# Shared Memory Parallel Subgraph Enumeration

## TL;DR

This paper introduces a shared-memory parallel algorithm for subgraph enumeration, significantly speeding up the process on real-world biochemical data by leveraging work stealing and improved pruning techniques.

## Contribution

It presents a novel parallelization of existing subgraph enumeration algorithms using work stealing and enhances the algorithms with better pruning, achieving faster empirical performance.

## Key findings

- Significant speedup on biochemical datasets
- Effective parallelization with work stealing
- Improved pruning reduces search space

## Abstract

The subgraph enumeration problem asks us to find all subgraphs of a target graph that are isomorphic to a given pattern graph. Determining whether even one such isomorphic subgraph exists is NP-complete---and therefore finding all such subgraphs (if they exist) is a time-consuming task. Subgraph enumeration has applications in many fields, including biochemistry and social networks, and interestingly the fastest algorithms for solving the problem for biochemical inputs are sequential. Since they depend on depth-first tree traversal, an efficient parallelization is far from trivial. Nevertheless, since important applications produce data sets with increasing difficulty, parallelism seems beneficial. We thus present here a shared-memory parallelization of the state-of-the-art subgraph enumeration algorithms RI and RI-DS (a variant of RI for dense graphs) by Bonnici et al. [BMC Bioinformatics, 2013]. Our strategy uses work stealing and our implementation demonstrates a significant speedup on real-world biochemical data---despite a highly irregular data access pattern. We also improve RI-DS by pruning the search space better; this further improves the empirical running times compared to the already highly tuned RI-DS.