Distributed (δ+1)-coloring in linear (in δ) time

@inproceedings{Barenboim2009DistributedI,
title={Distributed ($\delta$+1)-coloring in linear (in $\delta$) time},
author={Leonid Barenboim and Michael Elkin},
booktitle={STOC '09},
year={2009}
}
• Published in STOC '09 31 May 2009
• Mathematics, Computer Science
The distributed (Δ + 1)-coloring problem is one of most fundamental and well-studied problems in Distributed Algorithms. Starting with the work of Cole and Vishkin in 86, there was a long line of gradually improving algorithms published. The current state-of-the-art running time is O(Δ log Δ + log* n), due to Kuhn and Wattenhofer, PODC'06. Linial (FOCS'87) has proved a lower bound of 1/2 log* n for the problem, and Szegedy and Vishwanathan (STOC'93) provided a heuristic argument that shows that…
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References

SHOWING 1-10 OF 41 REFERENCES
Fast distributed graph coloring with O(Δ) colors
• Mathematics
SODA '01
• 2001
We consider the problem of deterministic distributed coloring of an n-vertex graph with maximum degree Δ, assuming that every vertex knows a priori only its own label and parameters n and Δ. The aim
A new technique for distributed symmetry breaking
• Mathematics, Computer Science
PODC
• 2010
Three randomized algorithms for distributed (vertex or edge) coloring improving on previous algorithms and showing a time/color trade-off are presented, obtaining new results for several graph classes.
Weak graph colorings: distributed algorithms and applications
• F. Kuhn
• Mathematics, Computer Science
SPAA '09
• 2009
A faster deterministic algorithm for the standard vertex coloring problem on graphs with moderate degrees is obtained, it is shown that in time O(Δ+log*n), a (Γ+1)-coloring can be computed, a task for which the best previous algorithm required time O (Δ*log(Γ) + log*n).
Improved distributed algorithms for coloring and network decomposition problems
• Mathematics, Computer Science
STOC '92
• 1992
It is shown that A-coloring G is reducible in 0(log3 n/log A) time to (A+ I)-vertex coloring G in a distributed model, which leads to fast distributed algorithms, and a linear–processor NC algorithm, for Acoloring.
A randomized distributed algorithm for the maximal independent set problem in growth-bounded graphs
• Mathematics, Computer Science
PODC '07
• 2007
The algorithm shows that for computing a MIS, randomization is a viable alternative to distance information and is close to optimal.
Coloring with defect
• Mathematics, Computer Science
SODA '97
• 1997
This paper is concerned with algorithms and complexity results for defective coloring, where a defective (k,d)-coloring is a k coloring of the vertices of a graph such that each vertex is adjacent to
Locality based graph coloring
• Computer Science
STOC '93
• 1993
A randomized algorithm for the problem of locality based graph coloring is designed and an upper bound of O(A. 2A log log n) is proved and lower bounds that match the upper bounds within a factor that is poly-logarithmic are obtained.
On the Complexity of Distributed Network Decomposition
• Mathematics, Computer Science
J. Algorithms
• 1996
In this paper, we improve the bounds for computing a network decomposition distributively and deterministically. Our algorithm computes an (n?(n),n?(n))-decomposition innO(?(n))time, whereformula. As
On the complexity of distributed graph coloring
• Mathematics, Computer Science
PODC '06
• 2006
This paper proves new strong lower bounds for two special kinds of coloring algorithms, and proves a time lower bound of Ω(Δ/log<sup>2</sup> Δ+ log*<i>m</i>) to obtain an <i>O</i>(Δ)-coloring.
A Fast and Simple Randomized Parallel Algorithm for the Maximal Independent Set Problem
• Mathematics, Computer Science
J. Algorithms
• 1986
A technique due to A. Joffe (1974) is applied and deterministic construction in fast parallel time of various combinatorial objects whose existence follows from probabilistic arguments is obtained.