# Distance-2 Coloring in the CONGEST Model

@article{Halldrsson2020Distance2CI,
title={Distance-2 Coloring in the CONGEST Model},
author={M. Halld{\'o}rsson and F. Kuhn and Yannic Maus},
journal={Proceedings of the 39th Symposium on Principles of Distributed Computing},
year={2020}
}
• Published 2020
• Computer Science
• Proceedings of the 39th Symposium on Principles of Distributed Computing
We give efficient randomized and deterministic distributed algorithms for computing a distance-2 vertex coloring of a graph G in the CONGEST model. In particular, if Δ is the maximum degree of G, we show that there is a randomized CONGEST model algorithm to compute a distance-2 coloring of G with Δ2 + 1 colors in O(log Δ · log n) rounds. Further if the number of colors is slightly increased to (1 + ∈)Δ2 for some ∈ > 1/polylog n, we show that it is even possible to compute a distance-2 coloring… Expand
4 Citations

#### Topics from this paper

Distributed Testing of Distance-k Colorings
• Computer Science, Mathematics
• SIROCCO
• 2020
It is shown that for one natural farness measure, significantly better algorithms are possible for testing distance-3 coloring than for testingdistance-k coloring for $$k \ge 4$$, and it is also shown that several farness criteria for measuring the distance to a valid coloring are considered. Expand
Efficient CONGEST Algorithms for the Lovasz Local Lemma
• Computer Science
• ArXiv
• 2021
A poly log log n time randomized CONGEST algorithm for a natural class of Lovász Local Lemma (LLL) instances on constant degree graphs implies that there are no LCL problems with randomized complexity between log n and poly loglog n. Expand
Structural Information and Communication Complexity: 27th International Colloquium, SIROCCO 2020, Paderborn, Germany, June 29–July 1, 2020, Proceedings
• Computer Science
• SIROCCO
• 2020
We overview a recent line of work [Rozhoň and Ghaffari at STOC 2020; Ghaffari, Harris, and Kuhn at FOCS 2018; and Ghaffari, Kuhn, and Maus at STOC 2017], which proved that any (locallycheckable)Expand
Coloring Fast Without Learning Your Neighbors' Colors
• Computer Science
• DISC
• 2020
An improved randomized CONGEST algorithm for distance-$2 coloring that uses$\Delta^2+1$colors and runs in$O(\log n)$rounds is given, improving the recent recent O(\log \Delta) + 2^{O(\sqrt{\log\log n})}$. Expand

#### References

SHOWING 1-10 OF 48 REFERENCES
(2Δ - l)-Edge-Coloring is Much Easier than Maximal Matching in the Distributed Setting
• Computer Science, Mathematics
• SODA
• 2015
It is shown that a (2Δ − 1)-edge-coloring can be computed in time smaller than loge n for any e > 0, specifically, in eO([EQUATION]log log n) rounds. Expand
An optimal distributed (Δ+1)-coloring algorithm?
• Mathematics, Computer Science
• STOC
• 2018
This paper presents a new algorithm for (Δ+1)-list coloring in the randomized LOCAL model running in O(log∗n + Detd(poly logn)) time, where Det d(n′) is the deterministic complexity of (deg+1-list coloring) on n′-vertex graphs. Expand
Distributed (δ+1)-coloring in linear (in δ) time
• Mathematics, Computer Science
• STOC '09
• 2009
A deterministic (Δ + 1)-coloring distributed algorithm with running time O(Δ) + 1/2 log* n is presented, which breaks the heuristic barrier of Szegedy and Vishwanathan, and achieves running time which is linear in the maximum degree Δ. Expand
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. Expand
Deterministic (Δ + 1)-Coloring in Sublinear (in Δ) Time in Static, Dynamic and Faulty Networks
The question of how to devise algorithms with the same running time also in the more complicated settings of dynamic and faulty networks is settled by devising deterministic algorithms that require O(Δ3/4 log Δ + log* n) time in the static, dynamic, and faulty settings. Expand
Local Conflict Coloring
• Computer Science, Mathematics
• 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
• 2016
This work introduces conflict coloring as a general symmetry-breaking task that includes all the aforementioned tasks as specific instantiations - conflict coloring includes all locally checkable labeling tasks from [Naor & Stockmeyer, STOC 1993] and yields an LCA which requires a smaller number of probes than the previously best known algorithm for vertex-coloring. Expand
Locally-Iterative Distributed (Δ+ 1): -Coloring below Szegedy-Vishwanathan Barrier, and Applications to Self-Stabilization and to Restricted-Bandwidth Models
• Computer Science
• PODC
• 2018
It is demonstrated that Szegedy-Vishwanathan barrier is not an inherent limitation for locally-iterative algorithms, and significant improvements for dynamic, self-stabilizing and bandwidth-restricted settings are achieved. Expand
Faster Deterministic Distributed Coloring Through Recursive List Coloring
• F. Kuhn
• Computer Science, Mathematics
• SODA
• 2020
An improved deterministic $2^{O(\sqrt{\log\Delta})}\cdot\log^3 n$-round algorithm for $\Delta$-coloring non-complete graphs with maximum degree $\Delta\geq 3$. Expand
Deterministic Distributed Dominating Set Approximation in the CONGEST Model
• Computer Science, Mathematics
• PODC
• 2019
Deterministic approximation algorithms for the minimum dominating set problem in the CONGEST model with an almost optimal approximation guarantee are developed and it is shown how dominating set approximations can be deterministically transformed into a connected dominating set in the congEST model while only increasing the approximation guarantee by a constant factor. Expand
Distributed Graph Coloring: Fundamentals and Recent Developments
• Computer Science
• Distributed Graph Coloring: Fundamentals and Recent Developments
• 2013
The objective of this monograph is to provide a treatise on theoretical foundations of distributed symmetry breaking in the message-passing model of distributed computing and to stimulate further progress in this exciting area. Expand