An Important Corollary for the Fast Solution of Dynamic Maximal Clique Enumeration Problems

TL;DR

This paper presents a modified algorithm for dynamic maximal clique enumeration that significantly improves efficiency, achieving linear time complexity for edge insertions compared to previous quadratic-time algorithms.

Contribution

It introduces a new algorithm that updates maximal clique enumeration in linear time after an edge insertion, enhancing performance over existing methods.

Findings

Linear time update for maximal clique enumeration after edge insertion

Significant reduction in computational complexity from quadratic to linear

Applicable to dynamic graph analysis scenarios

Abstract

In this paper we modify an algorithm for updating a maximal clique enumeration after an edge insertion to provide an algorithm that runs in linear time with respect to the number of cliques containing one of the edge's endpoints, whereas existing algorithms take quadratic time.