Two extended formulations for cardinality maximum flow network interdiction problem

Abstract

We consider the maximum flow network interdiction problem in its cardinality case. There is an integer programming model for this problem by Wood (Math Comput Model 17 (1993), 1–18). Two types of valid inequalities have also been proposed (Altner et al., Oper Res Lett 38 (2010), 33–38 and Wood, Math Comput Model 17 (1993), 1–18) to strengthen the LP relaxation of the integer model. However, due to their combinatorial nature, the number of these inequalities are exponential. Here, we present an equivalent reformulation (extended formulation) for this problem which has a polynomial number of constraints. We also introduce new valid inequalities, and show that the corresponding reformulation of the LP relaxation of the integer model augmented with these inequalities, significantly decreases the integrality gap for a class of network interdiction problems with proven large integrality gaps. Numerical results for some benchmark as well as randomly generated instances are also reported. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 69(4), 367–377 2017

An extended formulation for the 1‐wheel inequalities of the stable set polytope

“…Quadratic size extended formulations for independence polytopes of graphic and cographic matroids by application of this method are presented by Kaibel et al . Afshari Rad and Kakhki construct an extended formulation for the cardinality form of the maximum flow interdiction problem by using this technique.…”