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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Veröffentlicht in:Distributed computing Jg. 34; H. 4; S. 239 - 258
Hauptverfasser: Ghaffari, Mohsen, Hirvonen, Juho, Kuhn, Fabian, Maus, Yannic
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2021
Springer Nature B.V
Schlagworte:
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
Online-Zugang:Volltext
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Zusammenfassung: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).
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ISSN:0178-2770
1432-0452
DOI:10.1007/s00446-021-00397-4