A fast distributed algorithm for (Δ + 1)-edge-coloring
We present a deterministic distributed algorithm in the LOCAL model that finds a proper (Δ+1)-edge-coloring of an n-vertex graph of maximum degree Δ in poly(Δ,logn) rounds. This is the first nontrivial distributed edge-coloring algorithm that uses only Δ+1 colors (matching the bound given by Vizing...
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| Veröffentlicht in: | Journal of combinatorial theory. Series B Jg. 152; S. 319 - 352 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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01.01.2022
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| ISSN: | 0095-8956, 1096-0902 |
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| Abstract | We present a deterministic distributed algorithm in the LOCAL model that finds a proper (Δ+1)-edge-coloring of an n-vertex graph of maximum degree Δ in poly(Δ,logn) rounds. This is the first nontrivial distributed edge-coloring algorithm that uses only Δ+1 colors (matching the bound given by Vizing's theorem). Our approach is inspired by the recent proof of the measurable version of Vizing's theorem due to Grebík and Pikhurko. |
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| AbstractList | We present a deterministic distributed algorithm in the LOCAL model that finds a proper (Δ+1)-edge-coloring of an n-vertex graph of maximum degree Δ in poly(Δ,logn) rounds. This is the first nontrivial distributed edge-coloring algorithm that uses only Δ+1 colors (matching the bound given by Vizing's theorem). Our approach is inspired by the recent proof of the measurable version of Vizing's theorem due to Grebík and Pikhurko. |
| Author | Bernshteyn, Anton |
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| Cites_doi | 10.1007/978-3-031-02009-4 10.1137/0215074 10.1137/0401044 10.1016/0196-6774(86)90019-2 10.1137/0221015 |
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| Keywords | Edge-coloring LOCAL model Vizing's theorem Distributed algorithms |
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| References | Bernshteyn (br0040) 2021 Chang, He, Li, Pettie, Uitto (br0050) 2018 Linial (br0140) 1992; 21 Harris (br0120) 2019 Ghaffari, Kuhn, Maus, Uitto (br0090) 2018 Pikhurko (br0160) 2020 Fischer, Ghaffari, Kuhn (br0070) 2017 Rozhoň, Ghaffari (br0170) 2020 Stiebitz, Scheide, Toft, Favrholdt (br0180) 2012 Diestel (br0060) 2017 Grebík, Pikhurko (br0110) 2020; 374 Kechris, Marks (br0130) 2019 Su, Vu (br0190) 2019 Luby (br0150) 1986; 15 Barenboim, Elkin (br0020) 2013 Ghaffari, Harris, Kuhn (br0080) 2018 Vizing (br0200) 1964; 3 Goldberg, Plotkin, Shannon (br0100) 1988; 1 Alon, Babai, Itai (br0010) 1986; 7 Bernshteyn (br0030) 2020 Luby (10.1016/j.jctb.2021.10.004_br0150) 1986; 15 Goldberg (10.1016/j.jctb.2021.10.004_br0100) 1988; 1 Diestel (10.1016/j.jctb.2021.10.004_br0060) 2017 Alon (10.1016/j.jctb.2021.10.004_br0010) 1986; 7 Bernshteyn (10.1016/j.jctb.2021.10.004_br0030) Chang (10.1016/j.jctb.2021.10.004_br0050) 2018 Bernshteyn (10.1016/j.jctb.2021.10.004_br0040) Fischer (10.1016/j.jctb.2021.10.004_br0070) 2017 Grebík (10.1016/j.jctb.2021.10.004_br0110) 2020; 374 Linial (10.1016/j.jctb.2021.10.004_br0140) 1992; 21 Stiebitz (10.1016/j.jctb.2021.10.004_br0180) 2012 Vizing (10.1016/j.jctb.2021.10.004_br0200) 1964; 3 Ghaffari (10.1016/j.jctb.2021.10.004_br0090) 2018 Barenboim (10.1016/j.jctb.2021.10.004_br0020) 2013 Harris (10.1016/j.jctb.2021.10.004_br0120) 2019 Pikhurko (10.1016/j.jctb.2021.10.004_br0160) Ghaffari (10.1016/j.jctb.2021.10.004_br0080) 2018 Kechris (10.1016/j.jctb.2021.10.004_br0130) Su (10.1016/j.jctb.2021.10.004_br0190) 2019 Rozhoň (10.1016/j.jctb.2021.10.004_br0170) 2020 |
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| Snippet | We present a deterministic distributed algorithm in the LOCAL model that finds a proper (Δ+1)-edge-coloring of an n-vertex graph of maximum degree Δ in... |
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| SubjectTerms | Distributed algorithms Edge-coloring LOCAL model Vizing's theorem |
| Title | A fast distributed algorithm for (Δ + 1)-edge-coloring |
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