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Locally Checkable Labelings with Small Messages

Authors Alkida Balliu , Keren Censor-Hillel, Yannic Maus , Dennis Olivetti , Jukka Suomela



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Author Details

Alkida Balliu
  • Universität Freiburg, Germany
Keren Censor-Hillel
  • Technion, Haifa, Israel
Yannic Maus
  • Technion, Haifa, Israel
Dennis Olivetti
  • Universität Freiburg, Germany
Jukka Suomela
  • Aalto University, Finland

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Alkida Balliu, Keren Censor-Hillel, Yannic Maus, Dennis Olivetti, and Jukka Suomela. Locally Checkable Labelings with Small Messages. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 8:1-8:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.DISC.2021.8

Abstract

A rich line of work has been addressing the computational complexity of locally checkable labelings (LCLs), illustrating the landscape of possible complexities. In this paper, we study the landscape of LCL complexities under bandwidth restrictions. Our main results are twofold. First, we show that on trees, the CONGEST complexity of an LCL problem is asymptotically equal to its complexity in the LOCAL model. An analog statement for non-LCL problems is known to be false. Second, we show that for general graphs this equivalence does not hold, by providing an LCL problem for which we show that it can be solved in O(log n) rounds in the LOCAL model, but requires Ω̃(n^{1/2}) rounds in the CONGEST model.

Subject Classification

ACM Subject Classification
  • Networks → Network algorithms
  • Theory of computation → Distributed algorithms
Keywords
  • distributed graph algorithms
  • CONGEST
  • locally checkable labelings

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