TY - JOUR

T1 - Approximating survivable networks with β-metric costs

AU - David, Johnny

AU - Nutov, Zeev

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

PY - 2011/6

Y1 - 2011/6

N2 - The Survivable Network Design (SND) problem seeks a minimum-cost subgraph that satisfies prescribed node-connectivity requirements. We consider SND on both directed and undirected complete graphs with β-metric costs when c(xz)≤β[c(xy)+c(yz)] for all x,y,z ∈ V, which varies from uniform costs (β=1/2) to metric costs (β=1). For the k-Connected Subgraph (k-CS) problem our ratios are: 1+2βk(1-β)-12k-1 for undirected graphs, and 1+4β3k(1-3β2)-12k-1 for directed graphs and 12≤β<13. For undirected graphs this improves the ratios β1-β of Böckenhauer et al. (2008) [3] and 2+βkn of Kortsarz and Nutov (2003) [11] for all k≥4 and 12+3k-22(4k2-7k+2)≤β≤k2(k+1)2-2. We also show that SND admits the ratios 2β1-β for undirected graphs, and 4β31-3β2 for directed graphs with 1/2≤β<1/3. For two important particular cases of SND, so-called Subset k-CS and Rooted SND, our ratios are 2β31-3β2 for directed graphs and β1-β for subset k-CS on undirected graphs.

AB - The Survivable Network Design (SND) problem seeks a minimum-cost subgraph that satisfies prescribed node-connectivity requirements. We consider SND on both directed and undirected complete graphs with β-metric costs when c(xz)≤β[c(xy)+c(yz)] for all x,y,z ∈ V, which varies from uniform costs (β=1/2) to metric costs (β=1). For the k-Connected Subgraph (k-CS) problem our ratios are: 1+2βk(1-β)-12k-1 for undirected graphs, and 1+4β3k(1-3β2)-12k-1 for directed graphs and 12≤β<13. For undirected graphs this improves the ratios β1-β of Böckenhauer et al. (2008) [3] and 2+βkn of Kortsarz and Nutov (2003) [11] for all k≥4 and 12+3k-22(4k2-7k+2)≤β≤k2(k+1)2-2. We also show that SND admits the ratios 2β1-β for undirected graphs, and 4β31-3β2 for directed graphs with 1/2≤β<1/3. For two important particular cases of SND, so-called Subset k-CS and Rooted SND, our ratios are 2β31-3β2 for directed graphs and β1-β for subset k-CS on undirected graphs.

KW - Approximation algorithms

KW - Graph connectivity

KW - Metric costs

KW - Network design

UR - http://www.scopus.com/inward/record.url?scp=79952359726&partnerID=8YFLogxK

U2 - 10.1016/j.jda.2010.11.002

DO - 10.1016/j.jda.2010.11.002

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:79952359726

SN - 1570-8667

VL - 9

SP - 170

EP - 175

JO - Journal of Discrete Algorithms

JF - Journal of Discrete Algorithms

IS - 2

ER -