A near-optimal fully dynamic distributed algorithm for maintaining sparse spanners

Currently, there are no known explicit algorithms for the great majority of problems in the dynamic distributed message-passing model. Instead, most state-of-the-art dynamic distributed algorithms are constructed by composing a static algorithm for the problem at hand with a simulation technique that converts static algorithms to dynamic ones. We argue that this powerful methodology does not provide satisfactory solutions for many important dynamic distributed problems, and this necessitates developing algorithms for these problems from scratch. In this paper we develop the first fully dynamic distributed algorithm for maintaining sparse spanners. Our algorithm improves drastically the quiescence time of the state-of-the-art algorithm for the problem. Moreover, we show that the quiescence time of our algorithm is optimal up to a small constant factor. In addition, our algorithm improves significantly upon the state-of-the-art algorithm in all efficiency parameters, specifically, it has smaller quiescence message and space complexities, and smaller local processing time. Finally, we use our technique to improve the state-of-the-art streaming algorithm for constructing sparse spanners, and to devise an efficient fully dynamic centralized algorithm for maintaining sparse spanners. ∗Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel, [email protected]