Decentralized Constraint Satisfaction

We show that several important problems in wireless networks, including channel and power selection, 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 so do not meet these criteria. Thus we introduce a stochastic decentralized CSP solver proving that it will find a solution in almost surely finite time, should one exist, and 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 state of the art 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 joint power and channel allocation for a physical interference model network based on real data from downtown Manhattan.