Intersection and Decomposition Algorithms for Planar Arrangements
Intersection and Decomposition Algorithms for Planar Arrangements by Pankaj K. Agarwal, published by Cambridge University Press on April 26, 1991, is a comprehensive exploration of geometric problems related to the arrangement of curves in a plane. This edition spans 277 pages and is presented in English. The book delves into various algorithmic challenges, including the proof of bounds on (n,s)-Davenport-Schinzel sequences and the intersection problem, providing a foundation for understanding complex computational geometry topics.
Readers will find a detailed examination of partitioning algorithms, particularly those that aid in constructing spanning trees with low stabbing numbers, which are crucial for addressing geometric issues. The text also discusses several applications relevant to researchers in the fields of mathematics, algebra, discrete mathematics, and combinatorics. This work serves as a valuable resource for those interested in the intricacies of computational and combinatorial geometry.
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Several geometric problems can be formulated in terms of the arrangement of a collection of curves in a plane, which has made this one of the most widely studied topics in computational geometry. This book, first published in 1991, 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. Researchers in computational and combinatorial geometry should find much to interest them in this book.
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