On the Solution of Graph Isomorphism by Dynamical Algorithms

TL;DR

This paper examines dynamical algorithms for graph isomorphism, showing they are encompassed by combinatorial methods and share similar limitations, thus questioning their effectiveness.

Contribution

It generalizes a dynamical approach to graph isomorphism and demonstrates its equivalence to combinatorial methods, highlighting shared weaknesses.

Findings

Dynamical algorithms are covered by combinatorial approaches.

Polynomial dynamical algorithms share weaknesses with combinatorial methods.

The approach unifies different algorithmic strategies for graph isomorphism.

Abstract

In the recent years, several polynomial algorithms of a dynamical nature have been proposed to address the graph isomorphism problem. In this paper we propose a generalization of an approach exposed in cond-mat/0209112 and find that this dynamical algorithm is covered by a combinatorial approach. It is possible to infer that polynomial dynamical algorithms addressing graph isomorphism are covered by suitable polynomial combinatorial approaches and thus are tackled by the same weaknesses as the last ones.