02894nam a22003378i 4500001001600000003000700016008004100023020001800064020001800082035002000100041000800120082001400128100003000142245007500172264007100247300003800318336002600356337002600382338003600408500001300444505076600457520100901223650002502232650004302257650003102300700002702331856005502358932003202413596000602445949010502451CR9780511546884UkCbUP090508s2007||||enk o ||1 0|eng|d a9780511546884 a9780521815130 a(Sirsi) a798931 aeng00a005.12221 aNarasimhan, Giri,eauthor10aGeometric spanner networksh[E-Book] /cGiri Narasimhan, Michiel Smid. 1aCambridge :bCambridge University Press,c2007e(CUP)fCUP20200108 a1 online resource (xv, 500 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier aenglisch0 aAlgorithms and graphs -- The algebraic computation-tree model -- Spanners based on the q-graph -- Cones in higher dimensional space and q-graphs -- Geometric analysis : the gap property -- The gap-greedy algorithm -- Enumerating distances using spanners of bounded degree -- The well-separated pair decomposition -- Applications of well-separated pairs -- The dumbbell theorem -- Shortcutting trees and spanners with low spanner diameter -- Approximating the stretch factor of euclidean graphs -- Geometric analysis : the leapfrog property -- The path-greedy algorithm -- The distance range hierarchy -- Approximating shortest paths in spanners -- Fault-tolerant spanners -- Designing approximation algorithms with spanners -- Further results and open problems. aAimed 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. 0aComputer algorithms. 0aTrees (Graph theory)xData processing. 0aGeometryxData processing.1 aSmid, Michiel,eauthor40uhttps://doi.org/10.1017/CBO9780511546884zVolltext aCambridgeCore (Order 30059) a1 aXX(798931.1)wAUTOc1i798931-1001lELECTRONICmZBrNsYtE-BOOKu8/1/2020xUNKNOWNzUNKNOWN1ONLINE