In [8] an algorithm has been presented that computes a maximal independent set (MIS) within O(log2 n/F + log n polyloglog n) rounds in an n-node multichannel variant of the standard graph-based radio network, with F communication channels. The model assumes that there is no collision detection and it that the network is a polynomially bounded independence graph (BIG), a natural combinatorial generalization of well-known geographic families. The upper bound of [8] is known to be optimal up to the polyloglog n factor. In this paper, we adapt this algorithm and its analysis to improve the result of [8] in two ways. Mainly, we get rid of the polyloglog n factor in the runtime and we thus obtain an asymptotically optimal MIS algorithm. In addition, our new analysis allows to generalize the class of graphs from those with polynomially bounded local independence to graphs with arbitrarily bounded local independence.
CITATION STYLE
Daum, S., & Kuhn, F. (2015). Tight bounds for MIS in multichannel radio networks. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9363, pp. 573–587). Springer Verlag. https://doi.org/10.1007/978-3-662-48653-5_38
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