Locally Checkable Labelings with Small Messages

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

Research output: Contribution to conferencePaperpeer-review


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 Ω( n 1/ 2) rounds in the CONGEST model.

Original languageEnglish
Publication statusPublished - 1 Oct 2021
Externally publishedYes
Event35th International Symposium on Distributed Computing: DISC 2021 - Virtual, Freiburg, Germany
Duration: 4 Oct 20218 Oct 2021


Conference35th International Symposium on Distributed Computing
CityVirtual, Freiburg


  • Distributed graph algorithms
  • Locally checkable labelings

ASJC Scopus subject areas

  • Software


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