Abstract
The distributed complexity of computing a maximal independent set in a graph is of both practical and theoretical importance. While there exists an elegant O(log n) time randomized algorithm for general graphs [20], no deterministic polylogarithmic algorithm is known. In this paper, we study the problem in graphs with bounded growth, an important family of graphs which includes the well-known unit disk graph and many variants thereof. Particularly, we propose a deterministic algorithm that computes a maximal independent set in time O(log Δ· log* n) in graphs with bounded growth, where n and Δ denote the number of nodes and the maximal degree in G, respectively.
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Kuhn, F., Moscibroda, T., Nieberg, T., Wattenhofer, R. (2005). Fast Deterministic Distributed Maximal Independent Set Computation on Growth-Bounded Graphs. In: Fraigniaud, P. (eds) Distributed Computing. DISC 2005. Lecture Notes in Computer Science, vol 3724. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11561927_21
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DOI: https://doi.org/10.1007/11561927_21
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