Beeping an MIS

We consider an extremely harsh synchronous broadcast communication model and present two algorithms solving the Maximal Independent Set (MIS) problem in this model. The model consists of an anonymous broadcast network, in which nodes have no knowledge about the network topology nor any bound on the network size. Furthermore, nodes may start the algorithm spontaneously in an asynchronous manner. In this model we consider two weak communication models, beeping with collision detection and beeping without collision detection. We present a randomized MIS algorithm for the former model that works in O(log n) rounds. For the latter we present an algorithm that produces an MIS in O(log n) rounds but the nodes do not know that, and may continue to send messages indefinitely. Finally, we show that our algorithm is optimal under some restriction, by presenting a tight lower bound of Ω(log n) on the number of rounds required to construct a MIS for a restricted model. Intended for Regular Presentation. Contact Author: Ziv Bar-Joseph Email: [email protected] ∗The Blavatnik School of Computer Science, Tel-Aviv University, Israel 69978. [email protected] †School of Mathematics, & The Blavatnik School of Computer Science, Tel-Aviv University, Israel 69978. [email protected] ‡School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213, USA. [email protected]