Randomized Algorithms 2014 / 5 A Lecture 2 – Maximal Independent Set , Analysis of Randomized

We considered a distributed model of computing where nodes in a graph contain processors and they can talk to their immediate neighbors. The goal now is to collectively compute something. In particular for the maximal independent set problem the goal is to a pick a set of nodes S such that S is a maximal independent set of the underlying graph and each node determines whether or not it is in S. In this model we may need randomness simply to break symmetry (think of a cycle), but even if processors have unique id’s (so the greedy algorithm can be executed) no local deterministic algorithm is known (one that take polylog in n time, regardless of the graph). The algorithm we say in a variant of a 1986 algorithm by Mike Luby [5], see lecture notes by Wattenhaffer [6]. The expected number of edges removed in each phase is at least 1/3 and the expected number of rounds until all nodes know wether there are in the MIS or not is O(log n).