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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</italic>=(<italic>V,E</italic>) be an <italic>n</italic>-vertex connected graph with positive edge weights. A subgraph <italic>G</italic>′ = (<italic>V,E</italic>′) is a <italic>t-spanner</italic> of <italic>G</italic> if for all <italic>u, v ε V</italic>,the weighted distance between <italic>u</italic> and <italic>v</italic>… (More)

Let <italic>G=(V,E)</italic> be a <italic>n</italic>-vertex connected graph with positive edge weights. A subgraph <italic>G</italic>′ is a <italic>t</italic>-spanner if for all <italic>u,v</italic><inline-equation> <f> ∈</f> </inline-equation><italic>V</italic>, the distance between <italic>u</italic> and <italic>v</italic> in the subgraph is… (More)

Given a set V of n points in R d and a real constant t > 1, we present the first O(n log n)-time algorithm to compute a geometric t-spanner on V. A geometric t-spanner on V is a connected graph G = (V, E) with edge weights equal to the Euclidean distances between the endpoints, and with the property that, for all u, v ∈ V , the distance between u and v in G… (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+ε)-approximate shortest path queries in… (More)

Let S be a set of n points in lKd, and k m integer such that 1 5 k 5 n-2. Algorithms are given that construct fault-tolerant spanners for S. If in such a spanner at most k edges or vertices are removed, then each pair of points in the remaining graph is still connected by a short path. Our results include (i) an algorithm with running time O(n logdB1 n + kn… (More)