Distributed algorithm and reversible network

Motivated to design a feasible optical network architecture for the future Internet, we address the question of scheduling (wavelength assignment) in an optical network. The key challenge in designing a scheduling algorithm lies in solving a combinatorial optimization problem under very stringent distributed constraints. Specifically, given R random variables x1,... , xR taking integer values, each variable is required to find its assignment so that collectively they maximize SigmarWrxr subject to some linear constraints that Ax les C. In doing so, each variable can only avail of two pieces of information (and nothing else): one, its own weight Wr, two, given its current values (and the values of other variables being unknown), can it increase it by +1 or not. As the main result of this paper, we present a randomized algorithm that solves this problem. Our algorithm builds upon classical theory of reversible networks. To the best of our knowledge, this is the first such algorithm for such a stringent distributed problem.