A branch-and-cut algorithm for the Edge Interdiction Clique Problem

Given a graph G and an interdiction budget k∈N, the Edge Interdiction Clique Problem (EICP) asks to find subset of at most k edges remove from so that size maximum clique, in interdicted graph, is minimized. The EICP belongs family problems with aim reducing clique number graph. optimal solutions, called policies, determine vital which are crucial for preserving its number. We propose new set-covering-based Integer Linear Programming (ILP) formulation exponential constraints, clique-covering inequalities. design branch-and-cut algorithm enhanced by tailored separation procedure effective heuristic initialization phase. Thanks exact algorithm, we manage solve several sets instances literature. Extensive tests show greatly outperforms state-of-the-art approaches EICP.