Collective dynamics of phase-repulsive oscillators solves graph coloring problem

TL;DR

This paper introduces a novel dynamical system approach using coupled phase-repulsive oscillators to solve the graph coloring problem, translating it into a natural system's energy minimization process.

Contribution

It presents a new method that maps graph coloring to oscillator dynamics, offering an alternative to traditional algorithms and extending to weighted graph coloring.

Findings

Successfully solves graph coloring problems via oscillator dynamics.

Efficiently handles weighted graph coloring.

Serves as a viable alternative to combinatorial algorithms.

Abstract

We show how to couple phase-oscillators on a graph so that collective dynamics "searches" for the coloring of that graph as it relaxes toward the dynamical equilibrium. This translates a combinatorial optimization problem (graph coloring) into a functional optimization problem (finding and evaluating the global minimum of dynamical non-equilibrium potential, done by the natural system's evolution). Using a sample of graphs, we show that our method can serve as a viable alternative to the traditional combinatorial algorithms. Moreover, we show that, with the same computational cost, our method efficiently solves the harder problem of improper coloring of weighed graphs.