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Distributed Construction of Purely Additive Spanners

  • Keren Censor-Hillel
  • Telikepalli Kavitha
  • Ami PazEmail author
  • Amir Yehudayoff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9888)

Abstract

This paper studies the complexity of distributed construction of purely additive spanners in the CONGEST model. We describe algorithms for building such spanners in several cases. Because of the need to simultaneously make decisions at far apart locations, the algorithms use additional mechanisms compared to their sequential counterparts.

We complement our algorithms with a lower bound on the number of rounds required for computing pairwise spanners. The standard reductions from set-disjointness and equality seem unsuitable for this task because no specific edge needs to be removed from the graph. Instead, to obtain our lower bound, we define a new communication complexity problem that reduces to computing a sparse spanner, and prove a lower bound on its communication complexity using information theory. This technique significantly extends the current toolbox used for obtaining lower bounds for the CONGEST model, and we believe it may find additional applications.

Keywords

Cluster Center Wrong Edge Congest Model Graph Spanner Missing Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

We thank Merav Parter for a helpful discussion on the lower bound, and the anonymous referees for helpful comments.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Keren Censor-Hillel
    • 1
  • Telikepalli Kavitha
    • 2
  • Ami Paz
    • 1
    Email author
  • Amir Yehudayoff
    • 3
  1. 1.Department of Computer ScienceTechnionHaifaIsrael
  2. 2.Tata Institute of Fundamental ResearchMumbaiIndia
  3. 3.Department of MathematicsTechnionHaifaIsrael

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