Distributed algorithm and reversible network

• Published in: 2008 42nd Annual Conference on Information Sciences and Systems pp. 498 - 502
• Main Authors: Rajagopalan, S., Shah, D.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.03.2008
• Subjects: Algorithm design and analysis; Constraint optimization; Design optimization; Distributed algorithms; IP networks; Optical design; Optical fiber networks; Random variables; Scheduling algorithm; Wavelength assignment
• ISBN: 1424422469; 9781424422463
• DOI: 10.1109/CISS.2008.4558577

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 x 1 ,... , x R taking integer values, each variable is required to find its assignment so that collectively they maximize Sigma r W r x r 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 W r , 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.