Design of Survivable Networks Using Three-and Four-Partition Facets

Authors:
Yogesh Agarwal
Affiliations:
Indian Institute of Management, Prabandh Nagar, Lucknow 226 013, India
Venue:
Operations Research
Year:
2013

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Abstract

This paper considers the problem of designing a multicommodity network with single facility type subject to the requirement that under failure of any single edge, the network should permit a feasible flow of all traffic. We study the polyhedral structure of the problem by considering the multigraph obtained by shrinking the nodes, but not the edges, in a k-partition of the original graph. A key theorem is proved according to which a facet of the k-node problem defined on the multigraph resulting from a k-partition is also facet defining for the larger problem under a mild condition. After reviewing the prior work on two-partition inequalities, we develop two classes of three-partition inequalities and a large number of inequality classes based on four-partitions. Proofs of facet-defining status for some of these are provided, while the rest are stated without proof. Computational results show that the addition of three-and four-partition inequalities results in substantial increase in the bound values compared to those possible with two-partition inequalities alone. Problems of 35 nodes and 80 edges with fully dense traffic matrices have been solved optimally within a few minutes of computer time.