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- W1552552578 abstract "In an ideal point-to-point network, any node would simply choose a path of minimum latency to send packets to any other node; however, the distributed nature and the increasing size of modern communication networks may render such a solution infeasible, as it requires each node to store global information concerning the network. Thus it may be desirable to endow only a small subset of the nodes with global routing capabilites, which gives rise to the following graph-theoretic problem.Given an undirected graph G = (V,E), a metric l on the edges, and an integer k, a k-center is a set π ⊆ V of size k and an assignment πv that maps each node to a unique element in Π. We let dπ (u, v) denote the length of the shortest path from utov passing through πu and πv and let d l(u,v) be the length of the shortest u,v-path in G. We then refer to d π(u,v)/d l(u,v) as the stretch of the pair (u,v). We let the stretch of a k-center solution Π be the maximum stretch of any pair of nodes u, v ∈ V. The minimum edge-dilation k-center problem is that of finding a k-center of minimum stretch.We obtain combinatorial approximation algorithms with constant factor performance guarantees for this problem and variants in which the centers are capacitated or nodes may be assigned to more than one center. We also show that there can be no 5/4 - ε approximation for any ε > 0 unless ( mathcal{P} = mathcal{N}mathcal{P} ) ." @default.
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- W1552552578 date "2002-01-01" @default.
- W1552552578 modified "2023-09-27" @default.
- W1552552578 title "Approximation Algorithms for Edge-Dilation k-Center Problems" @default.
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- W1552552578 doi "https://doi.org/10.1007/3-540-45471-3_22" @default.
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