An optical solution for the set splitting problem

TL;DR

This paper presents an optical device leveraging time-delays and a graph-like structure to solve the NP-complete set splitting problem by generating and evaluating all potential paths simultaneously.

Contribution

It introduces a novel optical solution with a graph-based structure for efficiently addressing the NP-complete set splitting problem.

Findings

Successfully generates all potential paths in the graph.

Identifies paths satisfying the set splitting constraints.

Provides a new optical approach for solving NP-complete problems.

Abstract

We describe here an optical device, based on time-delays, for solving the set splitting problem which is well-known NP-complete problem. The device has a graph-like structure and the light is traversing it from a start node to a destination node. All possible (potential) paths in the graph are generated and at the destination we will check which one satisfies completely the problem's constrains.