TY - GEN

T1 - Approximating survivable networks with minimum number of Steiner points

AU - Kamma, Lior

AU - Nutov, Zeev

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011

Y1 - 2011

N2 - Given a graph H = (U,E) and connectivity requirements r = {r(u,v): u,v ∈ R ⊆ U}, we say that H satisfies r if it contains r(u,v) pairwise internally-disjoint uv-paths for all u,v ∈ R. We consider the Survivable Network with Minimum Number of Steiner Points (SN-MSP) problem: given a finite set V of points in a normed space (M, ||·||), and connectivity requirements, find a minimum size set S ⊂ M - V of additional points, such that the unit disc graph induced by V ∪ S satisfies the requirements. In the (node-connectivity version of the) Survivable Network Design Problem (SNDP) we are given a graph G = (V,E) with edge costs and connectivity requirements, and seek a min-cost subgraph H of G that satisfies the requirements. Let k = maxu,v∈V r(u, v) denote the maximum connectivity requirement. We will show a natural transformation of an SN-MSP instance (V,r) into an SNDP instance (G = (V,E),c,r), such that an α-approximation for the SNDP instance implies an α·O(k2)-approximation algorithm for the SN-MSP instance. In particular, for the most interesting case of uniform requirement r(u,v) = k for all u,v ∈ V, we obtain for SN-MSP the ratio O(k2 ln k), which solves an open problem from [3].

AB - Given a graph H = (U,E) and connectivity requirements r = {r(u,v): u,v ∈ R ⊆ U}, we say that H satisfies r if it contains r(u,v) pairwise internally-disjoint uv-paths for all u,v ∈ R. We consider the Survivable Network with Minimum Number of Steiner Points (SN-MSP) problem: given a finite set V of points in a normed space (M, ||·||), and connectivity requirements, find a minimum size set S ⊂ M - V of additional points, such that the unit disc graph induced by V ∪ S satisfies the requirements. In the (node-connectivity version of the) Survivable Network Design Problem (SNDP) we are given a graph G = (V,E) with edge costs and connectivity requirements, and seek a min-cost subgraph H of G that satisfies the requirements. Let k = maxu,v∈V r(u, v) denote the maximum connectivity requirement. We will show a natural transformation of an SN-MSP instance (V,r) into an SNDP instance (G = (V,E),c,r), such that an α-approximation for the SNDP instance implies an α·O(k2)-approximation algorithm for the SN-MSP instance. In particular, for the most interesting case of uniform requirement r(u,v) = k for all u,v ∈ V, we obtain for SN-MSP the ratio O(k2 ln k), which solves an open problem from [3].

KW - Approximation algorithms

KW - Node-connectivity

KW - Sensor networks

KW - Unit-disc graphs

UR - http://www.scopus.com/inward/record.url?scp=79551574228&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-18318-8_14

DO - 10.1007/978-3-642-18318-8_14

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AN - SCOPUS:79551574228

SN - 9783642183171

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 154

EP - 165

BT - Approximation and Online Algorithms - 8th International Workshop, WAOA 2010, Revised Papers

T2 - 8th International Workshop on Approximation and Online Algorithms, WAOA 2010

Y2 - 9 September 2010 through 10 September 2010

ER -