E-Book Overview
Aimed at an audience of researchers and graduate students in computational geometry and algorithm design, this book uses the Geometric Spanner Network Problem to showcase a number of useful algorithmic techniques, data structure strategies, and geometric analysis techniques with many applications, practical and theoretical. The authors present rigorous descriptions of the main algorithms and their analyses for different variations of the Geometric Spanner Network Problem. Though the basic ideas behind most of these algorithms are intuitive, very few are easy to describe and analyze. For most of the algorithms, nontrivial data structures need to be designed, and nontrivial techniques need to be developed in order for analysis to take place. Still, there are several basic principles and results that are used throughout the book. One of the most important is the powerful well-separated pair decomposition. This decomposition is used as a starting point for several of the spanner constructions.
E-Book Content
P1: JZP CUNY600-Main CUNY600-Narasimhan 0 521 86205 1 October 31, 2006 23:14 This page intentionally left blank ii P1: JZP CUNY600-Main CUNY600-Narasimhan 0 521 86205 1 October 31, 2006 23:14 Geometric Spanner Networks Aimed at an audience of researchers and graduate students in computational geometry and algorithm design, this book uses the Geometric Spanner Network Problem to showcase a number of useful algorithmic techniques, data structure strategies, and geometric analysis techniques with many applications, practical and theoretical. The authors present rigorous descriptions of the main algorithms and their analyses for different variations of the Geometric Spanner Network Problem. Although the basic ideas behind most of these algorithms are intuitive, very few are easy to describe and analyze. For most of the algorithms, nontrivial data structures need to be designed, and nontrivial techniques need to be developed in order for analysis to take place. Still, there are several basic principles and results that are used throughout the book. One of the most important is the powerful well-separated pair decomposition. This decomposition is used as a starting point for several of the spanner constructions. Giri Narasimhan earned a B. Tech. in Electrical Engineering from the Indian Institute of Technology in Mumbai, and a Ph.D. in Computer Science from the University of Wisconsin in Madison. He was a member of the faculty at the University of Memphis, Tennessee, and is currently a professor in the School of Computing and Information Sciences at Florida International University in Miami. Michiel Smid received an M.Sc. degree in Mathematics from the University of Technology in Eindhoven, The Netherlands, and a Ph.D. degree in Computer Science from the University of Amsterdam. He has held teaching positions at the Max-Planck-Institut f¨ur Informatik in Saarbr¨ucken, Germany, King’s College in London, and the Otto-von-Guericke-Universit¨at in Magdeburg, Germany. Since 2001, he has been at Carleton University, Ottawa, where he is currently a professor of Computer Science. i P1: JZP CUNY600-Main CUNY600-Narasimhan 0 521 86205 1 October 31, 2006 ii 23:14 P1: JZP CUNY600-Main CUNY600-Narasimhan 0 521 86205 1 October 31, 2006 23:14 Geometric Spanner Networks Giri Narasimhan Florida International University Michiel Smid Carleton University iii CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge