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Combinatorial and Computational Geometry
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Details

  • Page extent: 630 pages
  • Size: 234 x 156 mm
  • Weight: 1.05 kg

Library of Congress

  • Dewey number: 516/.11
  • Dewey version: 22
  • LC Classification: QA640.7 .C66 2005
  • LC Subject headings:
    • Discrete geometry
    • Combinatorial geometry
    • Geometry--Data processing

Library of Congress Record

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Hardback

 (ISBN-13: 9780521848626 | ISBN-10: 0521848628)

DOI: 10.2277/0521848628

  • Also available in Paperback
  • Published October 2005

Manufactured on demand: supplied direct from the printer

 (Stock level updated: 01:59 GMT, 29 August 2015)

£79.99

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.

• Over 30 surveys and research papers by leaders in the field • Contains several articles on new research areas, such as Geometric Graph Theory and the Theory of Core Sets and their applications

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.

Contributors

Pankaj K. Agarwal, Sariel Har-Peled, Kasturi Varadarajan, Imre Barany, Alexander Barvinok, Grigoriy Blekherman, Jacob E. Goodman, Andreas Holmsen, Richard Pollack, Saugata Basu, Richard Pollack, Marie-Francoise Roy, Margaret M. Bayer, Andras Bezdek, Karoly Bezdek, Tibor Bisztriczky, Karoly Boroczky, Alexander Bobenko, Peter Brass, Gruia Calinescu, Adrian Dumitrescu, Erik D. Demaine, Joseph O'Rourke, Mike Develin, Francisco Santos, Bernd Sturmfels, Herbert Edelsbrunner, Patrice Koehl, Richard G. Ehrenborg, David Eppstein, Eva Maria Feichtner, Gabor Fejes Toth, Peter Gritzmann, Thorsten Theobald, Aladar Heppes, Wlodzimierz Kuperberg, Michael Joswig, Hagit Last, Yuanxin Liu, Jack Snoeyink, Bernard Mourrain, Fabrice Rouillier, Niranjan Nilakantan, Janos Pach, Rom Pinchasi, Joerg Rambau, Istvan Talata, Csaba D. Toth, Geza Toth, Pavel Valtr, Santosh Vempala

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