$(Δ+ 1)$ Vertex Coloring in $O(n)$ Communication
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929652805664768 |
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| author | Flin, Maxime Mittal, Parth |
| author_facet | Flin, Maxime Mittal, Parth |
| contents | We study the communication complexity of $(Δ+ 1)$ vertex coloring, where the edges of an $n$-vertex graph of maximum degree $Δ$ are partitioned between two players. We provide a randomized protocol which uses $O(n)$ bits of communication and ends with both players knowing the coloring. Combining this with a folklore $Ω(n)$ lower bound, this settles the randomized communication complexity of $(Δ+ 1)$-coloring up to constant factors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19081 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $(Δ+ 1)$ Vertex Coloring in $O(n)$ Communication Flin, Maxime Mittal, Parth Data Structures and Algorithms We study the communication complexity of $(Δ+ 1)$ vertex coloring, where the edges of an $n$-vertex graph of maximum degree $Δ$ are partitioned between two players. We provide a randomized protocol which uses $O(n)$ bits of communication and ends with both players knowing the coloring. Combining this with a folklore $Ω(n)$ lower bound, this settles the randomized communication complexity of $(Δ+ 1)$-coloring up to constant factors. |
| title | $(Δ+ 1)$ Vertex Coloring in $O(n)$ Communication |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2404.19081 |