A Swap-Based Heuristic Algorithm for the Maximum <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Plex Problem

Abstract

The maximum $k$ -plex problem is intended to relax the clique definition with maximum cardinality. It helps people understand the structures of networks by considering them a problem of graph clustering; therefore, it is a useful model for social network analysis. In this paper, we propose a swap-based heuristic algorithm for the maximum $k$ -plex problem. Starting with a randomly selected solution, we use three types of swap operators to enlarge our current solution in different situations. The results of experiments conducted on various graphs from two benchmarks demonstrated that our proposed algorithm achieved desirable performance on specific graphs compared with other algorithms.

Keywords

• Clique relaxation
• heuristic algorithms
• graph algorithms
• social networks
• NP-complete