Improved distributed degree splitting and edge coloring
The degree splitting problem requires coloring the edges of a graph red or blue such that each node has almost the same number of edges in each color, up to a small additive discrepancy. The directed variant of the problem requires orienting the edges such that each node has almost the same number o...
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| Vydáno v: | Distributed computing Ročník 33; číslo 3-4; s. 293 - 310 |
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| Hlavní autoři: | , , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.06.2020
Springer Nature B.V |
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| ISSN: | 0178-2770, 1432-0452 |
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| Abstract | The degree splitting problem requires coloring the edges of a graph red or blue such that each node has almost the same number of edges in each color, up to a small additive discrepancy. The directed variant of the problem requires orienting the edges such that each node has almost the same number of incoming and outgoing edges, again up to a small additive discrepancy. We present deterministic distributed algorithms for both variants, which improve on their counterparts presented by Ghaffari and Su (Proc SODA 2017:2505–2523,
2017
): our algorithms are significantly simpler and faster, and have a much smaller discrepancy. This also leads to a faster and simpler deterministic algorithm for
(
2
+
o
(
1
)
)
Δ
-edge-coloring, improving on that of Ghaffari and Su. |
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| AbstractList | The degree splitting problem requires coloring the edges of a graph red or blue such that each node has almost the same number of edges in each color, up to a small additive discrepancy. The directed variant of the problem requires orienting the edges such that each node has almost the same number of incoming and outgoing edges, again up to a small additive discrepancy. We present deterministic distributed algorithms for both variants, which improve on their counterparts presented by Ghaffari and Su (Proc SODA 2017:2505–2523, 2017): our algorithms are significantly simpler and faster, and have a much smaller discrepancy. This also leads to a faster and simpler deterministic algorithm for (2+o(1))Δ-edge-coloring, improving on that of Ghaffari and Su. The degree splitting problem requires coloring the edges of a graph red or blue such that each node has almost the same number of edges in each color, up to a small additive discrepancy. The directed variant of the problem requires orienting the edges such that each node has almost the same number of incoming and outgoing edges, again up to a small additive discrepancy. We present deterministic distributed algorithms for both variants, which improve on their counterparts presented by Ghaffari and Su (Proc SODA 2017:2505–2523, 2017 ): our algorithms are significantly simpler and faster, and have a much smaller discrepancy. This also leads to a faster and simpler deterministic algorithm for ( 2 + o ( 1 ) ) Δ -edge-coloring, improving on that of Ghaffari and Su. |
| Author | Hirvonen, Juho Kuhn, Fabian Maus, Yannic Ghaffari, Mohsen Suomela, Jukka Uitto, Jara |
| Author_xml | – sequence: 1 givenname: Mohsen surname: Ghaffari fullname: Ghaffari, Mohsen organization: ETH Zurich – sequence: 2 givenname: Juho surname: Hirvonen fullname: Hirvonen, Juho organization: Aalto University – sequence: 3 givenname: Fabian surname: Kuhn fullname: Kuhn, Fabian email: kuhn@cs.uni-freiburg.de organization: University of Freiburg – sequence: 4 givenname: Yannic orcidid: 0000-0002-1025-5037 surname: Maus fullname: Maus, Yannic organization: University of Freiburg – sequence: 5 givenname: Jukka surname: Suomela fullname: Suomela, Jukka organization: Aalto University – sequence: 6 givenname: Jara surname: Uitto fullname: Uitto, Jara organization: ETH Zurich, University of Freiburg |
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| Cites_doi | 10.1007/PL00008932 10.1007/11685654_10 10.1137/S0895480100373121 10.1016/0020-0190(86)90141-9 10.1017/CBO9780511626371 10.1016/0166-218X(81)90022-6 10.1017/S0963548315000140 10.1137/1.9780898719772 10.1016/0196-6774(87)90026-5 10.1007/BF01196138 10.1109/FOCS.2018.00069 10.1109/FOCS.2019.00048 |
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| DOI | 10.1007/s00446-018-00346-8 |
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| Keywords | Distributed graph algorithms Degree splitting Discrepancy Edge coloring |
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| References | Chang, Kopelowitz, Pettie (CR6) 2016; 2016 Panconesi, Rizzi (CR21) 2001; 14 Peleg (CR22) 2000 Israeli, Shiloach (CR17) 1986; 22 Beck, Fiala (CR2) 1981; 3 Naor, Stockmeyer (CR20) 1993; 1993 Linial (CR19) 1987; 1987 Chazelle (CR7) 2000 CR16 Dinitz, Goldreich, Rosenberg, Selman (CR9) 2006 Czygrinow, Hańćkowiak, Karoński (CR8) 2001; 2001 CR13 CR12 CR11 CR10 Bednarchak, Helm (CR3) 1997; 17 Bukh (CR5) 2016; 25 Barenboim, Elkin (CR1) 2011; 2011 Brandt, Fischer, Hirvonen, Keller, Lempiäinen, Rybicki, Suomela, Uitto (CR4) 2016; 2016 Ghaffari, Su (CR14) 2017; 2017 Karloff, Shmoys (CR18) 1987; 8 Hańćkowiak, Karoński, Panconesi (CR15) 2001; 15 N Linial (346_CR19) 1987; 1987 Y Dinitz (346_CR9) 2006 A Panconesi (346_CR21) 2001; 14 J Beck (346_CR2) 1981; 3 D Bednarchak (346_CR3) 1997; 17 L Barenboim (346_CR1) 2011; 2011 M Ghaffari (346_CR14) 2017; 2017 M Naor (346_CR20) 1993; 1993 S Brandt (346_CR4) 2016; 2016 YJ Chang (346_CR6) 2016; 2016 M Hańćkowiak (346_CR15) 2001; 15 D Peleg (346_CR22) 2000 B Chazelle (346_CR7) 2000 346_CR10 A Czygrinow (346_CR8) 2001; 2001 346_CR11 HJ Karloff (346_CR18) 1987; 8 346_CR12 346_CR13 B Bukh (346_CR5) 2016; 25 A Israeli (346_CR17) 1986; 22 346_CR16 |
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| SubjectTerms | Algorithms Computer Communication Networks Computer Hardware Computer Science Computer Systems Organization and Communication Networks Graph coloring Graph theory Software Engineering/Programming and Operating Systems Theory of Computation |
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