CiNii Books - Combinatorial and computational geometry

During the past few decades, the gradual merger of Discrete Geometry and the newer discipline of Computational Geometry has provided enormous impetus to mathematicians and computer scientists interested in geometric problems. This 2005 volume, which contains 32 papers on a broad range of topics of interest in the field, is an outgrowth of that synergism. It includes surveys and research articles exploring geometric arrangements, polytopes, packing, covering, discrete convexity, geometric algorithms and their complexity, and the combinatorial complexity of geometric objects, particularly in low dimension. There are points of contact with many applied areas such as mathematical programming, visibility problems, kinetic data structures, and biochemistry, as well as with algebraic topology, geometric probability, real algebraic geometry, and combinatorics.

Table of Contents

1. Geometric approximation via core sets Pankaj K. Agarwal, Sariel Har-Peled and Kasturi Varadarajan
2. Applications of graph and hypergraph theory in geometry Imre Barany
3. Convex geometry of orbits Alexander Barvinok and Grigoriy Blekherman
4. The Hadwiger transversal theorem for pseudolines Saugata Basu, Jacob E. Goodman, Andreas Holmsen and Richard Pollack
5. Betti number bounds, applications, and algorithms Saugata Basu, Richard Pollack and Marie-Francoise Roy
6. Shelling and the h-vector of the (extra-)ordinary polytope Margaret M. Bayer
7. On the number of mutually touching cylinders Andras Bezdek
8. Edge-antipodal 3-polytopes Karoly Bezdek, Tibor Bisztriczky and Karoly Boroczky
9. A conformal energy for simplicial surfaces Alexander Bobenko
10. On the size of higher-dimensional triangulations Peter Brass
11. The carpenter's ruler folding problem Gruia Calinescu and Adrian Dumitrescu
12. A survey of folding and unfolding in computational geometry Erik D. Demaine and Joseph O'Rourke
13. On the rank of a tropical matrix Mike Develin, Francisco Santos and Bernd Sturmfels
14. The geometry of biomolecular solvation Herbert Edelsbrunner and Patrice Koehl
15. Inequalities for zonotopes Richard G. Ehrenborg
16. Quasiconvex programming David Eppstein
17. De Concini-Procesi wonderful arrangement models - a discrete geometer's point of view Eva Maria Feichtner
18. Thinnest covering of a circle by eight, nine, or ten congruent circles Gabor Fejes Toth
19. On the complexity of visibility problems with moving viewpoints Peter Gritzmann and Thorsten Theobald
20. Cylindrical partitions of convex bodies Aladar Heppes and Wlodzimierz Kuperberg
21. Tropical halfspaces Michael Joswig
22. Two proofs for Sylvester's problem using an allowable sequence of permutations Hagit Last
23. A comparison of five implementations of 3d Delaunay tessellation Yuanxin Liu and Jack Snoeyink
24. Bernstein's basis and real root isolation Bernard Mourrain, Fabrice Rouillier and Marie-Francoise Roy
25. On some extremal problems in combinatorial geometry Niranjan Nilakantan
26. A long non-crossing path among disjoint segments in the plane Janos Pach and Rom Pinchasi
27. On a generalization of Schoenhardt's polyhedron Joerg Rambau
28. On Hadwiger numbers of direct products of convex bodies Istvan Talata
29. Binary space partitions - recent developments Csaba D. Toth
30. Erdos-Szekeres theorem: upper bounds and related results Geza Toth and Pavel Valtr
31. On the pair-crossing number Pavel Valtr
32. Geometric random walks: a survey Santosh Vempala.

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Combinatorial and computational geometry

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