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

Given a graph G and an interdiction budget k E N , the Edge Interdiction Clique Problem (EICP) asks to find a subset of at most k edges to remove from G so that the size of the maximum clique, in the interdicted graph, is minimized. The EICP belongs to the family of interdiction problems with the aim of reducing the clique number of the graph. The EICP optimal solutions, called optimal interdiction policies, determine the subset of most vital edges of a graph which are crucial for preserving its clique number. We propose a new set-covering-based Integer Linear Programming (ILP) formulation for the EICP with an exponential number of constraints, called the clique-covering inequalities . We design a new branch-and-cut algorithm which is enhanced by a tailored separation procedure and by an effective heuristic initialization phase. Thanks to the new exact algorithm, we manage to solve the EICP in several sets of instances from the literature. Extensive tests show that the new exact algorithm greatly outperforms the state-of-the-art approaches for the EICP. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

The Edge Interdiction Clique Problem aims to minimize the size of the maximum clique in a graph by removing a subset of at most k edges. A new ILP formulation and branch-and-cut algorithm have been proposed to address this problem, which has shown significant improvement over existing approaches through extensive testing.