A Potts Neuron Approach to Communication Routing

TL;DR

This paper introduces a neural network-based method using Potts neurons for solving communication routing problems, especially multiple shortest path requests, with a focus on distributed implementation and high-quality solutions.

Contribution

It presents a novel Potts neuron approach for routing that handles multiple requests efficiently and can be implemented in a distributed manner, extending traditional shortest path algorithms.

Findings

High-quality solutions comparable to exact methods

Scales efficiently with network size and load

Effective for synthetic routing problems

Abstract

A feedback neural network approach to communication routing problems is developed with emphasis on Multiple Shortest Path problems, with several requests for transmissions between distinct start- and endnodes. The basic ingredients are a set of Potts neurons for each request, with interactions designed to minimize path lengths and to prevent overloading of network arcs. The topological nature of the problem is conveniently handled using a propagator matrix approach. Although the constraints are global, the algorithmic steps are based entirely on local information, facilitating distributed implementations. In the polynomially solvable single-request case the approach reduces to a fuzzy version of the Bellman-Ford algorithm. The approach is evaluated for synthetic problems of varying sizes and load levels, by comparing with exact solutions from a branch-and-bound method. With very few exceptions, the Potts approach gives legal solutions of very high quality. The computational demand scales merely as the product of the numbers of requests, nodes, and arcs.