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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(More)
Facility location problems are traditionally investigated with the assumption that <i>all</i> the clients are to be provided service. A significant shortcoming of this formulation is that a few very distant clients, called <i>outliers</i>, can exert a disproportionately strong influence over the final solution. In this paper we explore a generalization of(More)
Let <italic>G=(V,E)</italic> be a <italic>n</italic>-vertex connected graph with positive edge weights. A subgraph <italic>G</italic>&#8242; is a <italic>t</italic>-spanner if for all <italic>u,v</italic><inline-equation> <f> &#8712;</f> </inline-equation><italic>V</italic>, the distance between <italic>u</italic> and <italic>v</italic> in the subgraph is(More)
Let <italic>G</italic>=(<italic>V,E</italic>) be an <italic>n</italic>-vertex connected graph with positive edge weights. A subgraph <italic>G</italic>&#8242; = (<italic>V,E</italic>&#8242;) is a <italic>t-spanner</italic> of <italic>G</italic> if for all <italic>u, v &#949; V</italic>,the weighted distance between <italic>u</italic> and <italic>v</italic>(More)
There are several results available in the literature dealing with efficient construction of t-spanners for a given set S of n points in R d. t-spanners are Euclidean graphs in which distances between vertices in G are at most t times the Euclidean distances between them; in other words, distances in G are " stretched " by a factor of at most t. We consider(More)
Let <italic>V</italic> be a set of <italic>n</italic> points in 3-dimensional Euclidean space. A subgraph of the complete Euclidean graph is a <italic>t</italic>-spanner if for any <italic>u</italic> and <italic>v</italic> in <italic>V</italic>, the length of the shortest path from <italic>u</italic> to <italic>v</italic> in the spanner is at most(More)
Given a geometric <i>t</i>-spanner graph <i>G</i> in E<sup><i>d</i></sup> with <i>n</i> points and <i>m</i> edges, with edge lengths that lie within a polynomial (in <i>n</i>) factor of each other. Then, after <i>O</i>(<i>m</i>+<i>n</i> log <i>n</i>) preprocessing, we present an approximation scheme to answer (1+&#949;)-approximate shortest path queries in(More)