The probabilistic Weisfeiler-Leman algorithm

TL;DR

This paper introduces a probabilistic, Monte Carlo version of the Weisfeiler-Leman algorithm for graph analysis, offering a faster computational approach with complexity tied to matrix multiplication efficiency.

Contribution

It presents a novel probabilistic algorithm for graph coherent closure that improves computational speed over traditional methods.

Findings

Runs in time $O(n^{1+ ext{omega}} ext{log}^2 n)$, with $ ext{omega}<2.273$

Uses Monte Carlo method for probabilistic approximation

Enhances efficiency of graph isomorphism testing

Abstract

A probabilistic version of the Weisfeiler-Leman algorithm for computing the coherent closure of a colored graph is suggested. The algorithm is Monte Carlo and runs in time $ O(n^{1+\omega}\log^2 n) $, where $ n $ is the number of vertices of the graph and $ \omega < 2.273 $ is the matrix multiplication exponent.