# Distributed Graph Coloring Made Easy

@article{Maus2021DistributedGC,
author={Yannic Maus},
journal={Proceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures},
year={2021}
}
• Yannic Maus
• Published 12 May 2021
• Computer Science
• Proceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures
In this paper we present a deterministic CONGEST algorithm to compute an O(kΔ)-vertex coloring in O(Δ/k)+łog^* n rounds, where Δ is the maximum degree of the network graph and 1łeq kłeq O(Δ) can be freely chosen. The algorithm is extremely simple: Each node locally computes a sequence of colors and then it "tries colors" from the sequence in batches of size k. Our algorithm subsumes many important results in the history of distributed graph coloring as special cases, including Linial's color…
6 Citations
Distributed ∆-coloring plays hide-and-seek
• Computer Science, Mathematics
STOC
• 2022
Lower bounds as a function of Δ are proved for a large class of distributed symmetry breaking problems, which can all be solved by a simple sequential greedy algorithm, including the maximal independent set (MIS) in trees.
Distributed $\Delta$-Coloring Plays Hide-and-Seek
• Computer Science, Mathematics
• 2021
Lower bounds as a function of ∆ are proved for a large class of distributed symmetry breaking problems, which can all be solved by a simple sequential greedy algorithm.
Improved Distributed Fractional Coloring Algorithms
• Mathematics, Computer Science
OPODIS
• 2021
The fractional coloring problem can be approximated arbitrarily well by an efficient algorithm in the LOCAL model, and it is shown that in regular grids of bounded dimension, a fractional (2 + ε )-coloring can be computed in time O (log ∗ n ).
Brief Announcement: Fault Tolerant Coloring of the Asynchronous Cycle
• Computer Science
PODC
• 2022
A wait-free algorithm for proper coloring the n ≥ 3 nodes of the asynchronous cycle Cn, where each crash-prone node starts with its (unique) identifier as input, and each node terminates upon completing at most O(log*n) write-read-compute steps.
Fault Tolerant Coloring of the Asynchronous Cycle
• Computer Science
ArXiv
• 2022
The model coincides with the shared-memory model whenever 𝑛 = 3, and the minimum number of names for which renaming is possible in 3-process shared- memory systems is 5, which is optimal thanks to a known matching lower bound.
Linial for lists
• Computer Science, Art
Distributed Computing
• 2022
It is shown that when nodes are restricted to choose their color from a list of allowed colors: given an <jats:italic>m-coloring in a directed graph of maximum outdegree, the result is the same as when node selection is restricted.

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