Distributed Computing

, Volume 26, Issue 5–6, pp 289–308

Toward more localized local algorithms: removing assumptions concerning global knowledge

  • Amos Korman
  • Jean-Sébastien Sereni
  • Laurent Viennot
Article

Abstract

Numerous sophisticated local algorithm were suggested in the literature for various fundamental problems. Notable examples are the MIS and \((\Delta +1)\)-coloring algorithms by Barenboim and Elkin (Distrib Comput 22(5–6):363–379, 2010), by Kuhn (2009), and by Panconesi and Srinivasan (J Algorithms 20(2):356–374, 1996), as well as the \(O\mathopen {}(\Delta ^2)\)-coloring algorithm by Linial (J Comput 21:193, 1992). Unfortunately, most known local algorithms (including, in particular, the aforementioned algorithms) are non-uniform, that is, local algorithms generally use good estimations of one or more global parameters of the network, e.g., the maximum degree \(\Delta \) or the number of nodes \(n\). This paper provides a method for transforming a non-uniform local algorithm into a uniform one. Furthermore, the resulting algorithm enjoys the same asymptotic running time as the original non-uniform algorithm. Our method applies to a wide family of both deterministic and randomized algorithms. Specifically, it applies to almost all state of the art non-uniform algorithms for MIS and Maximal Matching, as well as to many results concerning the coloring problem (In particular, it applies to all aforementioned algorithms). To obtain our transformations we introduce a new distributed tool called pruning algorithms, which we believe may be of independent interest.

Keywords

Distributed algorithm Global knowledge Parameters MIS Coloring Maximal matching 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Amos Korman
    • 1
  • Jean-Sébastien Sereni
    • 1
    • 2
  • Laurent Viennot
    • 3
  1. 1.CNRS and Université Paris Diderot Paris Cedex 13France
  2. 2.Department of Applied Mathematics (KAM), Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic
  3. 3.INRIA and Université Paris Diderot Paris Cedex 13France

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