Combinatorial and Computational Geometry by J. E. Goodman

Book Contents :-
1. Geometric Approximation via Coresets 2. Applications of Graph and Hypergraph Theory in Geometry 3. Convex Geometry of Orbits 4. The Hadwiger Transversal Theorem for Pseudolines 5. Betti Number Bounds, Applications and Algorithms 6. Shelling and the h.Vector of the (Extra)ordinary Polytope 7. On the Number of Mutually Touching Cylinders 8. Edge -Antipodal -Polytopes 9. A Conformal Energy for Simplicial Surfaces 10. On the Size of Higher.Dimensional Triangulations 11. The Carpenter’s Ruler Folding Problem 12. A Survey of Folding and Unfolding in Computational Geometry 13. On the Rank of a Tropical Matrix 14. The Geometry of Biomolecular Solvation 15. Inequalities for Zonotopes 16. Quasiconvex Programming 17. De Concini–Procesi Wonderful Arrangement Models: A Discrete Geometer’s Point of View 18. Thinnest Covering of a Circle by Eight, Nine, or Ten Congruent Circles 19. On the Complexity of Visibility Problems with Moving Viewpoints 20. Cylindrical Partitions of Convex Bodies 21. Tropical Halfspaces 22. Two Proofs for Sylvester’s Problem Using an Allowable Sequence of Permutations 23. A Comparison of Five Implementations of 3D Delaunay Tessellation 24. The Bernstein Basis and Real Root Isolation 25. Extremal Problems Related to the Sylvester–Gallai Theorem 26. A Long Noncrossing Path Among Disjoint Segments in the Plane 27. On a Generalization of Sch¨onhardt’s Polyhedron 28. On Hadwiger Numbers of Direct Products of Convex Bodies 29. Binary Space Partitions: Recent Developments 30. The Erd?os–Szekeres Theorem: Upper Bounds and Related Results 31. On the Pair.Crossing Number 32. Geometric Random Walks: A Survey

About this book :-
"Combinatorial and Computational Geometry" is a well-known academic volume edited by J. E. Goodman, János Pach, and Emo Welzl. The book focuses on the interaction between "combinatorial geometry" and "computational geometry", two closely related areas that study discrete geometric structures and the algorithms used to process them. Rather than being a traditional textbook, it is a curated collection of research surveys and papers written by leading experts in the field. The book explores fundamental topics such as geometric arrangements, polytopes, packing and covering problems, and the "algorithmic complexity" of geometric objects. Many chapters highlight how combinatorial insights lead to efficient algorithms, while others examine theoretical limits through lower bounds and probabilistic methods. The material emphasizes rigorous proofs, deep mathematical structure, and modern research techniques, making it especially valuable for advanced study. Published by "Cambridge University Press" as part of the "MSRI Publications" series, this book is aimed at graduate students, researchers, and professionals in mathematics and computer science. It serves as a long-term reference for those interested in "geometric algorithms", discrete mathematics, and theoretical computer science, offering a clear snapshot of major developments and open problems in the field.

Book Detail :-
Title: Combinatorial and Computational Geometry by J. E. Goodman
Publisher: Cambridge University Press
Year: 2005
Pages: 628
Type: PDF
Language: English
ISBN-10 #: 0521848628
ISBN-13 #: 978-0521848626
License: Linked Content Owned by Author
Amazon: Amazon

About Author :-
The author Jacob E. Goodman, János Pach, and Emo Welzl are internationally recognized researchers in "combinatorial geometry" and "computational geometry". Goodman is known for his work on geometric configurations and discrete structures, Pach for major contributions to incidence geometry and geometric graph theory, and Welzl for influential research in "randomized algorithms" and geometric optimization. Together, they bring deep expertise in "geometric algorithms" and "discrete mathematics", making their editorial work highly authoritative. Their collaboration reflects decades of research leadership and has strongly influenced modern theoretical and algorithmic geometry.

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