Learning-Based Constraint Satisfaction With Sensing Restrictions

TL;DR

This paper introduces decentralized learning algorithms for graph-coloring in wireless networks, capable of handling sensing restrictions like hidden terminals, with proven conditions ensuring reliable performance.

Contribution

It establishes the existence of decentralized algorithms that succeed under sensing asymmetry, with mild connectivity conditions on the sensing graph, applicable to wireless resource allocation.

Findings

Algorithms succeed with probability one under mild sensing conditions

Performance remains robust with constrained sensing and no message passing

Conditions on sensing graph are practically satisfied in wireless scenarios

Abstract

In this paper we consider graph-coloring problems, an important subset of general constraint satisfaction problems that arise in wireless resource allocation. We constructively establish the existence of fully decentralized learning-based algorithms that are able to find a proper coloring even in the presence of strong sensing restrictions, in particular sensing asymmetry of the type encountered when hidden terminals are present. Our main analytic contribution is to establish sufficient conditions on the sensing behaviour to ensure that the solvers find satisfying assignments with probability one. These conditions take the form of connectivity requirements on the induced sensing graph. These requirements are mild, and we demonstrate that they are commonly satisfied in wireless allocation tasks. We argue that our results are of considerable practical importance in view of the prevalence of both communication and sensing restrictions in wireless resource allocation problems. The class of algorithms analysed here requires no message-passing whatsoever between wireless devices, and we show that they continue to perform well even when devices are only able to carry out constrained sensing of the surrounding radio environment.