Emergent chaotic iterations in hard sparse instances of hamiltonian path problem

TL;DR

This paper introduces a novel chaotic algorithm for solving the NP-Complete Hamiltonian path problem, demonstrating effectiveness on hard sparse instances with a specific polynomial runtime.

Contribution

The paper presents a new chaotic algorithm tailored for hard sparse Hamiltonian path instances, with analysis of its runtime and behavior.

Findings

Algorithm runs in $O(V^5(V + E))$ for challenging sparse instances.

Chaotic behavior observed in the proposed algorithm.

Effective on FHCP challenge dataset.

Abstract

A hamiltonian path is a path walk P that can be a hamiltonian path or hamiltonian circuit. Determining whether such hamiltonian path exists in a given graph G = (V, E) is a NP-Complete problem. In this paper, a novel algorithm with chaotic behaviour for hamiltonian path problem is proposed. We show that our algorithm runs in $O(V^5(V + E))$ for hard sparse instances from FHCP challenge dataset.