Simple Distributed Δ + 1 Coloring in the SINR Model

  • Fabian Fuchs
  • Roman Prutkin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9439)


In wireless ad hoc networks, distributed node coloring is a fundamental problem closely related to establishing efficient communication through TDMA schedules. For networks with maximum degree Δ, a Δ + 1 coloring is the ultimate goal in the distributed setting as this is always possible. In this work we propose a very simple 4Δ coloring along with a color reduction technique to achieve Δ + 1 colors. All algorithms have a runtime of \(\mathcal{O}(\Delta \log n)\) time slots. This improves on previous algorithms for the SINR model either in terms of the number of required colors or the runtime, and matches the runtime of local broadcasting in the SINR model (which can be seen as an asymptotical lower bound).


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  1. 1.
    Bardwell, J.: Converting signal strength percentage to dbm values. WildPackets’ White Paper (2002)Google Scholar
  2. 2.
    Barenboim, L., Elkin, M.: Distributed Graph Coloring: Fundamentals and Recent Developments. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool Publishers (2013)Google Scholar
  3. 3.
    Derbel, B., Talbi, E.G.: Distributed Node Coloring in the SINR Model. In: Proc. 30th Internat. Conf. on Distributed Computing Systems (ICDCS 2010). pp. 708–717. IEEE (2010)Google Scholar
  4. 4.
    Distributed Computing Group, ETH Zurich: Sinalgo - simulator for network algorithms (2008),, version 0.75.3
  5. 5.
    Fuchs, F.: On asynchronous node coloring in the SINR model (2015), (unpublished manuscript)
  6. 6.
    Fuchs, F., Prutkin, R.: Simple distributed delta + 1 coloring in the SINR model. CoRR abs/1502.02426 (2015),
  7. 7.
    Fuchs, F., Wagner, D.: On Local Broadcasting Schedules and CONGEST Algorithms in the SINR Model. In: Proc. 9th Internat. Workshop on Algorithmic Aspects of WSN (ALGOSENSORS 2013). pp. 170–184. Springer (2013)Google Scholar
  8. 8.
    Fuchs, F., Wagner, D.: Local broadcasting with arbitrary transmission power in the SINR model. In: Proc. 21st Internat. Colloq. Structural Inform. and Comm. Complexity (SIROCCO 2014), pp. 180–193. Springer (2014)Google Scholar
  9. 9.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co. (1979)Google Scholar
  10. 10.
    Goussevskaia, O., Moscibroda, T., Wattenhofer, R.: Local Broadcasting in the Physical Interference Model. In: Proc. 5th ACM Internat. Workshop on Foundations of Mobile Computing (DialM-POMC 2008), pp. 35–44. ACM (2008)Google Scholar
  11. 11.
    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) (November 2010)Google Scholar
  12. 12.
    Gupta, P., Kumar, P.R.: The capacity of wireless networks. IEEE Trans. on Inform. Theory 46(2), 388–404 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Halldórsson, M.M., Mitra, P.: Towards Tight Bounds for Local Broadcasting. In: Proc. 8th ACM Internat. Workshop on Foundations of Mobile Computing (FOMC 2012). ACM (2012)Google Scholar
  14. 14.
    Moscibroda, T., Wattenhofer, M.: Coloring Unstructured Radio Networks. J. Distr. Comp. 21(4), 271–284 (2008)CrossRefzbMATHGoogle Scholar
  15. 15.
    Moscibroda, T., Wattenhofer, R., Weber, Y.: Protocol design beyond graph-based models. In: Proc. of the ACM Workshop on Hot Topics in Networks (HotNets-V), pp. 25–30 (2006)Google Scholar
  16. 16.
    Roberts, L.G.: Aloha packet system with and without slots and capture. SIGCOMM Comput. Commun. Rev. 5(2), 28–42 (1975)CrossRefGoogle Scholar
  17. 17.
    Schneider, J., Wattenhofer, R.: Coloring unstructured wireless multi-hop networks. In: Proc. 28th ACM Symp. on Principles of Distributed Computing (PODC 2009), pp. 210–219. ACM (2009)Google Scholar
  18. 18.
    Yu, D., Hua, Q.S., Wang, Y., Lau, F.C.M.: An O(logn) Distributed Approximation Algorithm for Local Broadcasting in Unstructured Wireless Networks. In: Proc. 8th Internat. Conf. on Distributed Computing in Sensor Systems (DCOSS 2012), pp. 132–139. IEEE (2012)Google Scholar
  19. 19.
    Yu, D., Wang, Y., Hua, Q.S., Lau, F.C.M.: Distributed (Δ + 1) Coloring in the Physical Model. Theoret. Comput. Sci. 553, 37–56 (2014)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Karlsruhe Institute for Technology (KIT)KarlsruheGermany

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