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The Maximum Flow Network Interdiction Problem: Valid Inequalities, Integrality Gaps, and Approximability

Douglas Altner (altner***at***usna.edu)
Ozlem Ergun (oergun***at***isye.gatech.edu)
Nelson Uhan (nuhan***at***purdue.edu)

Abstract: We study the Maximum Flow Network Interdiction Problem (MFNIP). We present two classes of polynomially separable valid inequalities for Cardinality MFNIP. We also prove the integrality gap of the LP relaxation of Wood's (1993) integer program is not bounded by a constant factor, even when the LP relaxation is strengthened by our valid inequalities. Finally, we provide an approximation-factor-preserving reduction from the simpler R-Interdiction Covering Problem to MFNIP.

Keywords: Maximum Flow, Network Interdiction, Integrality Gap, Hardness of Approximation

Category 1: Network Optimization

Citation: Technical Report, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205 USA, March, 2008.

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Entry Submitted: 01/11/2008
Entry Accepted: 01/11/2008
Entry Last Modified: 12/09/2009

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