On the Bounding Boxes Obtained by Principal Component Analysis (2008)
Darko Dimitrov, Christian Knauer, Klaus Kriegel, Günter Rote
Principle component analysis (PCA) is commonly used to compute a bounding box of a point set in R d. In this paper we give bounds on the approximation factor of PCA bounding boxes of convex polygons...
On the Bounding Boxes Obtained by Principal Component Analysis Abstract (2008)
Darko Dimitrov, Christian Knauer, Klaus Kriegel, Günter Rote
Principle component analysis (PCA) is a commonly used to compute a bounding box of a point set in R d. In this paper we give bounds on the approximation factor of PCA bounding boxes of convex...
Abstract Matching 2D Patterns of Protein Spots (2008)
Frank Hoffmann, Klaus Kriegel, Carola Wenk
A new algorithmic approach to comparing 2D patterns of protein spots obtained by the 2D gel electrophoresis technique is presented. Both the matching of a local pattern vs. a full 2D gel image and...
Darko Dimitrov, Christian Knauer, Klaus Kriegel, Günter Rote
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We present a simple geometric and combinatorial algorithm for the approximate partial matching problem of small 3D point landmark patterns. It has been designed for and successfully applied in a...
A Competitive Strategy for Learning a Polygon (Short Version) (2007)
Frank Hoffmann, Christian Icking, Rolf Klein, Klaus Kriegel
this paper, we present the first strategy for general simple polygons and we prove a competitive factor of 133.
The polygon exploration problem (2007)
Frank Hoffmann, Christian Icking, Rolf Klein, Klaus Kriegel
Abstract. We present an on-line strategy that enables a mobile robot with vision to explore an unknown simple polygon. We prove that the resulting tour is less than 26.5 times as long as the shortest...
Upper and lower bounds on the quality of the PCA bounding boxes (2007)
Darko Dimitrov, Christian Knauer, Klaus Kriegel, Günter Rote
Principle component analysis (PCA) is commonly used to compute a bounding box of a point set in R d. The popularity of this heuristic lies in its speed, easy implementation and in the fact that...
DOI: 10.1007/s00453-003-1047-0 Covering with Ellipses 1 (2003)
Alon Efrat, Frank Hoffmann, Christian Knauer, Klaus Kriegel, Günter Rote, Carola Wenk
Abstract. We address the problem of how to cover a set of required points by a small number of axis-parallel ellipses that avoid a second set of forbidden points. We study geometric properties of...
DOI: 10.1007/s00453-003-1047-0 Covering with Ellipses 1 (2003)
Alon Efrat, Frank Hoffmann, Christian Knauer, Klaus Kriegel, Günter Rote, Carola Wenk
Abstract. We address the problem of how to cover a set of required points by a small number of axis-parallel ellipses that avoid a second set of forbidden points. We study geometric properties of...
Alon Efrat, Frank Hoffmann, Alon Efrat, Christian Knauer, Günter Rote, Christian Knauer, ...
We address the problem of how to cover a set of required points by a small number of axis{parallel ellipses that avoid a second set of forbidden points. We study geometric properties of such covers...
Triangles in Euclidean arrangements (1999)
Abstract. The number of triangles in arrangements of lines and pseudolines has been object of some research. Most results, however, concern arrangements in the projective plane. In this article we...
The polygon exploration problem I: A competitive strategy (1998)
Frank Hoffmann, Christian Icking, Rolf Klein, Klaus Kriegel
We present an on-line strategy that enables a mobile robot with vision to explore an unknown simple polygon. We prove that the resulting tour is less than 26.5 times as long as the shortest watchman...
The Polygon Exploration Problem II: The Angle Hull (1998)
Frank Hoffmann, Christian Icking, Rolf Klein, Klaus Kriegel
Let D be a connected region inside a simple polygon, P . We define the angle hull of D, to be the set of all points in P that can see two points of D at a right angle. We show that the perimeter of...
Matching 2D Patterns of Protein Spots (1997)
Frank Hoffmann, Klaus Kriegel, Carola Wenk
A new algorithmic approach to comparing 2D patterns of protein spots obtained by the 2D gel electrophoresis technique is presented. Both the matching of a local pattern vs. a full 2D gel image and...
An Efficient Competitive Strategy for Learning a Polygon (1996)
Frank Hoffmann, Christian Icking, Rolf Klein, Klaus Kriegel
We provide a competitive strategy for a mobile robot with vision, that has to explore an unknown simple polygon starting from and returning to a given point xo on the boundary. Our strategy creates a...
Universelle 1-Kiesel-Automaten [Ein-Kiesel-Automaten] für k-komponentige Labyrinthe / (1984)
Zugl.: Berlin, Akad. d. Wiss. d. DDR, Diss. A, 1984.
Universelle 1-Kiesel-Automaten [Ein-Kiesel-Automaten] für k-komponentige Labyrinthe / (1984)
Zugl.: Berlin, Akad. d. Wiss., Diss., 1984.