A Generic Framework for Engineering Graph Canonization Algorithms

TL;DR

This paper introduces a flexible software framework for graph canonization algorithms, enabling detailed comparison and analysis of heuristic choices, leading to improved performance on various graph classes.

Contribution

A novel, modular framework that allows independent implementation and testing of heuristics in graph canonization algorithms, facilitating performance analysis and development.

Findings

Framework supports diverse heuristics and detailed data extraction.

Performance analysis reveals the impact of specific heuristics.

Outperforms existing tools on several benchmark graph collections.

Abstract

The state-of-the-art tools for practical graph canonization are all based on the individualization-refinement paradigm, and their difference is primarily in the choice of heuristics they include and in the actual tool implementation. It is thus not possible to make a direct comparison of how individual algorithmic ideas affect the performance on different graph classes. We present an algorithmic software framework that facilitates implementation of heuristics as independent extensions to a common core algorithm. It therefore becomes easy to perform a detailed comparison of the performance and behaviour of different algorithmic ideas. Implementations are provided of a range of algorithms for tree traversal, target cell selection, and node invariant, including choices from the literature and new variations. The framework readily supports extraction and visualization of detailed data from separate algorithm executions for subsequent analysis and development of new heuristics. Using collections of different graph classes we investigate the effect of varying the selections of heuristics, often revealing exactly which individual algorithmic choice is responsible for particularly good or bad performance. On several benchmark collections, including a newly proposed class of difficult instances, we additionally find that our implementation performs better than the current state-of-the-art tools.