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Beeping an MIS (Extended Abstract)

Summary: Beeping an MIS
(Extended Abstract)
Yehuda Afek
Noga Alon
Ziv Bar-Joseph
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 net-
work 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(log2
n) rounds. For the latter
we present an algorithm that produces an MIS in O(log3
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 (log2
n) on the number
of rounds required to construct a MIS for a restricted model.


Source: Afek, Yehuda - School of Computer Science, Tel Aviv University


Collections: Computer Technologies and Information Sciences