A Faster Isomorphism Test for Graphs of Small Degree

TL;DR

This paper presents an improved algorithm for testing graph isomorphism in graphs with small maximum degree, significantly reducing the time complexity compared to previous methods.

Contribution

The authors develop a faster isomorphism test for graphs of small degree with a new running time of $n^{O((\log d)^{c})}$, improving upon the previous $n^{O(d/ \log d)}$.

Findings

Algorithm runs in time $n^{O((\log d)^{c})}$ for graphs of degree $d$

Significantly faster than previous $n^{O(d/ \log d)}$ algorithm

Applicable to graphs with small maximum degree

Abstract

In a recent breakthrough, Babai (STOC 2016) gave a quasipolynomial time graph isomorphism test. In this work, we give an improved isomorphism test for graphs of small degree: our algorithms runs in time $n^{O((\log d)^{c})}$, where $n$ is the number of vertices of the input graphs, $d$ is the maximum degree of the input graphs, and $c$ is an absolute constant. The best previous isomorphism test for graphs of maximum degree $d$ due to Babai, Kantor and Luks (FOCS 1983) runs in time $n^{O(d/ \log d)}$.