Distributed Delta-Coloring under Bandwidth Limitations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929345680900096 |
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| author | Maus, Yannic Halldórsson, Magnús M. |
| author_facet | Maus, Yannic Halldórsson, Magnús M. |
| contents | We consider the problem of coloring graphs of maximum degree $Δ$ with $Δ$ colors in the distributed setting with limited bandwidth. Specifically, we give a $\mathsf{poly}\log\log n$-round randomized algorithm in the CONGEST model. This is close to the lower bound of $Ω(\log \log n)$ rounds from [Brandt et al., STOC '16], which holds also in the more powerful LOCAL model. The core of our algorithm is a reduction to several special instances of the constructive Lovász local lemma (LLL) and the $deg+1$-list coloring problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09975 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distributed Delta-Coloring under Bandwidth Limitations Maus, Yannic Halldórsson, Magnús M. Data Structures and Algorithms Distributed, Parallel, and Cluster Computing We consider the problem of coloring graphs of maximum degree $Δ$ with $Δ$ colors in the distributed setting with limited bandwidth. Specifically, we give a $\mathsf{poly}\log\log n$-round randomized algorithm in the CONGEST model. This is close to the lower bound of $Ω(\log \log n)$ rounds from [Brandt et al., STOC '16], which holds also in the more powerful LOCAL model. The core of our algorithm is a reduction to several special instances of the constructive Lovász local lemma (LLL) and the $deg+1$-list coloring problem. |
| title | Distributed Delta-Coloring under Bandwidth Limitations |
| topic | Data Structures and Algorithms Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2405.09975 |