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Coloring unstructured radio networks

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Abstract

During and immediately after their deployment, ad hoc and sensor networks lack an efficient communication scheme rendering even the most basic network coordination problems difficult. Before any reasonable communication can take place, nodes must come up with an initial structure that can serve as a foundation for more sophisticated algorithms. In this paper, we consider the problem of obtaining a vertex coloring as such an initial structure. We propose an algorithm that works in the unstructured radio network model. This model captures the characteristics of newly deployed ad hoc and sensor networks, i.e. asynchronous wake-up, no collision-detection, and scarce knowledge about the network topology. When modeling the network as a graph with bounded independence, our algorithm produces a correct coloring with O(Δ) colors in time O(Δ log n) with high probability, where n and Δ are the number of nodes in the network and the maximum degree, respectively. Also, the number of locally used colors depends only on the local node density. Graphs with bounded independence generalize unit disk graphs as well as many other well-known models for wireless multi-hop networks. They allow us to capture aspects such as obstacles, fading, or irregular signal-propagation.

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Authors and Affiliations

  1. Microsoft Research, One Microsoft Way, Redmond, WA, 98052, USA

    Thomas Moscibroda

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

    Roger Wattenhofer

Authors
  1. Thomas Moscibroda
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  2. Roger Wattenhofer
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Correspondence to Thomas Moscibroda.

Additional information

A preliminary version of this work has been published in [20] as Coloring Unstructured Radio Networks, In Proceedings of the 17th Symposium on Parallel Algorithms and Architectures (SPAA), Las Vegas, Nevada, 2005.

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Moscibroda, T., Wattenhofer, R. Coloring unstructured radio networks. Distrib. Comput. 21, 271–284 (2008). https://doi.org/10.1007/s00446-008-0070-4

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  • DOI: https://doi.org/10.1007/s00446-008-0070-4

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