Fast Distributed Algorithms for Brooks–Vizing Colorings

Let G be a Δ-regular graph with n vertices and girth at least 4 such that Δ⪢logn. We give very simple, randomized, distributed algorithms for vertex coloring G with Δ/k colors in O(k+logn) communication rounds, where k=O(logΔ). The algorithm may fail or exceed the above running time, but the probabi...

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Vydané v:	Journal of algorithms Ročník 37; číslo 1; s. 85 - 120
Hlavní autori:	Grable, David A, Panconesi, Alessandro
Médium:	Journal Article Konferenčný príspevok..
Jazyk:	English
Vydavateľské údaje:	San Diego, CA Elsevier Inc 01.10.2000 Elsevier
Predmet:	Algorithmics. Computability. Computer arithmetics Applied sciences Combinatorics Combinatorics. Ordered structures Computer science; control theory; systems Exact sciences and technology Graph theory Mathematics Sciences and techniques of general use Theoretical computing Bounded variance method Randomization Brooks Vizing like problem Distributed algorithm Graph colouring Graph theory Complexity measure Bounded solution Azuma martingale inequality
ISSN:	0196-6774, 1090-2678
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Popis
Shrnutí:	Let G be a Δ-regular graph with n vertices and girth at least 4 such that Δ⪢logn. We give very simple, randomized, distributed algorithms for vertex coloring G with Δ/k colors in O(k+logn) communication rounds, where k=O(logΔ). The algorithm may fail or exceed the above running time, but the probability that this happens is o(1), a quantity that goes to zero as n grows. The probabilistic analysis relies on a powerful generalization of Azuma's martingale inequality that we dub the Method of Bounded Variances.
ISSN:	0196-6774 1090-2678
DOI:	10.1006/jagm.2000.1097