Improved distributed Δ-coloring

We present a randomized distributed algorithm that computes a Δ -coloring in any non-complete graph with maximum degree Δ ≥ 4 in O ( log Δ ) + 2 O ( log log n ) rounds, as well as a randomized algorithm that computes a Δ -coloring in O ( ( log log n ) 2 ) rounds when Δ ∈ [ 3 , O ( 1 ) ] . Both these...

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Published in:	Distributed computing Vol. 34; no. 4; pp. 239 - 258
Main Authors:	Ghaffari, Mohsen, Hirvonen, Juho, Kuhn, Fabian, Maus, Yannic
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2021 Springer Nature B.V
Subjects:	Algorithms Coloring Computer Communication Networks Computer Hardware Computer Science Computer Systems Organization and Communication Networks Lower bounds Software Engineering/Programming and Operating Systems Theory of Computation
ISSN:	0178-2770, 1432-0452
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Abstract	We present a randomized distributed algorithm that computes a Δ -coloring in any non-complete graph with maximum degree Δ ≥ 4 in O ( log Δ ) + 2 O ( log log n ) rounds, as well as a randomized algorithm that computes a Δ -coloring in O ( ( log log n ) 2 ) rounds when Δ ∈ [ 3 , O ( 1 ) ] . Both these algorithms improve on an O ( log 3 n / log Δ ) -round algorithm of Panconesi and Srinivasan (STOC’93), which has remained the state of the art for the past 25 years. Moreover, the latter algorithm gets (exponentially) closer to an Ω ( log log n ) round lower bound of Brandt et al. (STOC’16).
AbstractList	We present a randomized distributed algorithm that computes a Δ -coloring in any non-complete graph with maximum degree Δ ≥ 4 in O ( log Δ ) + 2 O ( log log n ) rounds, as well as a randomized algorithm that computes a Δ -coloring in O ( ( log log n ) 2 ) rounds when Δ ∈ [ 3 , O ( 1 ) ] . Both these algorithms improve on an O ( log 3 n / log Δ ) -round algorithm of Panconesi and Srinivasan (STOC’93), which has remained the state of the art for the past 25 years. Moreover, the latter algorithm gets (exponentially) closer to an Ω ( log log n ) round lower bound of Brandt et al. (STOC’16). We present a randomized distributed algorithm that computes a Δ -coloring in any non-complete graph with maximum degree Δ ≥ 4 in O ( log Δ ) + 2 O ( log log n ) rounds, as well as a randomized algorithm that computes a Δ -coloring in O ( ( log log n ) 2 ) rounds when Δ ∈ [ 3 , O ( 1 ) ] . Both these algorithms improve on an O ( log 3 n / log Δ ) -round algorithm of Panconesi and Srinivasan (STOC'93), which has remained the state of the art for the past 25 years. Moreover, the latter algorithm gets (exponentially) closer to an Ω ( log log n ) round lower bound of Brandt et al. (STOC'16).We present a randomized distributed algorithm that computes a Δ -coloring in any non-complete graph with maximum degree Δ ≥ 4 in O ( log Δ ) + 2 O ( log log n ) rounds, as well as a randomized algorithm that computes a Δ -coloring in O ( ( log log n ) 2 ) rounds when Δ ∈ [ 3 , O ( 1 ) ] . Both these algorithms improve on an O ( log 3 n / log Δ ) -round algorithm of Panconesi and Srinivasan (STOC'93), which has remained the state of the art for the past 25 years. Moreover, the latter algorithm gets (exponentially) closer to an Ω ( log log n ) round lower bound of Brandt et al. (STOC'16). We present a randomized distributed algorithm that computes a Δ-coloring in any non-complete graph with maximum degree Δ≥4 in O(logΔ)+2O(loglogn) rounds, as well as a randomized algorithm that computes a Δ-coloring in O((loglogn)2) rounds when Δ∈[3,O(1)]. Both these algorithms improve on an O(log3n/logΔ)-round algorithm of Panconesi and Srinivasan (STOC’93), which has remained the state of the art for the past 25 years. Moreover, the latter algorithm gets (exponentially) closer to an Ω(loglogn) round lower bound of Brandt et al. (STOC’16). We present a randomized distributed algorithm that computes a $$\Delta $$ Δ -coloring in any non-complete graph with maximum degree $$\Delta \ge 4$$ Δ ≥ 4 in $$O(\log \Delta ) + 2^{O(\sqrt{\log \log n})}$$ O ( log Δ ) + 2 O ( log log n ) rounds, as well as a randomized algorithm that computes a $$\Delta $$ Δ -coloring in $$O((\log \log n)^2)$$ O ( ( log log n ) 2 ) rounds when $$\Delta \in [3, O(1)]$$ Δ ∈ [ 3 , O ( 1 ) ] . Both these algorithms improve on an $$O(\log ^3 n / \log \Delta )$$ O ( log 3 n / log Δ ) -round algorithm of Panconesi and Srinivasan (STOC’93), which has remained the state of the art for the past 25 years. Moreover, the latter algorithm gets (exponentially) closer to an $$\Omega (\log \log n)$$ Ω ( log log n ) round lower bound of Brandt et al. (STOC’16).
Author	Hirvonen, Juho Kuhn, Fabian Maus, Yannic Ghaffari, Mohsen
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 orcidid: 0000-0002-1025-5037 surname: Kuhn fullname: Kuhn, Fabian email: kuhn@cs.uni-freiburg.de organization: University of Freiburg – sequence: 4 givenname: Yannic surname: Maus fullname: Maus, Yannic organization: Technion
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References	Erdős, P., Rubin, A., Taylor, H.: Choosability in graphs. In: Proceedings of West Coast Conference on Combinatorics, Graph Theory and Computing, vol. 26, pp. 125–157. Congressus Numerantium (1979) Chang, Y.-J., Li, W., Pettie, S.: An optimal distributed (Δ+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta + 1$$\end{document})-coloring algorithm? In: Proceedings 50th ACM Symposium on Theory of Computing (STOC 2018) (to appear) (2018) Rozhoň, V., Ghaffari, M.: Polylogarithmic-time deterministic network decomposition and distributed derandomization. In: Proceedings of the ACM Symposium on Theory of Computing (STOC), pp. 350–363 (2020) Aboulker, P., Bonamy, M., Bousquet, N., Esperet, L.: Distributed coloring in sparse graphs with fewer colors. In: Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, PODC 2018, Egham, UK, 23–27, 2018, pp. 419–425 (2018) Peleg, D.: Distributed Computing: A Locality-Sensitive Approach. SIAM (2000) Awerbuch, B., Goldberg, A.V., Luby, M., Plotkin, S.A.: Network decomposition and locality in distributed computation. In: Proceedings of 30th Symposium on Foundations of Computer Science (FOCS 1989), pp. 364–369 (1989) Bondy, J.A., Murty, U.: Graph Theory with Applications. Elsevier (1976) Ghaffari, M., Su, H.-H.: Distributed degree splitting, edge coloring, and orientations. In: Proceedings of 28th ACM-SIAM Symposium on Discrete Algorithms (SODA 2017), pp. 2505–2523. Society for Industrial and Applied Mathematics (2017) Chang, Y.-J., Kopelowitz, T., Pettie, S.: An exponential separation between randomized and deterministic complexity in the local model. In: Proceedings of 57th Symposium on Foundations of Computer Science (FOCS 2016), pp. 615–624. IEEE (2016) AlonNBabaiLItaiAA fast and simple randomized parallel algorithm for the maximal independent set problemJ. Algorithms19867456758386679210.1016/0196-6774(86)90019-2 CranstonDWRabernLBrooks’ theorem and beyondJ. Graph Theory2015803199225340372610.1002/jgt.21847 BrooksRLOn colouring the nodes of a networkMath. Proc. Camb. Philos. Soc.19413721941971223610.1017/S030500410002168X Leonard Brooks, R.: On colouring the nodes of a network. In: Classic Papers in Combinatorics, pp. 118–121. Springer (2009) Kuhn, F.: Faster deterministic distributed coloring through recursive list coloring. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1244–1259 (2020) Ghaffari, M., Kuhn, F., Maus, Y.: On the complexity of local distributed graph problems. In: Proceedings of 49th ACM Symposium on Theory of Computing (STOC 2017), pp. 784–797. ACM (2017) Panconesi, A., Srinivasan, A.: Improved distributed algorithms for coloring and network decomposition problems. In: Proceedings of 24th ACM Symposium on Theory of Computing (STOC 1992), pp. 581–592. ACM (1992) Ghaffari, M.: An improved distributed algorithm for maximal independent set. In: Proceedings of 27th ACM-SIAM Symposium on Discrete Algorithms (SODA 2016), pp. 270–277 (2016) Barenboim, L., Elkin, M., Goldenberg, U.: Locally-iterative distributed (Δ+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta +1$$\end{document})-coloring below szegedy-vishwanathan barrier, and applications to self-stabilization and to restricted-bandwidth models. In: Proceedings of 37th ACM Symposium on Principles of Distributed Computing (PODC 2018) (to appear) (2018) Brandt, S., Fischer, O., Hirvonen, J., Keller, B., Lempiäinen, T., Rybicki, J., Suomela, J., Uitto, J.: A lower bound for the distributed Lovász local lemma. In: Proceedings of 48th ACM Symposium on Theory of Computing (STOC 2016), pp. 479–488. ACM (2016) Fischer, M., Ghaffari, M.: Sublogarithmic distributed algorithms for Lovász local lemma, and the complexity hierarchy. In: Proceedings of the International Symposium on Distributed Computing (DISC), pp. 18:1–18:16 (2017) Barenboim, L., Elkin, M., Pettie, S., Schneider, J.: The locality of distributed symmetry breaking. In: Proceedings of 53rd Symposium on Foundations of Computer Science (FOCS 2012), pp. 321–330 (2012) Harris, D.G., Schneider, J., Su, H.-H.: Distributed (Δ+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta }+ 1$$\end{document})-coloring in sublogarithmic rounds. In: Proceedings of 48th ACM Symposium on Theory of Computing (STOC 2016) pp. 465–478. ACM (2016) Maus, Y., Tonoyan, T.: Local conflict coloring revisited: linial for lists. In: Proceedings of the International Symposium on Distributed Computing (DISC), pp. 16:1–16:18 (2020) Gfeller, B., Vicari, E.: A randomized distributed algorithm for the maximal independent set problem in growth-bounded graphs. In: Proceedings of 26th ACM Symposium on Principles of Distributed Computing (PODC 2007), pp. 53–60, New York, NY, USA (2007). ACM LubyMA simple parallel algorithm for the maximal independent set problemSIAM J. Comput.19861541036105386136910.1137/0215074 Molloy, M., Reed, B.: Graph Colouring and the Probabilistic Method, vol. 23. Springer (2013) PanconesiASrinivasanAThe local nature of Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta $$\end{document}-coloring and its algorithmic applicationsCombinatorica1995152255280133735710.1007/BF01200759 LovászLThree short proofs in graph theoryJ. Combin. Theory Ser. B197519326927139634410.1016/0095-8956(75)90089-1 BarenboimLElkinMPettieSSchneiderJThe locality of distributed symmetry breakingJ. ACM20166332012045354953010.1145/2903137 VizingVVextex coloring with given colorsMetody Diskretn. Anal.197629310 SchneiderJElkinMWattenhoferRSymmetry breaking depending on the chromatic number or the neighborhood growthTheoret. Comput. Sci.20135094050312345710.1016/j.tcs.2012.09.004 Fraigniaud, P., Heinrich, M., Kosowski, A.: Local conflict coloring. In: Proceedings of 57th Symposium on Foundations of Computer Science (FOCS 2016), pp. 625–634 (2016) BarenboimLElkinMDistributed graph coloring: fundamentals and recent developmentsSynth. Lect. Distrib. Comput. Theory201341117110.2200/S00520ED1V01Y201307DCT011 Chechik, S., Mukhtar, D.: Optimal distributed coloring algorithms for planar graphs in the local model. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), SODA’19, pp. 787–804 (2019) LinialNLocality in distributed graph algorithmsSIAM J. Comput.1992211193201114882510.1137/0221015 A Panconesi (397_CR31) 1995; 15 L Barenboim (397_CR7) 2016; 63 397_CR21 397_CR22 397_CR23 397_CR24 397_CR20 397_CR18 397_CR19 L Lovász (397_CR26) 1975; 19 397_CR14 397_CR16 V Vizing (397_CR35) 1976; 29 397_CR17 N Alon (397_CR2) 1986; 7 N Linial (397_CR25) 1992; 21 397_CR1 397_CR3 J Schneider (397_CR34) 2013; 509 397_CR32 397_CR9 397_CR11 DW Cranston (397_CR15) 2015; 80 397_CR33 397_CR12 397_CR13 397_CR6 397_CR5 397_CR8 397_CR30 397_CR29 M Luby (397_CR27) 1986; 15 397_CR28 L Barenboim (397_CR4) 2013; 4 RL Brooks (397_CR10) 1941; 37
References_xml	– reference: VizingVVextex coloring with given colorsMetody Diskretn. Anal.197629310 – reference: BarenboimLElkinMPettieSSchneiderJThe locality of distributed symmetry breakingJ. ACM20166332012045354953010.1145/2903137 – reference: Peleg, D.: Distributed Computing: A Locality-Sensitive Approach. SIAM (2000) – reference: Erdős, P., Rubin, A., Taylor, H.: Choosability in graphs. In: Proceedings of West Coast Conference on Combinatorics, Graph Theory and Computing, vol. 26, pp. 125–157. Congressus Numerantium (1979) – reference: Barenboim, L., Elkin, M., Pettie, S., Schneider, J.: The locality of distributed symmetry breaking. In: Proceedings of 53rd Symposium on Foundations of Computer Science (FOCS 2012), pp. 321–330 (2012) – reference: Aboulker, P., Bonamy, M., Bousquet, N., Esperet, L.: Distributed coloring in sparse graphs with fewer colors. In: Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, PODC 2018, Egham, UK, 23–27, 2018, pp. 419–425 (2018) – reference: BarenboimLElkinMDistributed graph coloring: fundamentals and recent developmentsSynth. Lect. Distrib. Comput. Theory201341117110.2200/S00520ED1V01Y201307DCT011 – reference: Molloy, M., Reed, B.: Graph Colouring and the Probabilistic Method, vol. 23. Springer (2013) – reference: Panconesi, A., Srinivasan, A.: Improved distributed algorithms for coloring and network decomposition problems. In: Proceedings of 24th ACM Symposium on Theory of Computing (STOC 1992), pp. 581–592. ACM (1992) – reference: Gfeller, B., Vicari, E.: A randomized distributed algorithm for the maximal independent set problem in growth-bounded graphs. In: Proceedings of 26th ACM Symposium on Principles of Distributed Computing (PODC 2007), pp. 53–60, New York, NY, USA (2007). ACM – reference: LovászLThree short proofs in graph theoryJ. Combin. Theory Ser. B197519326927139634410.1016/0095-8956(75)90089-1 – reference: Chechik, S., Mukhtar, D.: Optimal distributed coloring algorithms for planar graphs in the local model. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), SODA’19, pp. 787–804 (2019) – reference: Ghaffari, M.: An improved distributed algorithm for maximal independent set. In: Proceedings of 27th ACM-SIAM Symposium on Discrete Algorithms (SODA 2016), pp. 270–277 (2016) – reference: Ghaffari, M., Su, H.-H.: Distributed degree splitting, edge coloring, and orientations. In: Proceedings of 28th ACM-SIAM Symposium on Discrete Algorithms (SODA 2017), pp. 2505–2523. Society for Industrial and Applied Mathematics (2017) – reference: Maus, Y., Tonoyan, T.: Local conflict coloring revisited: linial for lists. In: Proceedings of the International Symposium on Distributed Computing (DISC), pp. 16:1–16:18 (2020) – reference: AlonNBabaiLItaiAA fast and simple randomized parallel algorithm for the maximal independent set problemJ. Algorithms19867456758386679210.1016/0196-6774(86)90019-2 – reference: CranstonDWRabernLBrooks’ theorem and beyondJ. Graph Theory2015803199225340372610.1002/jgt.21847 – reference: Rozhoň, V., Ghaffari, M.: Polylogarithmic-time deterministic network decomposition and distributed derandomization. In: Proceedings of the ACM Symposium on Theory of Computing (STOC), pp. 350–363 (2020) – reference: Chang, Y.-J., Kopelowitz, T., Pettie, S.: An exponential separation between randomized and deterministic complexity in the local model. In: Proceedings of 57th Symposium on Foundations of Computer Science (FOCS 2016), pp. 615–624. IEEE (2016) – reference: Fischer, M., Ghaffari, M.: Sublogarithmic distributed algorithms for Lovász local lemma, and the complexity hierarchy. In: Proceedings of the International Symposium on Distributed Computing (DISC), pp. 18:1–18:16 (2017) – reference: LinialNLocality in distributed graph algorithmsSIAM J. Comput.1992211193201114882510.1137/0221015 – reference: Fraigniaud, P., Heinrich, M., Kosowski, A.: Local conflict coloring. In: Proceedings of 57th Symposium on Foundations of Computer Science (FOCS 2016), pp. 625–634 (2016) – reference: LubyMA simple parallel algorithm for the maximal independent set problemSIAM J. Comput.19861541036105386136910.1137/0215074 – reference: Barenboim, L., Elkin, M., Goldenberg, U.: Locally-iterative distributed (Δ+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta +1$$\end{document})-coloring below szegedy-vishwanathan barrier, and applications to self-stabilization and to restricted-bandwidth models. In: Proceedings of 37th ACM Symposium on Principles of Distributed Computing (PODC 2018) (to appear) (2018) – reference: Brandt, S., Fischer, O., Hirvonen, J., Keller, B., Lempiäinen, T., Rybicki, J., Suomela, J., Uitto, J.: A lower bound for the distributed Lovász local lemma. In: Proceedings of 48th ACM Symposium on Theory of Computing (STOC 2016), pp. 479–488. ACM (2016) – reference: Kuhn, F.: Faster deterministic distributed coloring through recursive list coloring. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1244–1259 (2020) – reference: BrooksRLOn colouring the nodes of a networkMath. Proc. Camb. Philos. Soc.19413721941971223610.1017/S030500410002168X – reference: Harris, D.G., Schneider, J., Su, H.-H.: Distributed (Δ+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta }+ 1$$\end{document})-coloring in sublogarithmic rounds. In: Proceedings of 48th ACM Symposium on Theory of Computing (STOC 2016) pp. 465–478. ACM (2016) – reference: Ghaffari, M., Kuhn, F., Maus, Y.: On the complexity of local distributed graph problems. In: Proceedings of 49th ACM Symposium on Theory of Computing (STOC 2017), pp. 784–797. ACM (2017) – reference: Awerbuch, B., Goldberg, A.V., Luby, M., Plotkin, S.A.: Network decomposition and locality in distributed computation. In: Proceedings of 30th Symposium on Foundations of Computer Science (FOCS 1989), pp. 364–369 (1989) – reference: Chang, Y.-J., Li, W., Pettie, S.: An optimal distributed (Δ+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta + 1$$\end{document})-coloring algorithm? In: Proceedings 50th ACM Symposium on Theory of Computing (STOC 2018) (to appear) (2018) – reference: PanconesiASrinivasanAThe local nature of Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta $$\end{document}-coloring and its algorithmic applicationsCombinatorica1995152255280133735710.1007/BF01200759 – reference: SchneiderJElkinMWattenhoferRSymmetry breaking depending on the chromatic number or the neighborhood growthTheoret. Comput. Sci.20135094050312345710.1016/j.tcs.2012.09.004 – reference: Bondy, J.A., Murty, U.: Graph Theory with Applications. Elsevier (1976) – reference: Leonard Brooks, R.: On colouring the nodes of a network. In: Classic Papers in Combinatorics, pp. 118–121. Springer (2009) – ident: 397_CR23 doi: 10.1145/2897518.2897533 – volume: 19 start-page: 269 issue: 3 year: 1975 ident: 397_CR26 publication-title: J. Combin. Theory Ser. B doi: 10.1016/0095-8956(75)90089-1 – volume: 37 start-page: 194 issue: 2 year: 1941 ident: 397_CR10 publication-title: Math. Proc. Camb. Philos. Soc. doi: 10.1017/S030500410002168X – ident: 397_CR6 doi: 10.1109/FOCS.2012.60 – ident: 397_CR29 – ident: 397_CR5 doi: 10.1145/3212734.3212769 – ident: 397_CR22 doi: 10.1137/1.9781611974782.166 – ident: 397_CR30 doi: 10.1145/129712.129769 – volume: 80 start-page: 199 issue: 3 year: 2015 ident: 397_CR15 publication-title: J. Graph Theory doi: 10.1002/jgt.21847 – ident: 397_CR12 doi: 10.1109/FOCS.2016.72 – ident: 397_CR8 doi: 10.1007/978-1-349-03521-2 – volume: 63 start-page: 201 issue: 3 year: 2016 ident: 397_CR7 publication-title: J. ACM doi: 10.1145/2903137 – ident: 397_CR32 doi: 10.1137/1.9780898719772 – ident: 397_CR33 doi: 10.1145/3357713.3384298 – volume: 509 start-page: 40 year: 2013 ident: 397_CR34 publication-title: Theoret. Comput. Sci. doi: 10.1016/j.tcs.2012.09.004 – ident: 397_CR3 doi: 10.1109/SFCS.1989.63504 – ident: 397_CR19 doi: 10.1145/1281100.1281111 – ident: 397_CR18 doi: 10.1109/FOCS.2016.73 – volume: 29 start-page: 3 year: 1976 ident: 397_CR35 publication-title: Metody Diskretn. Anal. – ident: 397_CR16 – ident: 397_CR9 doi: 10.1145/2897518.2897570 – ident: 397_CR21 doi: 10.1145/3055399.3055471 – ident: 397_CR13 doi: 10.1145/3188745.3188964 – volume: 15 start-page: 255 issue: 2 year: 1995 ident: 397_CR31 publication-title: Combinatorica doi: 10.1007/BF01200759 – volume: 7 start-page: 567 issue: 4 year: 1986 ident: 397_CR2 publication-title: J. Algorithms doi: 10.1016/0196-6774(86)90019-2 – ident: 397_CR24 doi: 10.1137/1.9781611975994.76 – volume: 21 start-page: 193 issue: 1 year: 1992 ident: 397_CR25 publication-title: SIAM J. Comput. doi: 10.1137/0221015 – volume: 4 start-page: 1 issue: 1 year: 2013 ident: 397_CR4 publication-title: Synth. Lect. Distrib. Comput. Theory doi: 10.2200/S00520ED1V01Y201307DCT011 – ident: 397_CR11 doi: 10.1007/978-0-8176-4842-8_7 – ident: 397_CR28 – ident: 397_CR20 doi: 10.1137/1.9781611974331.ch20 – volume: 15 start-page: 1036 issue: 4 year: 1986 ident: 397_CR27 publication-title: SIAM J. Comput. doi: 10.1137/0215074 – ident: 397_CR14 doi: 10.1137/1.9781611975482.49 – ident: 397_CR17 – ident: 397_CR1 doi: 10.1145/3212734.3212740
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Snippet	We present a randomized distributed algorithm that computes a Δ -coloring in any non-complete graph with maximum degree Δ ≥ 4 in O ( log Δ ) + 2 O ( log log n... We present a randomized distributed algorithm that computes a $$\Delta $$ Δ -coloring in any non-complete graph with maximum degree $$\Delta \ge 4$$ Δ ≥ 4 in... We present a randomized distributed algorithm that computes a Δ-coloring in any non-complete graph with maximum degree Δ≥4 in O(logΔ)+2O(loglogn) rounds, as... We present a randomized distributed algorithm that computes a Δ -coloring in any non-complete graph with maximum degree Δ ≥ 4 in O ( log Δ ) + 2 O ( log log n...
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SubjectTerms	Algorithms Coloring Computer Communication Networks Computer Hardware Computer Science Computer Systems Organization and Communication Networks Lower bounds Software Engineering/Programming and Operating Systems Theory of Computation
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