Cambridge University Press, 10/20/2005EAN 9780521848626, ISBN10: 0521848628Hardcover, 630 pages, 23.4 x 15.6 x 3.5 cmLanguage: EnglishDuring 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.1. Geometric approximation via core sets Pankaj K. Agarwal, Sariel Har-Peled and Kasturi Varadarajan2. Applications of graph and hypergraph theory in geometry Imre Barany3. Convex geometry of orbits Alexander Barvinok and Grigoriy Blekherman4. The Hadwiger transversal theorem for pseudolines Saugata Basu, Jacob E. Goodman, Andreas Holmsen and Richard Pollack5. Betti number bounds, applications, and algorithms Saugata Basu, Richard Pollack and Marie-Francoise Roy6. Shelling and the h-vector of the (extra-)ordinary polytope Margaret M. Bayer7. On the number of mutually touching cylinders Andras Bezdek8. Edge-antipodal 3-polytopes Karoly Bezdek, Tibor Bisztriczky and Karoly Boroczky9. A conformal energy for simplicial surfaces Alexander Bobenko10. On the size of higher-dimensional triangulations Peter Brass11. The carpenter's ruler folding problem Gruia Calinescu and Adrian Dumitrescu12. A survey of folding and unfolding in computational geometry Erik D. Demaine and Joseph O'Rourke13. On the rank of a tropical matrix Mike Develin, Francisco Santos and Bernd Sturmfels14. The geometry of biomolecular solvation Herbert Edelsbrunner and Patrice Koehl15. Inequalities for zonotopes Richard G. Ehrenborg16. Quasiconvex programming David Eppstein17. De Concini-Procesi wonderful arrangement models - a discrete geometer's point of view Eva Maria Feichtner18. Thinnest covering of a circle by eight, nine, or ten congruent circles Gabor Fejes Toth19. On the complexity of visibility problems with moving viewpoints Peter Gritzmann and Thorsten Theobald20. Cylindrical partitions of convex bodies Aladar Heppes and Wlodzimierz Kuperberg21. Tropical halfspaces Michael Joswig22. Two proofs for Sylvester's problem using an allowable sequence of permutations Hagit Last23. A comparison of five implementations of 3d Delaunay tessellation Yuanxin Liu and Jack Snoeyink24. Bernstein's basis and real root isolation Bernard Mourrain, Fabrice Rouillier and Marie-Francoise Roy25. On some extremal problems in combinatorial geometry Niranjan Nilakantan26. A long non-crossing path among disjoint segments in the plane Janos Pach and Rom Pinchasi27. On a generalization of Schoenhardt's polyhedron Joerg Rambau28. On Hadwiger numbers of direct products of convex bodies Istvan Talata29. Binary space partitions - recent developments Csaba D. Toth30. Erdos-Szekeres theoremupper bounds and related results Geza Toth and Pavel Valtr31. On the pair-crossing number Pavel Valtr32. Geometric random walksa survey Santosh Vempala.
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