Pruning 2-connected graphs

Chandra Chekuri, Nitish Korula

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Given an edge-weighted undirected graph G with a specified set of terminals, let the density of any subgraph be the ratio of its weight/cost to the number of terminals it contains. If G is 2-connected, does it contain smaller 2-connected subgraphs of density comparable to that of G? We answer this question in the affirmative by giving an algorithm to prune G and find such subgraphs of any desired size, at the cost of only a logarithmic increase in density (plus a small additive factor). We apply the pruning techniques to give algorithms for two NP-Hard problems on finding large 2-vertex-connected subgraphs of low cost; no previous approximation algorithm was known for either problem. In the k-2VC problem, we are given an undirected graph G with edge costs and an integer k; the goal is to find a minimum-cost 2-vertex-connected subgraph of G containing at least k vertices. In the Budget-2VC problem, we are given the graph G with edge costs, and a budget B; the goal is to find a 2-vertex-connected subgraph H of G with total edge cost at most B that maximizes the number of vertices in H. We describe an O (log n log k) approximation for the k-2VC problem, and a bicriteria approximation for the Budget-2VC problem that gives an O(1/ε log2n) approximation, while violating the budget by a factor of at most 3 + ε.

Original languageEnglish (US)
Title of host publicationFSTTCS 2008 - IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
Pages119-130
Number of pages12
StatePublished - 2008
Event28th International Conference on the Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2008 - Bangalore, India
Duration: Dec 9 2008Dec 11 2008

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume2
ISSN (Print)1868-8969

Other

Other28th International Conference on the Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2008
Country/TerritoryIndia
CityBangalore
Period12/9/0812/11/08

Keywords

  • 2-Connected Graphs
  • Approximation
  • Density
  • K-MST

ASJC Scopus subject areas

  • Software

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