Survivable network design: the capacitated minimum spanning network problem

Authors:
Raja Jothi;Balaji Raghavachari
Affiliations:
Department of Computer Science, University of Texas at Dallas, Richardson, TX;Department of Computer Science, University of Texas at Dallas, Richardson, TX
Venue:
Information Processing Letters
Year:
2004

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Abstract

We are given an undirected graph G = (V,E) with positive weights on its vertices representing demands, and non-negative costs on its edges. Also given are a capacity constraint k, and root vertex r ∈ V. In this paper, we consider the capacitated minimum spanning network (CMSN) problem, which asks for a minimum cost spanning network such that the removal of r and its incident edges breaks the network into a number of components (groups), each of which is 2-edge-connected with a total weight of at most k. We show that the CMSN problem is NP-hard, and present a 4-approximation algorithm for graphs satisfying triangle inequality. We also show how to obtain similar approximation results for a related 2-vertex-connected CMSN problem.