Engineering a Preprocessor for Symmetry Detection

TL;DR

This paper introduces a preprocessor for symmetry detection that reduces large, sparse substructures in graphs, significantly improving the performance of existing solvers on practical instances with minimal overhead.

Contribution

The paper presents a novel preprocessor that enhances symmetry detection by shrinking large sparse substructures, leading to more efficient and universally competitive algorithms.

Findings

Significant performance improvements on practical instances

Negligible overhead introduced by the preprocessor

Outperforms previous state-of-the-art methods on benchmark graphs

Abstract

State-of-the-art solvers for symmetry detection in combinatorial objects are becoming increasingly sophisticated software libraries. Most of the solvers were initially designed with inputs from combinatorics in mind (nauty, bliss, Traces, dejavu). They excel at dealing with a complicated core of the input. Others focus on practical instances that exhibit sparsity. They excel at dealing with comparatively easy but extremely large substructures of the input (saucy). In practice, these differences manifest in significantly diverging performances on different types of graph classes. We engineer a preprocessor for symmetry detection. The result is a tool designed to shrink sparse, large substructures of the input graph. On most of the practical instances, the overall running time improves significantly for many of the state-of-the-art solvers. At the same time, our benchmarks show that the additional overhead is negligible. Overall we obtain single algorithms with competitive performance across all benchmark graphs. As such the preprocessor bridges the disparity between solvers that focus on combinatorial graphs and large practical graphs. In fact, on most of the practical instances the combined setup significantly outperforms previous state-of-the-art.