English

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

Data Structures and Algorithms 2024-05-14 v1 Distributed, Parallel, and Cluster Computing

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.

Keywords

Cite

@article{arxiv.2405.07353,
  title  = {Distributed Lov\'{a}sz Local Lemma under Bandwidth Limitations},
  author = {Magnús M. Halldórsson and Yannic Maus and Saku Peltonen},
  journal= {arXiv preprint arXiv:2405.07353},
  year   = {2024}
}
R2 v1 2026-06-28T16:24:42.637Z