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Message Reduction in the LOCAL Model Is a Free Lunch

Authors Shimon Bitton, Yuval Emek, Taisuke Izumi, Shay Kutten

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Subject Classification

ACM Subject Classification
  • Theory of computation → Sparsification and spanners
  • Theory of computation → Distributed algorithms
Keywords
  • distributed graph algorithms
  • spanner
  • LOCAL model
  • message complexity

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Abstract

A new spanner construction algorithm is presented, working under the LOCAL model with unique edge IDs. Given an n-node communication graph, a spanner with a constant stretch and O(n^{1 + epsilon}) edges (for an arbitrarily small constant epsilon > 0) is constructed in a constant number of rounds sending O(n^{1 + epsilon}) messages whp. Consequently, we conclude that every t-round LOCAL algorithm can be transformed into an O(t)-round LOCAL algorithm that sends O(t * n^{1 + epsilon}) messages whp. This improves upon all previous message-reduction schemes for LOCAL algorithms that incur a log^{Omega (1)} n blow-up of the round complexity.

Cite As Get BibTex

Shimon Bitton, Yuval Emek, Taisuke Izumi, and Shay Kutten. Message Reduction in the LOCAL Model Is a Free Lunch. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.DISC.2019.7

Author Details

Shimon Bitton
  • Technion - Israel Institute of Technology, Haifa, Israel
Yuval Emek
  • Technion - Israel Institute of Technology, Haifa, Israel
Taisuke Izumi
  • Nagoya Institute of Technology, Japan
Shay Kutten
  • Technion - Israel Institute of Technology, Haifa, Israel

Funding

  • Emek, Yuval: This work has been funded in part by an Israeli Ministry of Science and Technology grant number 3-13565.
  • Izumi, Taisuke: This work was supported by JST SICORP Grant Number JPMJSC1606 and JSPS KAKENHI Grant Number JP19K11824, Japan.
  • Kutten, Shay: This work has been funded in part by an Israeli Ministry of Science and Technology grant number 3-13565.

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