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Connectivity Upgrade Models for Survivable Network Design

McCombs School of Business, The University of Texas at Austin, Austin, Texas 78712
Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
School of Business Administration, University of Miami, Coral Gables, Florida 33124
anantb{at}mail.utexas.edu
pmirchan{at}katz.pitt.edu
hari{at}miami.edu

Disruptions in infrastructure networks to transport material, energy, and information can have serious economic, and even catastrophic, consequences. Since these networks require enormous investments, network service providers emphasize both survivability and cost effectiveness in their topological design decisions. This paper addresses the survivable network design problem, a core model incorporating the cost and redundancy trade-offs facing network planners. Using a novel connectivity upgrade strategy, we develop several families of inequalities to strengthen a multicommodity flow-based formulation for the problem, and show that some of these inequalities are facet defining. By increasing the linear programming lower bound, the valid inequalities not only lead to better performance guarantees for heuristic solutions, but also accelerate exact and approximate solution methods. We also consider a heuristic strategy that sequentially rounds the fractional values, starting with the linear programming solution to our strong model. Extensive computational tests confirm that the valid inequalities, added via a cutting plane algorithm, and the heuristic procedure are very effective, and their performance is robust to changes in the network dimensions and connectivity structure. Our solution approach generates tight lower and upper bounds with average gaps that are less than 1.2% for various problem sizes and connectivity requirements.

Subject classifications: integer programming; cutting plane/facet; networks/graphs; applications; theory.
History: Received July 2005; revision received November 2007; accepted November 2007.