Incremental Maintenance of Maximal Cliques in a Dynamic Graph

TL;DR

This paper introduces change-sensitive algorithms for maintaining all maximal cliques in a dynamic graph, providing theoretical bounds and demonstrating significant practical efficiency improvements over previous methods.

Contribution

It presents the first change-sensitive algorithms for maximal clique maintenance in dynamic graphs, with nearly tight bounds and practical efficiency.

Findings

Algorithms are faster than prior work by 100-1000x.

Theoretical bounds on change magnitude are nearly tight.

Experimental results confirm practical efficiency.

Abstract

We consider the maintenance of the set of all maximal cliques in a dynamic graph that is changing through the addition or deletion of edges. We present nearly tight bounds on the magnitude of change in the set of maximal cliques, as well as the first change-sensitive algorithms for clique maintenance, whose runtime is proportional to the magnitude of the change in the set of maximal cliques. We present experimental results showing these algorithms are efficient in practice and are faster than prior work by two to three orders of magnitude.