Deep Analysis on Subgraph Isomorphism

TL;DR

This paper re-implements and compares seven subgraph isomorphism algorithms, analyzing their correctness and performance across various datasets to identify strengths, weaknesses, and potential improvements.

Contribution

It provides a comprehensive, standardized experimental evaluation of leading algorithms, addressing previous inconsistencies and errors in subgraph isomorphism research.

Findings

Different algorithms have distinct strengths and weaknesses.

Optimization ideas can be complementary and lead to better performance.

Some existing algorithms contain errors affecting their application.

Abstract

Subgraph isomorphism is a well-known NP-hard problem which is widely used in many applications, such as social network analysis and knowledge graph query. Its performance is often limited by the inherent hardness. Several insightful works have been done since 2012, mainly optimizing pruning rules and matching orders to accelerate enumerating all isomorphic subgraphs. Nevertheless, their correctness and performance are not well studied. First, different languages are used in implementation with different compilation flags. Second, experiments are not done on the same platform and the same datasets. Third, some ideas of different works are even complementary. Last but not least, there exist errors when applying some algorithms. In this paper, we address these problems by re-implementing seven representative subgraph isomorphism algorithms as well as their improved versions, and conducting comprehensive experiments on various graphs. The results show pros and cons of state-of-the-art solutions and explore new approaches to optimization.