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arXiv · 2108.02638

Efficient CONGEST Algorithms for the Lovasz Local Lemma

Yannic Maus·Jara Uitto
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Abstract

We present a poly $\log \log n$ time randomized CONGEST algorithm for a natural class of Lovasz Local Lemma (LLL) instances on constant degree graphs. This implies, among other things, that there are no LCL problems with randomized complexity between $\log n$ and poly $\log \log n$. Furthermore, we provide extensions to the network decomposition algorithms given in the recent breakthrough by Rozhon and Ghaffari [STOC2020] and the follow up by Ghaffari, Grunau, and Rozhon [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.

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Yannic Maus, Jara Uitto. 2021-08-05. Efficient CONGEST Algorithms for the Lovasz Local Lemma. https://arxiv.org/abs/2108.02638

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