Solving the subset-sum problem with a light-based device

TL;DR

This paper introduces a novel optical device that leverages light traversal through a graph-like structure to efficiently solve the subset-sum problem by encoding subset sums as delays in light rays.

Contribution

The paper presents a new light-based computational device that encodes subset sums through delays, offering an innovative physical approach to solving the subset-sum problem.

Findings

The device can generate all subset sums via light traversal.

It can determine if a subset sum equals a target value.

The approach demonstrates potential for physical computation of combinatorial problems.

Abstract

We propose a special computational device which uses light rays for solving the subset-sum problem. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes. The nodes are connected by arcs in a special way which lets us to generate all possible subsets of the given set. To each arc we assign either a number from the given set or a predefined constant. When the light is passing through an arc it is delayed by the amount of time indicated by the number placed in that arc. At the destination node we will check if there is a ray whose total delay is equal to the target value of the subset sum problem (plus some constants).