann sweep line algorithm [1] based on the LEDA platform of combinatorial and geometric computing [9, 8]. The program computes the...

Average-case complexity of shortest-paths problems in the vertex-potential model (1997)

Colin Cooper, Alan Frieze, Kurt Mehlhorn, Volker Priebe

ABSTRACT: We study the average-case complexity of shortest-paths problems in the vertexpotential model. The vertex-potential model is a family of probability distributions on complete directed graphs...

Kürzeste-Wege-Berechnung bei sehr großen Datenmengen (1997)

Crauser, Andreas, Mehlhorn, Kurt, Meyer, Ulrich, Spaniol, Otto

In diesem Report untersuchen wir die Ein/Ausgabe-Komplexität (I/O Komplexität) des Kürzesten-Wege-Problems mit einem Startknoten (single source shortest path) auf Graphen mit nicht-negativen...

On the All-Pairs Shortest-Path Algorithm of Moffat and {Takaoka} (1997)

Mehlhorn, Kurt, Priebe, Volker

We review how to solve the all-pairs shortest-path problem in a non-negatively weighted digraph with $n$ vertices in expected time $O(n^2 \log n)$. This bound is shown to hold with high probability...

Average-case complexity of shortest-paths problems in the vertex-potential model (1997)

Cooper, Colin, Frieze, Alan M., Mehlhorn, Kurt, Priebe, Volker, Rolim, José

We study the average-case complexity of shortest-paths problems in the vertex-potential model. The vertex-potential model is a family of probability distributions on complete directed graphs with...

The LEDA class real number (1996)

Christoph Burnikel, Kurt Mehlhorn, Stefan Schirra

We describe the implementation of the LEDA [MN95, Nah95] data type real. Every integer is a real and reals are closed under the operations addition, subtraction, multiplication, division and...

The LEDA class real number (1996)

Christoph Burnikel, Kurt Mehlhorn, Stefan Schirra

We describe the implementation of the LEDA [MN95, Nah95] data type real. Every integer is a real and reals are closed under the operations addition, subtraction, multiplication, division and...

Checking geometric programs or verification of geometric structures (1996)

Kurt Mehlhorn, Stefan Naher, Michael Seel, Raimund Seidel, Thomas Schilz, Stefan Schirra, ...

A program checker verifies that a particular program execution is correct. We give simple and efficient program checkers for some basic geometric tasks. We report about our experiences with program...

Convex Hulls (chull) (1996)

Michael Müller, Joachim Ziegler, Kurt Mehlhorn

We define and implement the data type chull. It maintains convex hulls in arbitrary dimensions and supports insertions of points and membership queries. The interior of the hull and the boundary of...

Higher-dimensional Convex Hulls and Delaunay Triangulations Specification and Implementation (1996)

Kurt Mehlhorn, Michael Müller, Stefan Näher, Joachim Ziegler

Introduction We discuss the specification and implementation of the data types convex hull and Delaunay triangulation for higher-dimensional space. We aimed for ffl rich functionality and ease of use...

The LEDA class real number (1996)

Christoph Burnikel, Kurt Mehlhorn, Stefan Schirra

We describe the implementation of the LEDA [MN95, Nah95] data type real. Every integer is a real and reals are closed under the operations addition, subtraction, multiplication, division and...

A Method for Obtaining Randomized Algorithms with Small Tail Probabilities (1996)

Alt, Helmut, Guibas, L., Mehlhorn, Kurt, Karp, Richard M., Wigderson, A.

We study strategies for converting randomized algorithms of the Las Vegas type into randomized algorithms with small tail probabilities.

LEDA - A Platform for Combinatorial and Geometric Computing (1995)

Kurt Mehlhorn, Stefan Näher, Stefan N Aher

Contents Preface page xi 1 Introduction 1 1.1 Some Programs 1 1.2 The LEDA System 8 1.3 The LEDA Web-Site 10 1.4 Systems that Go Well with LEDA 11 1.5 Design Goals and Approach 11 1.6 History 13 2...

On the Embedding Phase of the Hopcroft and Tarjan Planarity Testing Algorithm (1995)

Kurt Mehlhorn, Petra Mutzel

We give a detailed description of the embedding phase of the Hopcroft and Tarjan planarity testing algorithm. The embedding phase runs in linear time. An implementation based on this paper can be...

LEDA A Platform for Combinatorial and Geometric Computing (1995)

Kurt Mehlhorn, Stefan Naher

LEDA is a library of efficient data types and algorithms in combinatorial and geometric computing. The main features of the library are its wide collection of data types and algorithms, the precise...

LEDA - A Platform for Combinatorial and Geometric Computing (1995)

Kurt Mehlhorn, Stefan Näher

LEDA is a library of efficient data types and algorithms in combinatorial and geometric computing. The main features of the library are its wide collection of data types and algorithms, the precise...

On the All-Pairs Shortest-Path Algorithm (1995)

Of Moffat, Kurt Mehlhorn, Volker Priebe

ABSTRACT: We review how to solve the all-pairs shortest-path problem in a nonnegatively Ž 2 weighted digraph with n vertices in expected time On log n.. This bound is shown to hold with high...

A communication-randomness tradeoff for two-processor systems (1995)

Fleischer, Rudolf, Jung, Hermann, Mehlhorn, Kurt

We present a tight tradeoff between the expected communication complexity $\bar{C}$ (for a two-processor system) and the number $R$ of random bits used by any Las Vegas protocol for the...

LEDA : A Platform for Combinatorial and Geometric Computing (1995)

Mehlhorn, Kurt, Näher, Stefan

LEDA is a library of efficient data types and algorithms in combinatorial and geometric computing. The main features of the library are its wide collection of data types and algorithms, the precise...

Implementation of a sweep line algorithm for the straight line segment intersection problem (1994)

Kurt Mehlhorn, Stefan Naher

We describe a robust and efficient implementation of the Bentley-Ottmann sweep line algorithm [7] based on the LEDA library of efficient data types and algorithms [7]. The program computes the planar...

A lower bound for area-universal graphs (1994)

Bilardi, Gianfranco, Chaudhuri, Shiva, Dubhashi, Devdatt, Mehlhorn, Kurt

We establish a lower bound on the efficiency of rea--universal circuits. The area A u of every graph H that can host any graph G of area (at most) A with dilation d, and congestion c p A= log log A...

A Complete and efficient algorithm for the intersection of a general ans a convex polyhedron (1993)

Dobrindt, Katrin, Mehlhorn, Kurt, Yvinec, Mariette

A polyhedron is any set that can be obtained from the open halfspaces by a finite number of set complement and set intersection operations. We give an efficient and complete algorithm for...

A Complete and efficient algorithm for the intersection of a general ans a convex polyhedron (1993)

Dobrindt, Katrin, Mehlhorn, Kurt, Yvinec, Mariette

A polyhedron is any set that can be obtained from the open halfspaces by a finite number of set complement and set intersection operations. We give an efficient and complete algorithm for...

A Complete and efficient algorithm for the intersection of a general ans a convex polyhedron (1993)

Dobrindt, Katrin, Mehlhorn, Kurt, Yvinec, Mariette

A polyhedron is any set that can be obtained from the open halfspaces by a finite number of set complement and set intersection operations. We give an efficient and complete algorithm for...

A Complete and Efficient Algorithm for the Intersection of a General and a Convex Polyhedron (1993)

Katrin Dobrindt, Katrin Dobrindt, Kurt Mehlhorn, Kurt Mehlhorn, Mariette Yvinec, Mariette Yvinec, ...

: A polyhedron is any set that can be obtained from the open halfspaces by a finite number of set complement and set intersection operations. We give an efficient and complete algorithm for...

An Implementation of the Hopcroft and Tarjan Planarity Test and Embedding Algorithm (1993)

Kurt Mehlhorn, Petra Mutzel, Stefan Näher

We describe an implementation of the Hopcroft and Tarjan planarity test and embedding algorithm. The program tests the planarity of the input graph and either constructs a combinatorial embedding (if...

An Implementation of the Hopcroft and Tarjan Planarity Test and Embedding Algorithm (1993)

Kurt Mehlhorn, Petra Mutzel, Stefan Näher

We describe an implementation of the Hopcroft and Tarjan planarity test and embedding algorithm. The program tests the planarity of the input graph and either constructs a combinatorial embedding (if...

A Complete and Efficient Algorithm for the Intersection of a General and a Convex Polyhedron (1993)

Dobrindt, Katrin, Mehlhorn, Kurt, Yvinec, Mariette

Un polyedre est tout ensemble qui peut etre obtenu a partir de demi-espaces par un nombre fini d{'}operations de complement et d{'}intersection. Nous proposons ici un algorithme complet et efficace...

Algorithm design and software libraries: Recent developments in the LEDA project (1992)

Kurt Mehlhorn, Stefan Naher

LEDA (Library of Efficient Data Types and Algorithms) is an ongoing project which aims to build a library of the efficient data structures and algorithms used in combinatorial computing [12]. We...

A Method for Obtaining Randomized Algorithms with Small Tail Probabilities (1991)

Alt, Helmut, Guibas, L., Mehlhorn, Kurt, Karp, Richard M., Wigderson, A.

We study strategies for converting randomized algorithms of the Las Vegas type into randomized algorithms with small tail probabilities.

Dynamic Perfect Hashing: Upper and Lower Bounds (1991)

Dietzfelbinger, Martin, Karlin, Anna, Mehlhorn, Kurt, Rohnert, Hans, Tarjan, Robert E.

The dynamic dictionary problem is considered: provide an algorithm for storing a dynamic set, allowing the operations insert, delete, and lookup. A dynamic perfect hashing strategy is given: a...

Bounded ordered dictionaries in O(log log N) time and O(n) space (1990)

Kurt Mehlhorn, Stefan Naher

Abstract. In this paper we show how to implement bounded ordered dictionaries, also called bounded priority queues, in O(log log N) time per operation and O(n) space. Here n denotes the number of...

Can a Maximum Flow be Computed in o(nm) Time (1990)

Joseph Cheriyan, Torben Hagerup, Kurt Mehlhorn

Abstract. We show that a maximum flow in a network with n vertices can be computed deterministically in O(n3/logn) time on a uniform-cost RAM. For dense graphs, this improves the previous best bound...

Faster Algorithms for the Shortest Path Problem (1990)

Ravindra K. Ahuja, Kurt Mehlhorn, James B. Orlin, Robert E. Tarjan

Abstract. Efficient implementations of Dijkstra’s shortest path algorithm are investigated. A new data structure, called the radix heap, is proposed for use in this algorithm. On a network with n...

A faster compaction algorithm with automatic jog insertion (1990)

Mehlhorn, Kurt, Näher, Stefan

The work of F.M. Maley (Proc. Chapel Hill Conf. on VLSI, p.261-83, 1985) on one-dimensional compaction with automatic jog insertion is refined. More precisely, an algorithm with running time...

Compaction on the torus (1990)

Mehlhorn, Kurt, Rülling, W.

A compacter takes as input a VLSI layout and produces as output an equivalent layout of smaller area. An effective compaction system frees the designer from the details of the design rules, and...

a Library of Efficient Data Types and Algorithms (1989)

Kurt Mehlhorn

LEDA is a library of efficient data types and algorithms. At present, its strength is graph algorithms and the data structures related to them. The computational geometry part is evolving. The main...

Area-Time Optimal Division for $T=\Omega((\log n)^1+\epsilon)$ (1987)

Mehlhorn, Kurt, Preparata, Franco P.

Area-time optimal VLSI division circuits are described for all computation times in the range for arbitrary > 0.

Deterministic Simulation of Idealized Parallel Computers on More Realistic Ones (1987)

Alt, Helmut, Hagerup, Torben, Mehlhorn, Kurt, Preparata, Franco P.

The authors describe a nonuniform deterministic simulation of PRAMs on module parallel computers (MPCs) and on processor networks of bounded degree. The simulating machines have the same number $n$...

Routing through a Rectangle (1986)

Mehlhorn, Kurt, Preparata, F. P.

In this paper an O(N log N) algorithm for routing through a rectangle is presented. Consider an n-by-m rectangular grid and a set of N two-terminal nets. A net is a pair of points on the boundary of...

Space Sweep Solves Intersection of Convex Polyhedra (1984)

Hertel, Stefan, Mäntylä, Martti, Mehlhorn, Kurt, Nievergelt, Jurg

Summary  Plane-sweep algorithms form a fairly general approach to two-dimensional problems of computational geometry. No corresponding general space-sweep algorithms for geometric problems in 3-...

Randomized and deterministic simulations of PRAMs by parallel machines with restricted granularity of parallel memories (1984)

Mehlhorn, Kurt, Vishkin, Uzi

The present paper provides a comprehensive study of the following problem. Consider algorithms which are designed for shared memory models of parallel computation (PRAMs) in which processors are...

The Recognition of Deterministic CFL's in Small Time and Space (1983)

Von Braunmühl, Burchard, Cook, Stephen, Mehlhorn, Kurt, Verbeek, Rutger

Let S(n) be a nice space bound such that log2 n S(n) n. Then every DCFL is recognized by a multitape Turing machine simultaneously in time O(n2/S(n)) and space O(S(n)), and this time bound is...

Cost Trade-offs in Graph Embeddings, with Applications (1983)

Hong, Jia-Wei, Mehlhorn, Kurt, Rosenberg, Arnold L.

An embedding of the graph G in the graph H is a one-to-one association of the vertices of G with the vertices of H. There are two natural measures of the cost of a graph embedding, namely, the...

Codes: Unequal Probabilities, Unequal Letter Cost (1980)

Altenkamp, Doris, Mehlhorn, Kurt

The construction of alphabetic prefix codes with unequal letter costs and unequal probabilities is considered. A variant of the noiseless coding theorem is proved giving closely matching lower and...

Dynamic Binary Search (1979)

Mehlhorn, Kurt

We consider search trees under time-varying access probabilities. Let $S = \{ B_1 , \cdots ,B_n \} $ and let $p_i^t $ be the number of accesses to object $B_i $ up to time $t$, $W^t = \sum {p_i^t }...

Some Remarks on Boolean Sums (1979)

Mehlhorn, Kurt

Summary  Neciporuk, Lamagna/Savage and Tarjan determined the monotone network complexity of a set of Boolean sums if any two sums have at most one variable in common. Wegener then solved the case...

A best possible bound for the weighted path length of binary search trees (1977)

Mehlhorn, Kurt

The weighted path length of optimum binary search trees is bounded above by $\sum \beta_i + 2\sum \alpha_j + H$ where $H$ is the entropy of the frequency distribution, $\sum \beta _i $ is the total...

Van Wijngaarden Grammars and Space Complexity Class {EXSPACE} (1977)

Deussen, Peter, Mehlhorn, Kurt

Summary  Top-down and bottom-up decision strategies for van Wijngaarden grammars led to type R and type L van Wijngaarden grammars. The corresponding language families are now shown to be equal...

Monotone Switching Circuits and Boolean Matrix Product (1976)

Mehlhorn, Kurt, Galil, Zvi

We explore the concept of local transformations of monotone switching circuits, i.e. what kind of local changes in a network leave the input/output behavior invariant. We obtain several general...

9 by Springer-Verlag 1975 Nearly Optimal Binary Search Trees (1975)

Kurt Mehlhorn

Summary. We discuss two simple strategies for constructing binary search trees: "Place the most frequently occurring name at the root of the tree, then proceed similary on the subtrees...

Nearly Optimal Binary Search Trees (1975)

Mehlhorn, Kurt

Summary  We discuss two simple strategies for constructing binary search trees: Place the most frequently occurring name at the root of the tree, then proceed similary on the subtrees and choose...

Polynomial and Abstract Subrecursive Classes (1974)

Mehlhorn, Kurt

We define polynomial time computable operator. Our definition generalizes Cook's definition to arbitrary function inputs. Polynomial classes are defined in terms of these operators; the properties of...

Polynomial and Abstract Subrecursive Classes (1974)

Mehlhorn, Kurt

We define polynomial time computable operator. Our definition generalizes Cook's definition to arbitrary function inputs. Polynomial classes are defined in terms of these operators; the properties of...

Polynomial and Abstract Subrecursive Classes (1974)

Mehlhorn, Kurt

We define polynomial time computable operator. Our definition generalizes Cook's definition to arbitrary function inputs. Polynomial classes are defined in terms of these operators; the properties of...

The "Almost All" Theory of Subrecursive Degrees is Decidable (1973)

Mehlhorn, Kurt

We use constructive measure theory to show the decidability pf the "almost all" theory of subrecursive degrees. The formulas of this theory are built up using the constant 0 standing for the minimum...

The "Almost All" Theory of Subrecursive Degrees is Decidable (1973)

Mehlhorn, Kurt

We use constructive measure theory to show the decidability pf the "almost all" theory of subrecursive degrees. The formulas of this theory are built up using the constant 0 standing for the minimum...

On the Embedding Phase of the Hopcroft and Tarjan Planarity Testing Algorithm

Kurt Mehlhorn And, Kurt Mehlhorn, Petra Mutzel

We give a detailed description of the embedding phase of the Hopcroft and Tarjan planarity testing algorithm. The embedding phase runs in linear time. An implementation based on this paper can be...

On the Embedding Phase of the Hopcroft and Tarjan Planarity Testing Algorithm

Kurt Mehlhorn, Petra Mutzel

We give a detailed description of the embedding phase of the Hopcroft and Tarjan planarity testing algorithm. The embedding phase runs in linear time. An implementation based on this paper can be...