Search Space Contraction in Canonical Labeling of Graphs

TL;DR

This paper introduces a new algorithm and tool called "Traces" that significantly reduces the search space in canonical graph labeling, enabling the analysis of complex graphs that are challenging for existing methods.

Contribution

The paper presents a novel search space contraction technique and the Traces tool, improving the efficiency of canonical labeling algorithms compared to prior approaches.

Findings

Huge reduction in search space size

Enables canonical labeling of previously intractable graphs

Outperforms existing tools like nauty in experiments

Abstract

The individualization-refinement paradigm for computing a canonical labeling and the automorphism group of a graph is investigated. A new algorithmic design aimed at reducing the size of the associated search space is introduced, and a new tool, named "Traces", is presented, together with experimental results and comparisons with existing software, such as McKay's "nauty". It is shown that the approach presented here leads to a huge reduction in the search space, thereby making computation feasible for several classes of graphs which are hard for all the main canonical labeling tools in the literature.