Mordecai J. Golin

Online Dynamic Programming Speedups ∗ (2009)

Amotz Bar-noy, Mordecai J. Golin, Yan Zhang

Consider the dynamic program h(n) = min1≤j≤n a(n, j), where a(n, j) is some formula that may (online) or may not (offline) depend on the previously computed h(i), for i < n. The goal is to...

The (2009)

Mordecai J. Golin

number of spanning trees in a class of double fixed-step loop networks

Permanents of Circulants: a Transfer Matrix Approach ∗ (Extended Abstract) (2009)

Mordecai J. Golin, Yiu Cho, Leung Yajun Wang

Calculating the permanent of a (0,1) matrix is a #P-complete problem but there are some classes of structured matrices for which the permanent is calculable in polynomial time. The most well-known...

The Two-Median Problem on Manhattan Meshes (2009)

Mordecai J. Golin, Yan Zhang

We investigate the two-median problem on a mesh with M columns and N rows (M ≥ N), under the Manhattan (L1) metric. We derive exact algorithms with respect to m, n, and r, the number of columns,...

Abstract Counting Structures in Grid Graphs, Cylinders and Tori Using Transfer Matrices: Survey and New Results (2009)

Mordecai J. Golin, Yiu Cho, Leung Yajun, Wang Xuerong Yong

There is a very large literature devoted to counting structures, e.g., spanning trees, Hamiltonian cycles, independent sets, acyclic orientations, in the n × m grid graph G(n, m). In particular the...

Permanents of Circulants: a Transfer Matrix Approach (Extended Abstract) (2008)

Mordecai J. Golin, Yiu Cho Leung, Yajun Wang

Calculating the permanent of a (0,1) matrix is a #P-complete problem but there are some classes of structured matrices for which the permanent is calculable in polynomial time. The most well-known...

The Structure of Optimal Prefix-Free Codes in Restricted Languages: the Uniform Probability Case (Extended Abstract) ⋆ (2008)

Mordecai J. Golin, Zhenming Liu

Abstract. In this paper we discuss the problem of constructing minimum-cost, prefix-free codes for equiprobable words under the assumption that all codewords are restricted to belonging to an...

Online maintenance of k-medians and k-covers on a line. http://www.cs.ust.hk/faculty/golin/pubs/KMedian SWAT04.pdf (2008)

Rudolf Fleischer, Mordecai J. Golin, Zhang Yan

Abstract. The standard dynamic programming solution to finding kmedians on a line with n nodes requires O(kn 2) time. Dynamic programming speed-up techniques, e.g., use of the quadrangle inequality...

Algorithms (2008)

Mordecai J. Golin

It is well known that the complexity, i.e., the number of vertices, edges and faces, of the 3-dimensional Voronoi diagram of n pointscanbeasbadasΘ(n 2). Interest has recently arisen as to what...

Online Dynamic Programming Speedups ⋆ (2008)

Amotz Bar-noy, Mordecai J. Golin, Yan Zhang

Abstract. Consider the Dynamic Program h(n) = min1≤j≤n a(n, j) for n =1, 2,...,N. For arbitrary values of a(n, j), calculating all the h(n) requires Θ(N 2) time. It is well known that, if the...

Chapter 29 Limit Theorems for Minimum-Weight Triangulations, Other Euclidean Functionals, and Probabilistic Recurrence Relations (2008)

Extended Abstract, Mordecai J. Golin

Let MWT(n) be the weight of a minimum-weight triangu-lation of n points chosen independently from the uniform distribution over [0, 112. Previous work [ll] has shown that E(MWT(n)) = e(&). In...

Abstract Algorithms for Infinite Huffman-Codes ∗ (Extended Abstract) (2008)

Mordecai J. Golin, Kin Keung Ma

Optimal (minimum cost) binary prefix-free codes for infinite sources with geometrically distributed frequencies, e.g., P = {pi (1 − p)} ∞ i=0, 0 < p < 1, were first (implicitly) suggested...

Online maintenance of k-medians and k-covers on a line. http://www.cs.ust.hk/faculty/golin/pubs/KMedian SWAT04.pdf (2007)

Rudolf Fleischer, Mordecai J. Golin, Zhang Yan

Abstract. The standard dynamic programming solution to finding k-medians on a line with n nodes requires O(kn 2) time. Dynamic programming speed-up techniques, e.g., use of the quadrangle inequality...

HKUST Theoretical Computer Science (2007)

Yuanping Zhang, Mordecai J. Golin, Clear Water Bay

Chebyshev polynomials and spanning tree formulas for circulant and related graphs

n log n) time, in a random tree O(k (2007)

Antoine Vigneron, Lixin Gao, Mordecai J. Golin, Bo Li

We consider the problem of finding a k-median in a directed tree. We present an algorithm that computes a k-median in O(Pk 2) time where k is the number of resources to be placed and P is the path...

A Dynamic Programming Algorithm for Constructing Optimal Prefix-Free Codes with Unequal Letter Costs (2007)

Mordecai J. Golin, Mordecai J. Golin, Günter Rote, Günter Rote, ...

We consider the problem of constructing prefix-free codes of minimum cost when the encoding alphabet contains letters of unequal length. The complexity of this problem has been unclear for thirty...

y (2007)

Mordecai J. Golin, Claire Kenyon, Neal E. Young

In the standard Human coding problem, one is given a set of words and for each word a positive frequency. The goal is to encode each word w as a codeword c(w) over a given alphabet. The encoding must...

n (2006)

Mordecai J. Golin, Xuerong Yong, Yuanping Zhang

Let T(G) be the number of spanning trees in graph G. In this note we explore the asymptotics of T(G) for circulant graphs. The circulant graph C s1,s2,···,sk

The Asymptotic Number of Spanning Trees in Circulant Graphs (Extended Abstract) ∗ (2006)

Mordecai J. Golin, Xuerong Yong, Yuanping Zhang

Let T(G) be the number of spanning trees in graph G. In this note we explore the asymptotics of T(G) for circulant graphs. The circulant graph Cs1,s2,···,sk n is the 2k regular graph with n...

Unhooking circulant graphs: A combinatorial method for counting spanning trees and other parameters (2004)

Mordecai J. Golin, Yiu Cho Leung

Abstract It has long been known that the number of spanning trees in n node circulant graphs with fixed jumps satisfies a bounded order, constant coefficient, recurrence relation in n. The proof of...

Online Maintenance of KMedians and K-Covers on a Line (2004)

Rudolf Fleischer, Mordecai J. Golin, Yan Zhang

The standard dynamic programming solution to finding k-medians on a line with n nodes requires O(kn 2) time. Dynamic programming speedup techniques, e.g., use of the quadrangle inequality or...

Counting spanning trees and other structures in non constant-jump circulant graphs (2004)

Mordecai J. Golin, Yiu Cho Leung, Yajun Wang

Abstract. Circulant graphs are an extremely well-studied subclass of regular graphs, partially because they model many practical computer network topologies. It has long been known that the number of...

Online Maintenance of KMedians and K-Covers on a Line (2004)

Rudolf Fleischer, Mordecai J. Golin, Yan Zhang

The standard dynamic programming solution to finding k-medians on a line with n nodes requires O(kn 2) time. Dynamic programming speedup techniques, e.g., use of the quadrangle inequality or...

Unhooking circulant graphs: A combinatorial method for counting spanning trees and other parameters (2004)

Mordecai J. Golin, Yiu Cho Leung

Abstract. It has long been known that the number of spanning trees in circulant graphs with fixed jumps and n nodes satisfies a recurrence relation in n. The proof of this fact was algebraic...

Algorithms for infinite Huffman-codes (2003)

Golin, Mordecai J., Ma, Kin Keung

Optimal (minimum cost) binary prefix-free codes for infinite sources with geometrically distributed frequencies, e.g., P = {pi(1 - p)}∞i=0, 0 < p < 1, were first (implicitly) suggested by Golomb...

Maximum residual energy routing with reverse energy cost (2003)

Xie, Qiling, Lea, Chin-Tau, Golin, Mordecai J., Fleischer, Rudolf H.

The Maximum Residual Energy Path (MREP) routing has been shown an effective routing scheme for energy conservation in a battery wireless network. Past studies on MREP are based on the assumption that...

Finding optimal paths in MREP routing (2003)

Fleischer, Rudolf H., Golin, Mordecai J., Lea, Chin-Tau, Wong, Steven

Maximum Residual Energy Path (MREP) routing has been shown an effective routing scheme for energy conservation in battery powered wireless networks. Past studies on MREP routing are based on the...

Curve reconstruction from noisy samples (2003)

Cheng, Siu-Wing, Funke, Stefan, Golin, Mordecai J., Kumar, Piyush, Poon, Sheung-Hung, Ramos, Edgar A.

We present an algorithm to reconstruct a collection of disjoint smooth closed curves from noisy samples. Our noise model assumes that the samples are obtained by first drawing points on the curves...

Maximum residual energy routing with reverse energy cost (2003)

Qiling Xie, Chin-tau Lea, Mordecai J. Golin, Rudolf Fleischer

Abstract-The Maximum Residual Energy Path (MREP) routing has been shown an effective routing scheme for energy conservation in a battery wireless network. Past studies on MREP are based on the...

The Convex hull for random lines in the plane (2002)

Golin, Mordecai J., Langerman, Stefan, Steiger, William

An arrangement of n lines chosen at random from R2 has a vertex set whose convex hull has constant (expected) size.

Chebyshev polynomials and spanning tree formulas for circulant and related graphs (2002)

Zhang, Yuanping, Golin, Mordecai J.

Kirchhoff's Matrix Tree Theorem permits the calculation of the number of spanning trees in any given graph G through the evaluation of the determinant of an associated matrix. In the case of some...

Meeting the Welch and Karystinos-Pados bounds on DS-CDMA binary signature sets (2002)

Ding, Cunsheng, Golin, Mordecai J., KlΦve, Torleiv

The Welch lower bound on the total-squared-correlation (TSC) of binary signature sets is loose for binary signature sets whose length L is not a multiple of 4. Recently Karystinos and Pados developed...

Huffman coding with unequal letter costs (2002)

Golin, Mordecai J., Kenyon, Claire, Young, Neal E.

In the standard Huffman coding problem, one is given a set of words and for each word a positive frequency. The goal is to encode each word w as a codeword c(w) over a given alphabet. The encoding...

Huffman coding with unequal letter costs (2002)

Mordecai J. Golin

In the standard Huffman coding problem, one is given a set of words and for each word a positive frequency. The goal is to encode each word w as a codeword c(w) over a given alphabet. The encoding...

Huffman coding with unequal letter costs (2002)

Mordecai J. Golin, Claire Kenyon, Neal E. Young

In the standard Hu#man coding problem, one is given a set of words and for each word a positive frequency. The goal is to encode each word w as a codeword c(w) over a given alphabet. The encoding...

The probabilistic complexity of the Voronoi diagram of points on a polyhedron (2001)

Na, Hyeon-Suk, Golin, Mordecai J.

It is well known that the complexity, i.e., the number of vertices, edges and faces, of the 3-dimensional Voronoi diagram of n points can be as bad as Θ(n2). Interest has recently arisen as to what...

On the proofs of two lemmas describing the intersections of spheres with the boundary of a convex polytope (2001)

Golin, Mordecai J., Na, Hyeon-Suk

Let P be the boundary of a convex polytope and Sn be a set of points drawn from the 2-dimensional Poisson distribution with rate n over P. In a companion paper [1] the authors show that the expected...

Fun-sort (2001)

Biedl, Therese, Chan, Timothy, Demaine, Erik D., Fleischer, Rudolf H., Golin, Mordecai J., Munro, J. Ian

In this paper we study greedy in-place sorting algorithms which miraculously happen to work in reasonable time. Dumb-Sort which repeatedly compares all possible pairs of array cells sorts n elements...

Protection of keys against modification attack (2001)

Fung, Wai W., Golin, Mordecai J.

In recent work, Anderson and Kuhn [3] described an attack against tamper-resistant devices wherein a secret key stored in EEPROM is compromised using a simple and lowcost attack. The attack consists...

On the average complexity of 3D-Voronoi diagrams of random points on convex polytopes (2001)

Golin, Mordecai J., Na, Hyeon-Suk

It is well known that the complexity, i.e., the number of vertices, edges and faces, of the 3-dimensional Voronoi diagram of n points can be as bad as ⊝(n2). It is also known that if the points are...

Competitive facility location along a highway (2001)

Ahn, Hee-Kap, Cheng, Siu-Wing, Cheong, Otfried, Golin, Mordecai J., Van Oostrum, Rene

We consider a competitive facility location problem with two players. Players alternate placing points, one at a time, into the playing arena, until each of them has placed n points. The arena is...

Competitive facility location : the Voronoi game (2001)

Ahn, Hee-Kap, Cheng, Siu-Wing, Cheong, Otfried, Golin, Mordecai J., Van Oostrum, Rene

We consider a competitive facility location problem with two players. Players alternate placing points, one at a time, into the playing arena, until each of them has placed n points. The arena is...

Protection of Keys against Modification Attack (2001)

Wai W. Fung, Mordecai J. Golin, James W. Gray

In recent work, Anderson and Kuhn [3] described an attack against tamper-resistant devices wherein a secret key stored in EEPROM is compromised using a simple and lowcost attack. The attack consists...

The Probabilistic Complexity of the Voronoi Diagram of Points on (2001)

Theoretical Computer Science, A Polyhedron, Mordecai J. Golin, Hyeon-suk Na

It is well known that the complexity, i.e., the number of vertices, edges and faces, of the 3dimensional Voronoi diagram of n points can be as bad as \Theta(n ): Interest has recently arisen as to...

Lopsided trees : analyses, algorithms, and applications (2000)

Choi, Vicky, Golin, Mordecai J.

Lopsided trees are rooted, ordered, trees in which the length of an edge from a node to its ith child depends upon the value of i. These trees model a variety of problems and have therefore been...

New upper and lower bounds on the channel capacity of read/write isolated memory (2000)

Golin, Mordecai J., Yong, Xuerong, Zhang, Yuanping, Sheng, Li

In this paper we refine upper and lower bounds for the channel capacity of a serial, binary rewritable medium in which no consecutive locations may store '1's and no consecutive locations may be...

An Algorithm for finding a k-median in a directed tree (2000)

Vigneron, Antoine, Gao, Lixin, Golin, Mordecai J., Italiano, Giuseppe F., Li, Bo

We consider the problem of finding a k-median in a directed tree. We present an algorithm that computes a k-median in O(Pk2) time where k is the number of resources to be placed and P is the path...

Optimal prefix-free codes for unequal letter costs : dynamic programming with the Monge property (2000)

Bradford, Phil, Golin, Mordecai J., Larmore, Lawrence L., Rytter, Wojciech

In this paper we discuss the problem of finding optimal prefix-free codes for unequal letter costs, a variation of the classical Huffman coding problem. Our problem consists of finding a minimal cost...

An algorithm for finding a k-median in a directed tree (2000)

Antoine Vigneron, Lixin Gao, Mordecai J. Golin

We consider the problem of finding a k-median in a directed tree. We present an algorithm that computes a k-median in O(P k 2) time where k is the number of resources to be placed and P is the path...

A dynamic programming algorithm for constructing optimal “1”-ended binary prefix-free codes (2000)

Sze-lok Chan, Mordecai J. Golin

[9] , “Coding for a binary independent piecewise-identically-distributed-source,”

On the optimal placement of web proxies in the internet: the linear topology (1999)

Li, Bo, Deng, Xin, Golin, Mordecai J., Sohraby, Kazem

Web caching or web proxy has been considered as the prime vehicle to cope with the ever-increasing demand for information retrieval over the Internet, WWW being a typical example. The existing work...

The Number of spanning trees in circulant graphs (1999)

Zhang, Yuanping, Yong, Xuerong, Golin, Mordecai J.

In this paper we develop a method for determining the exact number of spanning trees in (directed or undirected) circulant graphs. Using this method we can, for any class of circulant graph, exhibit...

THE NUMBER OF SPANNING TREES IN CIRCULANT GRAPHS\Lambda (1999)

Yuanping Zhangy, Xuerong Yongz, Mordecai J. Golin

Abstract In this paper we develop a method for determining the exact number of spanning trees in (directed or undirected) circulant graphs. Using this method we can, for any class of circulant graph,...

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...

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...

Dynamic and distributed web caching in active networks (1998)

Li, Bo, Deng, Xin, Golin, Mordecai J., Sohraby, Kazem

Web caching or web proxy has been considered as the prime vehicle of coping with the ever-increasing demand for information retrieval over wide-area networks, WWW being a typical example. Existing...

Randomized data structures for the dynamic closest-pair problem (1998)

Golin, Mordecai J., Raman, Rajeev, Schwarz, Christian, Smid, Michiel

We describe a new randomized data structure, the sparse partition, for solving the dynamic closest-pair problem. Using this data structure the closest pair of a set of n points in D-dimensional...

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...

A Dynamic Programming Algorithm for Constructing Optimal Prefix-Free Codes with Unequal Letter Costs (1998)

Günter Rote, Mordecai J. Golin

We consider the problem of constructing prefix-free codes of minimum cost when the encoding alphabet contains letters of unequal length. The complexity of this problem has been unclear for...

Optimal Prefix-Free Codes for Unequal Letter Costs and Dynamic Programming with the Monge Property (1998)

Phil Bradford, Mordecai J. Golin, Lawrence L. Larmore, Wojciech Rytter

The Monge property emerges, sometimes quite mysteriously, in many optimization problems and usually leads to running time improvements of at least a linear factor. In this paper a novel application...

Optimal Prefix-Free Codes for Unequal Letter Costs: Dynamic Programming with the Monge Property (1998)

Phil Bradford, Mordecai J. Golin, Lawrence L. Larmore, Wojciech Rytter

In this paper we discuss a variation of the classical Huffman coding problem: finding optimal prefix-free codes for unequal letter costs. Our problem consists of finding a minimal cost prefix-free...

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...

Prefix codes: Equiprobable words, unequal letter costs (1996)

Mordecai J. Golin, Neal Young

Abstract. We consider the following variant of Huffman coding in which the costs of the letters, rather than the probabilities ofthe words, are nonuniform: &quot;Given an alphabet of r letters of...

Lopsided trees: analyses, algorithms, and applications (1996)

Vicky Choi, Mordecai J. Golin

Lopsided trees are rooted, ordered, trees in which the length of an edge from a node to its i th child depends upon the value of i: These trees model a variety of problems and have therefore been...

Prefix codes: Equiprobable words, unequal letter costs (1996)

Mordecai J. Golin, Neal Young

Abstract. We consider the following variant of Huffman coding in which the costs of the letters, rather than the probabilities of the words, are non-uniform: &quot;Given an alphabet of r letters...

Incremental algorithms for finding the convex hulls of circles and the lower envelopes of parabolas (1994)

Olivier Devillers, Mordecai J. Golin

Abstract: The existing O(n log n) algo rithms for nding the convex hulls of circles and the lower envelope of parabolas follow the di vide-and-conquer paradigm. The diOEculty with developing...

Mellin transforms and asymptotics : the mergesort recurrence (1993)

Flajolet, Philippe, Golin, Mordecai J.

Mellin transforms and Dirichlet series are useful in quantifying periodicity phenomena present in recursive divide-and-conquer algorithms. This note illustrates the techniques by providing a precise...