Mining Patterns in Networks using Homomorphism

TL;DR

This paper introduces a polynomial-time algorithm for mining tree patterns in networks using subgraph homomorphism, addressing computational complexity issues of traditional isomorphism-based methods.

Contribution

It proposes a novel approach leveraging homomorphism for pattern mining, formalizes related problems, and integrates solutions into an efficient algorithm.

Findings

Homomorphism-based mining is polynomial-time feasible.

Two key problems of homomorphism are identified and addressed.

The approach enables efficient mining of large network patterns.

Abstract

In recent years many algorithms have been developed for finding patterns in graphs and networks. A disadvantage of these algorithms is that they use subgraph isomorphism to determine the support of a graph pattern; subgraph isomorphism is a well-known NP complete problem. In this paper, we propose an alternative approach which mines tree patterns in networks by using subgraph homomorphism. The advantage of homomorphism is that it can be computed in polynomial time, which allows us to develop an algorithm that mines tree patterns in arbitrary graphs in incremental polynomial time. Homomorphism however entails two problems not found when using isomorphism: (1) two patterns of different size can be equivalent; (2) patterns of unbounded size can be frequent. In this paper we formalize these problems and study solutions that easily fit within our algorithm.