How much does randomness help with locally checkable problems?

Alkida Balliu, Sebastian Brandt, Dennis Olivetti, Jukka Suomela

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

12 Citations (Scopus)


Locally checkable labeling problems (LCLs) are distributed graph problems in which a solution is globally feasible if it is locally feasible in all constant-radius neighborhoods. Vertex colorings, maximal independent sets, and maximal matchings are examples of LCLs. On the one hand, it is known that some LCLs benefit exponentially from randomness - -for example, any deterministic distributed algorithm that finds a sinkless orientation requires Θ(log n) rounds in the LOCAL model, while the randomized complexity of the problem is Θ(log log n) rounds. On the other hand, there are also many LCLs in which randomness is useless. Previously, it was not known whether there are any LCLs that benefit from randomness, but only subexponentially. We show that such problems exist: for example, there is an LCL with deterministic complexity Θ(log2 n) rounds and randomized complexity Θ(log n log log n) rounds.

Original languageEnglish
Title of host publicationPODC 2020 - Proceedings of the 39th Symposium on Principles of Distributed Computing
Number of pages10
ISBN (Electronic)9781450375825
Publication statusPublished - 31 Jul 2020
MoE publication typeA4 Conference publication
EventACM Symposium on Principles of Distributed Computing - Virtual, Online, Italy
Duration: 3 Aug 20207 Aug 2020
Conference number: 39


ConferenceACM Symposium on Principles of Distributed Computing
Abbreviated titlePODC
CityVirtual, Online


  • distributed computational complexity
  • LOCAL model
  • locally checkable labeling problems


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