Decentralized Constraint Satisfaction

TL;DR

This paper introduces a stochastic decentralized CSP solver tailored for resource allocation in wireless networks, demonstrating its theoretical guarantees and practical effectiveness in real-world scenarios and benchmark problems.

Contribution

It presents the first decentralized CSP solver with proven finite-time convergence and practical utility for wireless network resource allocation.

Findings

The solver finds solutions in almost surely finite time if they exist.

Performance is competitive with centralized solvers on large random k-SAT problems.

Successfully applied to real-world channel allocation in Manhattan network.

Abstract

We show that several important resource allocation problems in wireless networks fit within the common framework of Constraint Satisfaction Problems (CSPs). Inspired by the requirements of these applications, where variables are located at distinct network devices that may not be able to communicate but may interfere, we define natural criteria that a CSP solver must possess in order to be practical. We term these algorithms decentralized CSP solvers. The best known CSP solvers were designed for centralized problems and do not meet these criteria. We introduce a stochastic decentralized CSP solver and prove that it will find a solution in almost surely finite time, should one exist, also showing it has many practically desirable properties. We benchmark the algorithm's performance on a well-studied class of CSPs, random k-SAT, illustrating that the time the algorithm takes to find a satisfying assignment is competitive with stochastic centralized solvers on problems with order a thousand variables despite its decentralized nature. We demonstrate the solver's practical utility for the problems that motivated its introduction by using it to find a non-interfering channel allocation for a network formed from data from downtown Manhattan.