Intersection and Decomposition Algorithms for Planar Arrangements
Intersection and Decomposition Algorithms for Planar Arrangements by Pankaj K. Agarwal, published by Cambridge University Press on August 11, 2011, is a comprehensive exploration of various mathematical problems concerning the arrangements of lines, segments, or curves in a plane. This edition spans 296 pages and is presented in English, focusing on significant topics within discrete mathematics and combinatorics.
Readers will find a detailed examination of several key problems, including a proof of almost tight bounds on (n,s)-Davenport-Schinzel sequences, which aids in deriving optimal bounds for various algorithmic challenges. The book also addresses the intersection problem and enhances the efficiency of partitioning algorithms, particularly in constructing spanning trees with low stabbing numbers. Additionally, it discusses numerous applications relevant to these mathematical concepts, making it a valuable resource for those interested in the intricacies of planar arrangements.
Official synopsis Publisher
This book presents a study of various problems related to arrangements of lines, segments, or curves in the plane. The first problem is a proof of almost tight bounds on the length of (n,s)-Davenport-Schinzel sequences, a technique for obtaining optimal bounds for numerous algorithmic problems. Then the intersection problem is treated. The final problem is improving the efficiency of partitioning algorithms, particularly those used to construct spanning trees with low stabbing numbers, a very versatile tool in solving geometric problems. A number of applications are also discussed.
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