Combinatorial and Computational Geometry by J. E. Goodman
Combinatorial and Computational Geometry - Table of 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
What You Will Learn in Combinatorial and Computational Geometry
"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 Details & Specifications
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 the Author: Jacob E. Goodman, János Pach, and Emo Welzl
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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