MIS on trees

Christoph Lenzen, Roger Wattenhofer

Abstract: A maximal independent set on a graph is an inclusion-maximal set of mutually non-adjacent nodes. This basic symmetry breaking structure is vital for many distributed algorithms, which by now has been fueling the search for fast local algorithms to find such sets over several decades. In this paper, we present a solution with randomized running time O(√log n log log n) on trees, improving roughly quadratically on the state-of-the-art bound. Our algorithm is uniform and nodes need to exchange merely O(log n) many bits with high probability. In contrast to previous techniques achieving sublogarithmic running times, our approach does not rely on any bound on the number of independent neighbors (possibly with regard to an orientation of the edges).