An optimal bit complexity randomized distributed MIS algorithm

Abstract

We present a randomized distributed maximal independent set (MIS) algorithm for arbitrary graphs of size n that halts in time O(log n) with probability 1 − o(n −1 ), and only needs messages containing 1 bit. Thus, its bit complexity par channel is O(log n). We assume that the graph is anonymous: unique identities are not available to distinguish between the processes; we only assume that each vertex distinguishes between its neighbours by locally known channel names. Furthermore we do not assume that the size (or an upper bound on the size) of the graph is known. This algorithm is optimal (modulo a multi- plicative constant) for the bit complexity and improves the best previous randomized distributed MIS algorithms (deducedfromtherandomizedPRAMalgorithmduetoLuby (SIAM J. Comput. 15:1036-1053, 1986)) for general graphs which is O(log 2 n) per channel (it halts in time O(log n)