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Efficient CONGEST Algorithms for the Lovász Local Lemma

Authors Yannic Maus , Jara Uitto

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Author Details

Yannic Maus
  • Technion, Haifa, Israel
Jara Uitto
  • Aalto University, Espoo, Finland

Funding

This project was partially supported by the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement no. 755839 (Yannic Maus).

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Yannic Maus and Jara Uitto. Efficient CONGEST Algorithms for the Lovász Local Lemma. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.DISC.2021.31

Abstract

We present a poly log log n time randomized CONGEST algorithm for a natural class of Lovász Local Lemma (LLL) instances on constant degree graphs. This implies, among other things, that there are no LCL problems with randomized complexity between Ω(log n) and poly log log n. Furthermore, we provide extensions to the network decomposition algorithms given in the recent breakthrough by Rozhoň and Ghaffari [STOC2020] and the follow up by Ghaffari, Grunau, and Rozhoň [SODA2021]. In particular, we show how to obtain a large distance separated weak network decomposition with a negligible dependency on the range of unique identifiers.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • distributed graph algorithms
  • CONGEST
  • Lovász Local Lemma
  • locally checkable labelings

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