Advertisement

Distributed (Δ + 1)-Coloring in the Physical Model

  • Dongxiao Yu
  • Yuexuan Wang
  • Qiang-Sheng Hua
  • Francis C. M. Lau
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7111)

Abstract

In multi-hop radio networks, such as wireless ad-hoc and sensor networks, nodes employ a MAC (Medium Access Control) protocol such as TDMA to coordinate accesses to the shared medium and to avoid interference of close-by transmissions. These protocols can be implemented using standard node coloring. The (Δ + 1)-coloring problem is to color all nodes in as few timeslots as possible using at most Δ + 1 colors such that any two nodes within distance R are assigned different colors, where R is a given parameter and Δ is the maximum degree of the modeled unit disk graph using the scaling factor R. Being one of the most fundamental problems in distributed computing, this problem is well studied and there are a long chain of algorithms for it. However, all previous work are based on models that are highly abstract, such as message passing models and graph based interference models, which limit the utility of these algorithms in practice.

In this paper, for the first time, we consider the distributed Δ + 1-coloring problem under the more practical SINR interference model. In particular, without requiring any knowledge about the neighborhood, we propose a novel randomized (Δ + 1)-coloring algorithm with time complexity O(Δlogn + log2 n). For the case where nodes can not adjust their transmission power, we give an O(Δlog2 n) randomized algorithm, which only incurs a logarithmic multiplicative factor overhead.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Barenboim, L., Elkin, M.: Distributed (Δ + 1)-coloring in linear (in Δ) time. In: STOC (2009)Google Scholar
  2. 2.
    Cole, R., Vishkin, U.: Deterministic coin tossing with applications to optimal parallel list ranking. Inf. Control 70(1), 32–53 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Derbel, B., Talbi, E.-G.: Distributed node coloring in the SINR model. In: ICDCS (2010)Google Scholar
  4. 4.
    Goussevskaia, O., Moscibroda, T., Wattenhofer, R.: Local broadcasting in the physical interference model. In: DialM-POMC (2008)Google Scholar
  5. 5.
    Goussevskaia, O., Oswald, Y.A., Wattenhofer, R.: Complexity in geometric SINR. In: Mobihoc (2007)Google Scholar
  6. 6.
    Goussevskaia, O., Pignolet, Y.A., Wattenhofer, R.: Efficiency of wireless networks: approximation algorithms for the physical interference model. Foundations and Trends in Networking 4(3), 313–420 (2010)CrossRefzbMATHGoogle Scholar
  7. 7.
    Gupta, P., Kumar, P.R.: The capacity of wireless networks. IEEE Transaction on Infromation Theorey 46(2), 388–404 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Kesselheim, T., Vöcking, B.: Distributed Contention Resolution in Wireless Networks. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 163–178. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Kuhn, F., Moscibroda, T., Wattenhofer, R.: Initializing newly deployed Ad Hoc and sensor networks. In: MOBICOM (2004)Google Scholar
  10. 10.
    Moscibroda, T., Wattenhofer, R.: Coloring unstructured radio networks. In: SPAA (2005)Google Scholar
  11. 11.
    Moscibroda, T., Wattenhofer, R.: Coloring unstructured radio networks. Distributed Computing 21(4), 271–284 (2008)CrossRefzbMATHGoogle Scholar
  12. 12.
    Moscibroda, T., Wattenhofer, R.: Maximal independent sets in radio networks. In: PODC (2005)Google Scholar
  13. 13.
    Scheideler, C., Richa, A., Santi, P.: An O(logn) dominating set protocol for wireless ad-hoc networks under the physical interference model. In: Mobihoc (2008)Google Scholar
  14. 14.
    Schneider, J., Wattenhofer, R.: A log-star distributed maximal independent set algorithm for growth-bounded graphs. In: PODC (2008)Google Scholar
  15. 15.
    Schneider, J., Wattenhofer, R.: Coloring unstructured wireless multi-hop networks. In: PODC (2009)Google Scholar
  16. 16.
    Yu, D., Hua, Q.-S., Wang, Y., Lau, F.C.M.: Distributed (Δ + 1)-Coloring in the Physical Model, http://i.cs.hku.hk/~qshua/algosensorsfullversion.pdf
  17. 17.
    Yu, D., Wang, Y., Hua, Q.-S., Lau, F.C.M.: Distributed local broadcasting algorithms in the physical interference model. In: DCOSS (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Dongxiao Yu
    • 1
  • Yuexuan Wang
    • 2
  • Qiang-Sheng Hua
    • 2
    • 1
  • Francis C. M. Lau
    • 1
  1. 1.Department of Computer ScienceThe University of Hong KongHong KongP.R. China
  2. 2.Institute for Interdisciplinary Information SciencesTsinghua UniversityBeijingP.R. China

Personalised recommendations