The Maximum Flow Network Interdiction Problem: Valid inequalities, integrality gaps, and approximability

Authors:
Douglas S. Altner;ÖZlem Ergun;Nelson A. Uhan
Affiliations:
Department of Mathematics, United States Naval Academy, Annapolis, MD, United States;H.Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, United States;School of Industrial Engineering, Purdue University, West Lafayette, IN, United States
Venue:
Operations Research Letters
Year:
2010

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Abstract

We present two classes of polynomially separable valid inequalities for the Maximum Flow Network Interdiction Problem. We prove that the integrality gap of the standard integer program is not bounded by a constant, even when strengthened by our valid inequalities. Finally, we provide an approximation-factor-preserving reduction from a simpler interdiction problem.