Local Routing Algorithms Based on Potts Neural Networks

TL;DR

This paper introduces a neural network-based approach for static communication routing in asymmetric networks, leveraging a mean field formulation of Bellman-Ford to develop algorithms for various multicast and unicast problems, emphasizing locality and efficiency.

Contribution

It presents a novel neural network method based on Potts neurons and mean field theory for solving complex routing problems with capacity constraints.

Findings

Method achieves solutions close to exact for test cases.

Computational demand remains modest.

Applicable to multiple routing scenarios.

Abstract

A feedback neural approach to static communication routing in asymmetric networks is presented, where a mean field formulation of the Bellman-Ford method for the single unicast problem is used as a common platform for developing algorithms for multiple unicast, multicast and multiple multicast problems. The appealing locality and update philosophy of the Bellman-Ford algorithm is inherited. For all problem types the objective is to minimize a total connection cost, defined as the sum of the individual costs of the involved arcs, subject to capacity constraints. The methods are evaluated for synthetic problem instances by comparing to exact solutions for cases where these are accessible, and else with approximate results from simple heuristics. The computational demand is modest.