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 volume, which contains 32 papers on a broad range of topics of current 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.
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págs. 51-85
The Hadwiger Transversal Theorem for Pseudolines
Saugata Basu, Jacob E. Goodman, Andreas F. Holmsen, Richard Pollack
págs. 85-86
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págs. 97-120
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A Survey of Folding and Unfolding in Computational Geometry
Erik D. Demaine, Joseph O'Rourke
págs. 167-211
On the Rank of a Tropical Matrix
Mike Develin, Francisco Santos , Bernd Sturmfels
págs. 213-242
págs. 243-275
págs. 277-286
págs. 287-331
De Concini--Procesi Wonderful Arrangement Models: a Discrete Geometer's Point of View
Eva María Feichtner
págs. 333-360
págs. 361-376
On the Complexity of Visibility Problems with Moving Viewpoints
Peter Gritzmann, Thorsten Theobald
págs. 377-397
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págs. 409-431
págs. 433-437
Yuanxin Liu, Jack Snoeyink
págs. 439-458
págs. 459-478
págs. 479-494
A Long Noncrossing Path Among Disjoint Segments in the Plane
János Pach, Rom Pinchasi
págs. 495-500
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págs. 517-528
págs. 529-556
The Erdo"s-Szekeres Theorem: upper Bounds and Related Results
Géza Tóth, Pavel Valtr
págs. 557-568
págs. 569-575
págs. 577-616
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