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An optimal maximal independent set algorithm for bounded-independence graphs

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Abstract

We present a novel distributed algorithm for the maximal independent set problem (This is an extended journal version of Schneider and Wattenhofer in Twenty-seventh annual ACM SIGACT-SIGOPS symposium on principles of distributed computing, 2008). On bounded-independence graphs our deterministic algorithm finishes in O(log* n) time, n being the number of nodes. In light of Linial’s Ω(log* n) lower bound our algorithm is asymptotically optimal. Furthermore, it solves the connected dominating set problem for unit disk graphs in O(log* n) time, exponentially faster than the state-of-the-art algorithm. With a new extension our algorithm also computes a δ + 1 coloring and a maximal matching in O(log* n) time, where δ is the maximum degree of the graph.

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  1. Computer Engineering and Networks Laboratory, ETH Zurich, 8092, Zurich, Switzerland

    Johannes Schneider & Roger Wattenhofer

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  1. Johannes Schneider
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  2. Roger Wattenhofer
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Correspondence to Johannes Schneider.

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Schneider, J., Wattenhofer, R. An optimal maximal independent set algorithm for bounded-independence graphs. Distrib. Comput. 22, 349–361 (2010). https://doi.org/10.1007/s00446-010-0097-1

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