A fast algorithm on average for solving the Hamilton Cycle problem

TL;DR

This paper introduces CertifyHAM, an efficient algorithm that quickly determines the existence of a Hamilton cycle in random graphs with high probability, outperforming previous methods in expected runtime.

Contribution

The paper presents CertifyHAM, a novel algorithm with improved average-case performance for solving the Hamilton Cycle problem in certain random graphs.

Findings

Expected runtime of CertifyHAM is O(n/p) for p > 2000/n in G(n, p) graphs.

CertifyHAM reliably finds Hamilton cycles or certifies their absence in random graphs.

Outperforms previous algorithms in expected running time for specified graph densities.

Abstract

We present CertifyHAM, an algorithm which takes as input a graph G and either finds a Hamilton cycle of G or it outputs that such a cycle does not exists. If G=G(n, p) and p >2000/n then the expected running time of CertifyHAM is O(n/p). This improves upon previous results due to Gurevich and Shelah, Thomason and Alon and Krivelevich.