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An iterative rounding 2-approximation algorithm for the element connectivity problem

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3 Author(s)
Fleischer, L. ; Carnegie Mellon Univ., Pittsburgh, PA, USA ; Jain, K. ; Williamson, D.P.

In the survivable network design problem (SNDP), given an undirected graph and values rij for each pair of vertices i and j, we attempt to find a minimum-cost subgraph such that there are rij disjoint paths between vertices i and j. In the edge connected version of this problem (EC-SNDP), these paths must be edge-disjoint. In the vertex connected version of the problem (VC-SNDP), the paths must be vertex disjoint. K. Jain et al. (1999) propose a version of the problem intermediate in difficulty to these two, called the element connectivity problem (ELC-SNDP, or ELC). These variants of SNDP are all known to be NP-hard. The best known approximation algorithm for the EC-SNDP has performance guarantee of 2 (K. Jain, 2001), and iteratively rounds solutions to a linear programming relaxation of the problem. ELC has a primal-dual O (log k) approximation algorithm, where k=maxi,j rij. VC-SNDP is not known to have a non-trivial approximation algorithm; however, recently L. Fleischer (2001) has shown how to extend the technique of K. Jain ( 2001) to give a 2-approximation algorithm in the case that rij∈{0, 1, 2}. She also shows that the same techniques will not work for VC-SNDP for more general values of rij. The authors show that these techniques can be extended to a 2-approximation algorithm for ELC. This gives the first constant approximation algorithm for a general survivable network design problem which allows node failures.

Published in:

Foundations of Computer Science, 2001. Proceedings. 42nd IEEE Symposium on

Date of Conference:

8-11 Oct. 2001