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Tight Bounds for MIS in Multichannel Radio Networks

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Distributed Computing (DISC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9363))

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Abstract

In [8] an algorithm has been presented that computes a maximal independent set (MIS) within \(O(\log ^2 n/\mathcal {F}+\log n {{\mathrm{\mathrm {polyloglog~}}}} n)\) rounds in an n-node multichannel radio network with \(\mathcal {F}\) communication channels. The paper uses a multichannel variant of the standard graph-based radio network model without collision detection and it assumes that the network graph 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 \({{\mathrm{\mathrm {polyloglog~}}}} n\) 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 \({{\mathrm{\mathrm {polyloglog~}}}} n\) factor in the running time and we thus obtain an asymptotically optimal multichannel radio network MIS algorithm. In addition, our new analysis allows to generalize the class of graphs from those with polynomially bounded local independence to graphs where the local independence is bounded by an arbitrary function of the neighborhood radius.

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Authors and Affiliations

  1. Department of Computer Science, University of Freiburg, Freiburg im Breisgau, Germany

    Sebastian Daum & Fabian Kuhn

Authors
  1. Sebastian Daum
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  2. Fabian Kuhn
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Correspondence to Sebastian Daum .

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Editors and Affiliations

  1. Technion, Haifa, Israel

    Yoram Moses

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Daum, S., Kuhn, F. (2015). Tight Bounds for MIS in Multichannel Radio Networks. In: Moses, Y. (eds) Distributed Computing. DISC 2015. Lecture Notes in Computer Science(), vol 9363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48653-5_38

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  • DOI: https://doi.org/10.1007/978-3-662-48653-5_38

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