Recent Advances on the Graph Isomorphism Problem

TL;DR

This paper reviews recent progress on the graph isomorphism problem, highlighting Babai's quasi-polynomial algorithm and developments involving the Weisfeiler-Leman method, with implications for parameterized complexity.

Contribution

It provides a comprehensive overview of recent algorithmic advances and theoretical insights in solving the graph isomorphism problem.

Findings

Babai's quasi-polynomial time isomorphism test

Development of algorithms with $n^{ ext{polylog}(k)}$ complexity

Insights into the Weisfeiler-Leman algorithm

Abstract

We give an overview of recent advances on the graph isomorphism problem. Our main focus will be on Babai's quasi-polynomial time isomorphism test and subsequent developments that led to the design of isomorphism algorithms with a quasi-polynomial parameterized running time of the from $n^{\text{polylog}(k)}$, where $k$ is a graph parameter such as the maximum degree. A second focus will be the combinatorial Weisfeiler-Leman algorithm.