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arXiv · 2405.07353

Distributed Lov\'{a}sz Local Lemma under Bandwidth Limitations

Magnús M. Halldórsson·Yannic Maus·Saku Peltonen
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Abstract

The constructive Lov\'{a}sz Local Lemma has become a central tool for designing efficient distributed algorithms. While it has been extensively studied in the classic LOCAL model that uses unlimited bandwidth, much less is known in the bandwidth-restricted CONGEST model. In this paper, we present bandwidth- and time-efficient algorithms for various subclasses of LLL problems, including a large class of subgraph sampling problems that are naturally formulated as LLLs. Lastly, we use our LLLs to design efficient CONGEST algorithms for coloring sparse and triangle-free graphs with few colors. These coloring algorithms are exponentially faster than previous LOCAL model algorithms.

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Magnús M. Halldórsson, Yannic Maus, Saku Peltonen. 2024-05-12. Distributed Lov\'{a}sz Local Lemma under Bandwidth Limitations. https://arxiv.org/abs/2405.07353

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