Hardcover. This book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view. Written with minimal prerequisites and featuring plenty of figures, this engaging book will be of interest to undergraduate students and researchers in mathematics and computer science. Most topics are introduced with a related puzzle or brain-teaser. The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathematics including number theory, graph theory, and the theory of permutation patterns. Pseudocode is included for many algorithms that compute properties of point sets. This engaging book unifies mathematical and computational properties of finite sets of points in the plane using forbidden configurations, which are patterns that cannot appear in sets with a given property, and helps students and researchers explore the implications of this unified view of discrete geometry. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

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Detalles bibliogr�ficos

T�tulo: Forbidden Configurations in Discrete Geometry (Hardcover)
Editor: Cambridge University Press, Cambridge
Fecha de publicaci�n: 2018
Idioma: Ingl�s
ISBN 10: 1108423914
ISBN 13: 9781108423915
Encuadernaci�n: Hardcover
Estado: new

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Sinopsis

Unifies discrete and computational geometry by using forbidden patterns of points to characterize many of its problems.

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David Eppstein is Chancellor's Professor of Computer Science at the University of California, Irvine. He has over 350 publications on subjects including discrete and computational geometry, graph theory, graph algorithms, data structures, robust statistics, social network analysis and visualization, mesh generation, biosequence comparison, exponential algorithms, and recreational mathematics. He has been the moderator for data structures and algorithms on arXiv.org since 2006, and is a major contributor to Wikipedia's articles on mathematics and theoretical computer science. He was elected as an ACM fellow in 2012.

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