Fast Algorithms for the Maximum Clique Problem on Massive Graphs with Applications to Overlapping Community Detection

TL;DR

This paper introduces a new exact algorithm with advanced pruning techniques for efficiently finding maximum cliques in large, sparse graphs, significantly outperforming existing methods and enabling applications like overlapping community detection.

Contribution

The paper presents a novel exact algorithm and a heuristic for the maximum clique problem tailored for massive graphs, with demonstrated superior speed and applicability.

Findings

The exact algorithm is several orders of magnitude faster on large graphs.

The heuristic provides near-optimal solutions much faster than the exact method.

Applications include improved overlapping community detection in networks.

Abstract

The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, information retrieval and many other areas related to the World Wide Web. There exist several algorithms for the problem with acceptable runtimes for certain classes of graphs, but many of them are infeasible for massive graphs. We present a new exact algorithm that employs novel pruning techniques and is able to find maximum cliques in very large, sparse graphs quickly. Extensive experiments on different kinds of synthetic and real-world graphs show that our new algorithm can be orders of magnitude faster than existing algorithms. We also present a heuristic that runs orders of magnitude faster than the exact algorithm while providing optimal or near-optimal solutions. We illustrate a simple application of the algorithms in developing methods for detection of overlapping communities in networks.