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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Bibliographic Details
Published in:Journal of algorithms Vol. 37; no. 1; pp. 85 - 120
Main Authors: Grable, David A, Panconesi, Alessandro
Format: Journal Article Conference Proceeding
Language:English
Published: San Diego, CA Elsevier Inc 01.10.2000
Elsevier
Subjects:
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
Online Access:Get full text
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Summary: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