Solving the Hamiltonian path problem with a light-based computer

TL;DR

This paper introduces a light-based computational device that leverages the properties of light rays to solve the Hamiltonian path problem efficiently for small to medium-sized graphs.

Contribution

It presents a novel optical computing approach using light traversal and unique marking at nodes to identify Hamiltonian paths in directed graphs.

Findings

Device can solve small instances quickly

Method effectively identifies Hamiltonian paths

Suitable for medium-sized problems

Abstract

In this paper we propose a special computational device which uses light rays for solving the Hamiltonian path problem on a directed graph. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes. In each node the rays are uniquely marked so that they can be easily identified. At the destination node we will search only for particular rays that have passed only once through each node. We show that the proposed device can solve small and medium instances of the problem in reasonable time.