A Reduction-based Algorithm for the Clique Interdiction Problem

TL;DR

This paper introduces RECIP, a reduction-based algorithm that effectively simplifies and solves the Clique Interdiction Problem, which is crucial for applications like pandemic control and terrorism prevention.

Contribution

The paper proposes novel reduction rules and a reduction-based algorithm, RECIP, to efficiently solve the challenging bilevel Clique Interdiction Problem.

Findings

RECIP significantly outperforms existing methods on large real-world networks.

The reduction rules effectively simplify the problem, enabling faster solutions.

Experimental results validate the effectiveness of the proposed approach.

Abstract

The Clique Interdiction Problem (CIP) aims to minimize the size of the largest clique in a given graph by removing a given number of vertices. The CIP models a special Stackelberg game and has important applications in fields such as pandemic control and terrorist identification. However, the CIP is a bilevel graph optimization problem, making it very challenging to solve. Recently, data reduction techniques have been successfully applied in many (single-level) graph optimization problems like the vertex cover problem. Motivated by this, we investigate a set of novel reduction rules and design a reduction-based algorithm, RECIP, for practically solving the CIP. RECIP enjoys an effective preprocessing procedure that systematically reduces the input graph, making the problem much easier to solve. Extensive experiments on 124 large real-world networks demonstrate the superior performance of RECIP and validate the effectiveness of the proposed reduction rules.