The complexity of finding most vital arcs and nodes
The complexity of finding most vital arcs and nodes
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Introduction to Algorithms
Stochastic Network Interdiction
Operations Research
Minimizing a stochastic maximum-reliability path
Networks - Games, Interdiction, and Human Interaction Problems on Networks
Optimal Interdiction of Unreactive Markovian Evaders
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Deterministic network interdiction
Mathematical and Computer Modelling: An International Journal
Packing interdiction and partial covering problems
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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In the matrix interdiction problem, a real-valued matrix and an integer k is given. The objective is to remove a set of k matrix columns that minimizes in the residual matrix the sum of the row values, where the value of a row is defined to be the largest entry in that row. This combinatorial problem is closely related to bipartite network interdiction problem that can be applied to minimize the probability that an adversary can successfully smuggle weapons. After introducing the matrix interdiction problem, we study the computational complexity of this problem. We show that the matrix interdiction problem is NP-hard and that there exists a constant γ such that it is even NP-hard to approximate this problem within an nγ additive factor. We also present an algorithm for this problem that achieves an (n−k) multiplicative approximation ratio.