Finding Maximum k-Cliques Faster using Lazy Global Domination

TL;DR

This paper introduces a lazy global domination rule to accelerate maximum k-clique algorithms, demonstrating practical improvements through experiments on various real-world, benchmark, and random graphs.

Contribution

The paper adapts a maximum clique algorithm for maximum k-cliques and introduces a lazy global domination rule that significantly reduces search space in practice.

Findings

Lazy global domination rule reduces search space

Algorithm performs well on real-world and benchmark graphs

Effective on random graphs as well

Abstract

A clique in a graph is a set of vertices, each of which is adjacent to every other vertex in this set. A k-clique relaxes this requirement, requiring vertices to be within a distance k of each other, rather than directly adjacent. In theory, a maximum clique algorithm can easily be adapted to solve the maximum k-clique problem. We use a state of the art maximum clique algorithm to show that this is feasible in practice, and introduce a lazy global domination rule which sometimes vastly reduces the search space. We include experimental results for a range of real-world and benchmark graphs, and a detailed look at random graphs.