A Reduction-based Algorithm for the Clique Interdiction Problem

2025-05-17

AI Summary

This paper studies the Clique Interdiction Problem (CIP): deleting at most *k* vertices from a given graph to minimize the size of the largest clique in the residual graph—a problem with critical applications in epidemic containment and counter-terrorism network analysis. To overcome the poor scalability of existing methods on large-scale graphs, we propose RECIP, the first framework integrating systematic data reduction with bilevel optimization. Its core contributions are: (1) multiple graph-structure-driven reduction rules specifically designed for CIP; (2) a preprocessing-guided heuristic search strategy; and (3) a vertex-importance-aware pruning mechanism under bilevel constraints. Experiments on 124 large real-world networks demonstrate that RECIP achieves, on average, a two-order-of-magnitude speedup in solution time and reduces instance sizes by 60%–95% after reduction—substantially outperforming state-of-the-art approaches.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

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.

Problem

• Minimizing largest clique size by removing vertices
• Modeling Stackelberg game for pandemic and security applications
• Solving bilevel graph optimization with reduction-based algorithm

Innovation

• Novel reduction rules for Clique Interdiction Problem
• RECIP algorithm with effective preprocessing procedure
• Systematically reduces input graph for easier solving