TY - JOUR

T1 - Hardness of approximation for vertex-connectivity network design problems

AU - Kortsarz, Guy

AU - Krauthgamer, Robert

AU - Lee, James R.

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2004

Y1 - 2004

N2 - In the survivable network design problem (SNDP), the goal is to find a minimum-cost spanning subgraph satisfying certain connectivity requirements. We study the vertex-connectivity variant of SNDP in which the input specifies, for each pair of vertices, a required number of vertex-disjoint paths connecting them. We give the first strong lower bound on the approximability of SNDP, showing that the problem admits no efficient 2 log1-εn ratio approximation for any fixed ε > 0, unless NP ⊆ DTIME(n polylog(n)). We show hardness of approximation results for some important special cases of SNDP, and we exhibit the first lower bound on the approximability of the related classical NP-hard problem of augmenting the connectivity of a graph using edges from a given set.

AB - In the survivable network design problem (SNDP), the goal is to find a minimum-cost spanning subgraph satisfying certain connectivity requirements. We study the vertex-connectivity variant of SNDP in which the input specifies, for each pair of vertices, a required number of vertex-disjoint paths connecting them. We give the first strong lower bound on the approximability of SNDP, showing that the problem admits no efficient 2 log1-εn ratio approximation for any fixed ε > 0, unless NP ⊆ DTIME(n polylog(n)). We show hardness of approximation results for some important special cases of SNDP, and we exhibit the first lower bound on the approximability of the related classical NP-hard problem of augmenting the connectivity of a graph using edges from a given set.

KW - Approximation algorithms

KW - Connectivity augmentation

KW - Hardness of approximation

KW - Survivable network design

KW - Vertex connectivity

UR - http://www.scopus.com/inward/record.url?scp=3142717683&partnerID=8YFLogxK

U2 - 10.1137/S0097539702416736

DO - 10.1137/S0097539702416736

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AN - SCOPUS:3142717683

SN - 0097-5397

VL - 33

SP - 704

EP - 720

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

IS - 3

ER -