A Fully Asynchronous and Fault Tolerant Distributed Algorithm to Compute a Minimum Graph Orientation

  • Noël GilletEmail author
  • Nicolas Hanusse
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10616)


The minimum orientation problem is a classical graph theoretical problem in which we aim at finding an orientation of a graph G that minimizes the maximum out-degree \(D^+(G)\). Graph orientation is motivated by load balancing problems in which a set of tasks have to be allocated to a set of processes in order to minimize the completion time. If we consider load balancing in networks, the decisions for the allocation have to be made by the nodes without a global knowledge of the graph. In this paper, we propose a distributed algorithm that computes a graph orientation that provides a \(2(2+\epsilon )\)-approximation of the optimal. The algorithm is asynchronous and runs in \(O((\log n +diam(G))\log D^+(OPT(G))\) rounds, where n is the number of nodes, diam is the diameter of the graph and \(D^+(OPT(G))\) is the maximum out-degree with an optimal orientation. The algorithm does not need any global knowledge on G and tolerates initial faults.


  1. [AKM+93]
    Awerbuch, B., Kutten, S., Mansour, Y., Patt-Shamir, B., Varghese, G.: Time optimal self-stabilizing synchronization. In: Rao Kosaraju, S., Johnson, D.S., Aggarwal, A. (eds.) Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, 16–18 May 1993, San Diego, CA, USA, pp. 652–661. ACM (1993)Google Scholar
  2. [AMOZ06]
    Asahiro, Y., Miyano, E., Ono, H., Zenmyo, K.: Graph orientation algorithms to minimize the maximum outdegree. In: Proceedings of the 12th Computing: The Australasian Theory Symposium, vol. 51, pp. 11–20. Australian Computer Society Inc. (2006)Google Scholar
  3. [APPS92]
    Awerbuch, B., Patt-Shamir, B., Peleg, D., Saks, M.E.: Adapting to asynchronous dynamic networks (extended abstract). In: Rao Kosaraju, S., Fellows, M., Wigderson, A., Ellis, J.A. (eds.) Proceedings of the 24th Annual ACM Symposium on Theory of Computing, 4–6 May 1992, Victoria, British Columbia, Canada, pp. 557–570. ACM (1992)Google Scholar
  4. [AS88]
    Awerbuch, B., Sipser, M.: Dynamic networks are as fast as static networks (preliminary version). In 29th Annual Symposium on Foundations of Computer Science, White Plains, New York, USA, 24–26 , pp. 206–220. IEEE Computer Society, October 1988Google Scholar
  5. [Awe85]
    Awerbuch, B.: Complexity of network synchronization. J. ACM 32(4), 804–823 (1985)MathSciNetCrossRefGoogle Scholar
  6. [BE10]
    Barenboim, L., Elkin, M.: Sublogarithmic distributed MIS algorithm for sparse graphs using Nash-Williams decomposition. Distrib. Comput. 22(5–6), 363–379 (2010)CrossRefGoogle Scholar
  7. [BE13]
    Barenboim, L., Elkin, M.: Distributed Graph Coloring: Fundamentals and Recent Developments Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool Publishers, San Rafael (2013)zbMATHGoogle Scholar
  8. [Cas]
    Apache Cassandra.
  9. [FLP85]
    Fischer, M.J., Lynch, N.A., Paterson, M.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374–382 (1985)MathSciNetCrossRefGoogle Scholar
  10. [FT14]
    Farach-Colton, M., Tsai, M.-T.: Computing the degeneracy of large graphs. In: Pardo, A., Viola, A. (eds.) LATIN 2014. LNCS, vol. 8392, pp. 250–260. Springer, Heidelberg (2014). doi: 10.1007/978-3-642-54423-1_22CrossRefGoogle Scholar
  11. [GF78]
    Gyárfás, A., Frank, A.: How to orient the edges of a graph. Combinatorics 18, 353–362 (1978)Google Scholar
  12. [GW92]
    Gabow, H.N., Westermann, H.H.: Forests, frames, and games: algorithms for matroid sums and applications. Algorithmica 7(5&6), 465–497 (1992)MathSciNetCrossRefGoogle Scholar
  13. [HBa]
  14. [Kow06]
    Kowalik, Ł.: Approximation scheme for lowest outdegree orientation and graph density measures. In: Asano, T. (ed.) ISAAC 2006. LNCS, vol. 4288, pp. 557–566. Springer, Heidelberg (2006). doi: 10.1007/11940128_56CrossRefzbMATHGoogle Scholar
  15. [Mit96]
    Mitzenmacher, M.D.: The power of two choices in randomized load balancing. Ph.D. thesis, University of California at Berkeley (1996)Google Scholar
  16. [O’R87]
    O’Rourke, J.: Art Gallery Theorems and Algorithms. Oxford University Press, Oxford (1987)zbMATHGoogle Scholar
  17. [Pel00]
    Peleg, D.: Distributed Computing: A Locality-Sensitive Approach. Society for Industrial and Applied Mathematics (2000). doi: 10.1137/1.9780898719772
  18. [PNV13]
    Pantazis, N.A., Nikolidakis, S.A., Vergados, D.D.: Energy-efficient routing protocols in wireless sensor networks: a survey. IEEE Commun. Surv. Tutorials 15(2), 551–591 (2013)CrossRefGoogle Scholar
  19. [Tel94]
    Tel, G.: Network orientation. Int. J. Found. Comput. Sci. 5(1), 23–57 (1994)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of Bordeaux, LaBRI, UMR 5800TalenceFrance
  2. 2.CNRS, LaBRI, UMR 5800TalenceFrance

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