Combinatorial and Computational Geometry

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Cambridge University Press, Aug 8, 2005 - Computers - 616 pages
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This volume, containing 32 papers on a broad range of topics of current interest in the field, is an outgrowth of the synergism of Discrete and Computational Geometry. 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, and with algebraic topology, geometric probability, real algebraic geometry, and combinatorics.

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Geometric Approximation via Coresets 1
Convex Geometry of Orbits
The Hadwiger Transversal Theorem for Pseudolines
Betti Number Bounds Applications and Algorithms
Shelling and the hVector of the Extraordinary Polytope
On the Number of Mutually Touching Cylinders
EdgeAntipodal 3Polytopes
A Conformal Energy for Simplicial Surfaces
A Discrete
Thinnest Covering of a Circle by Eight Nine or Ten Congruent Circles
On the Complexity of Visibility Problems with Moving Viewpoints
Cylindrical Partitions of Convex Bodies
Two Proofs for Sylvesters Problem Using an Allowable Sequence
The Bernstein Basis and Real Root Isolation
Extremal Problems Related to the SylvesterGallai Theorem

On the Size of HigherDimensional Triangulations
The Carpenters Ruler Folding Problem
A Survey of Folding and Unfolding in Computational Geometry
On the Rank of a Tropical Matrix
The Geometry of Biomolecular Solvation
Inequalities for Zonotopes
A Long Noncrossing Path Among Disjoint Segments in the Plane
On Hadwiger Numbers of Direct Products of Convex Bodies
Recent Developments
Upper Bounds and Related Results
A Survey

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About the author (2005)

Jacob E. Goodman is a professor of Mathematics at City College, CUNY, and the author of a number of papers in Geometry. He is the co-founder and co-editor-in-chief of The Journal of Discrete and Computational Geometry. He is also the co-editor of many other leading books in the field, most notably, The Handbook of Discrete and Computational Geometry, published by CRC Press, whose second edition has just appeared, and several volumes published by the American Mathematical Society. A past winner of the MAA's Lester R. Ford award, Goodman was also the founder and first president of the New York Composers Circle. He is a member of the American Mathematical Society.

About the authors JANOS PACH is Professor of Computer Science at City College of New York and Senior Research Fellow at the Mathematical Institute of the Hungarian Academy of Sciences. He received his PhD in mathematics from Eotvos University, Budapest, in 1980 and has had visiting positions at various universities, including the University College of London, McGill University, the Courant Institute of New York University, and Tel Aviv University. He serves on the editorial boards of three mathematical and computer science journals and has been an invited speaker at many conferences. He has published more than one hundred research papers, mostly in discrete and computational geometry and in combinatorics. He received the Lester R. Ford Award in 1990 and the Renyi Prize in 1993. PANKAJ K. AGARWAL is Associate Professor in the Computer Science Department of Duke University. He received his PhD in computer science from the Courant Institute of Mathematical Sciences, New York University, in 1989. He is the author of Intersection and Decomposition Algorithms for Planar Arrangements, and a coauthor of Davenport--Schinzel Sequences and Their Geometric Applications. He has published several research papers and has given talks at many conferences. He was awarded the National Young Investigator Award in 1992.

Emo Welzl is a full professor of Computer Science at the Institute for Theoretical Computer Science of Eth Zurich. His research interests are in the Foundations of Computer Science, mainly Algorithms and Data Structures, in particular, Computational Geometry and Applications, Analysis of Geometric Structures, Randomized Methods, and Discrete Gometry. He was awarded the Max Planck Prize in 1992 and the Gottfried Wilhelm Leibniz Prize in 1995. He has been an ACM Fellow since 1998.

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