A Constant Factor Approximation for Minimum λ-Edge-Connected k-Subgraph with Metric Costs

Authors:
Mohammadali Safari;Mohammad R. Salavatipour
Affiliations:
Department of Computing Science, University of Alberta, Edmonton, Canada T6G 2E8;Department of Computing Science, University of Alberta, Edmonton, Canada T6G 2E8
Venue:
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Year:
2008

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Abstract

In the (k,λ)-subgraph problem, we aregiven an undirected graph G= (V,E) withedge costs and two parameters kand λandthe goal is to find a minimum cost λ-edge-connectedsubgraph of Gwith at least knodes. Thisgeneralizes several classical problems, such as the minimum costk-Spanning Tree problem or k-MST (which is a(k,1)-subgraph), and minimum costλ-edge-connected spanning subgraph (which is a(|V(G)|,λ)-subgraph). The onlypreviously known results on this problem [12,5] show that the(k,2)-subgraph problem has an O(log2n)-approximation (even for 2-node-connectivity) and thatthe (k,¿)-subgraph problem in general isalmost as hard as the densest k-subgraph problem [12]. Inthis paper we show that if the edge costs are metric (i.e. satisfytriangle inequality), like in the k-MST problem, thenthere is an O(1)-approximation algorithm for(k,λ)-subgraph problem. This essentiallygeneralizes the k-MST constant factor approximability tohigher connectivity.