# New Subgraph Isomorphism Algorithms: Vertex versus Path-at-a-time Matching

## TL;DR

This paper introduces two novel algorithms, Fast-ON and Fast-P, for subgraph isomorphism that significantly outperform existing methods by applying vertex- and path-at-a-time matching strategies with effective heuristics.

## Contribution

The paper presents two new algorithms for subgraph isomorphism, utilizing vertex- and path-at-a-time matching approaches with heuristics, achieving substantial speed improvements.

## Key findings

- Fast-ON and Fast-P outperform existing algorithms by 1-4 orders of magnitude.
- Both algorithms are effective for dense and sparse graphs.
- Use of heuristics significantly reduces search space.

## Abstract

Graphs are widely used to model complicated data semantics in many application domains. In this paper, two novel and efficient algorithms Fast-ON and Fast-P are proposed for solving the subgraph isomorphism problem. The two algorithms are based on Ullman algorithm [Ullmann 1976], apply vertex-at-a-time matching manner and path-at-a-time matching manner respectively, and use effective heuristics to cut the search space. Comparing to the well-known algorithms, Fast-ON and Fast-P achieve up to 1-4 orders of magnitude speed-up for both dense and sparse graph data.