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A constant factor approximation for minimum λ-edge-connected k-subgraph with metric costs

Safari, M ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1137/080729918
  3. Abstract:
  4. In the (k, λ)-subgraph problem, we are given an undirected graph G = (V,E) with edge costs and two positive integers k and λ, and the goal is to find a minimum cost simple λ-edge-connected subgraph of G with at least k nodes. This generalizes several classical problems, such as the minimum cost k-spanning tree problem, or k-MST (which is a (k, 1)-subgraph), and the minimum cost λ-edge-connected spanning subgraph (which is a (|V(G)|, λ)-subgraph). The only previously known results on this problem [L. C. Lau, J. S. Naor, M. R. Salavatipour, and M. Singh, SIAM J. Comput., 39 (2009), pp. 1062-1087], [C. Chekuri and N. Korula, in Proceedings of the IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS), Bangalore, India, LIPIcs 2, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 2008, pp. 119-130] show that the (k, 2)-subgraph problem has an O(log2 n)-approximation (even for 2-node-connectivity) and that the (k, λ)-subgraph problem in general is almost as hard as the densest k-subgraph problem.In this paper we show that if the edge costs are metric(i.e., satisfy the triangle inequality), like in the k-MST problem, then there is an O(1)-approximation algorithm for the (k, λ)-subgraph problem. This essentially generalizes the k-MST constant factor approximability to higher connectivity
  5. Keywords:
  6. λ-edge-connectivity ; Approximation algorithm ; Bangalore , India ; Classical problems ; Constant factor approximation ; Constant-factor approximability ; Edge connectivity ; Germany ; k-subgraph ; Metric cost ; Minimum cost ; Positive integers ; Software technology ; Subgraph problems ; Subgraphs ; Theoretical computer science ; Triangle inequality ; Undirected graph ; Approximation algorithms ; Graph theory ; Software engineering ; Costs
  7. Source: SIAM Journal on Discrete Mathematics ; Volume 25, Issue 3 , 2011 , Pages 1089-1102 ; 08954801 (ISSN)
  8. URL: http://epubs.siam.org/doi/abs/10.1137/080729918