Abstract
Finding a maximal independent set (MIS) is a classic problem in graph theory that has been widely study in the context of distributed algorithms. Standard distributed MIS solutions focus on time complexity. Here we focus on a novel attribute, fairness, where we consider an MIS algorithm fair if all nodes have similar probabilities of joining the set. In many contexts, fairness is important because a node's election to the MIS can have an impact on the resources it consumes. This paper addresses fairness by providing a provably fair and efficient distributed MIS algorithm for unrooted trees. The algorithm runs in O(logn) time and guarantees a correct MIS such that each node enters the set with probability at least 1/4 - e, for arbitrarily small e.
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