• Corpus ID: 238259161

# Distributed $\Delta$-Coloring Plays Hide-and-Seek

@inproceedings{Balliu2021DistributedP,
title={Distributed \$\Delta\$-Coloring Plays Hide-and-Seek},
author={Alkida Balliu and Sebastian Brandt and Fabian Kuhn and Dennis Olivetti},
year={2021}
}
• Published 1 October 2021
• Computer Science, Mathematics
We prove several new tight or near-tight distributed lower bounds for classic symmetry breaking graph problems. As a basic tool, we first provide a new insightful proof that any deterministic distributed algorithm that computes a ∆-coloring on ∆-regular trees requires Ω(log∆ n) rounds and any randomized algorithm requires Ω(log∆ log n) rounds. We prove this result by showing that a natural relaxation of the ∆-coloring problem is a fixed point in the round elimination framework. As a first…

## References

SHOWING 1-10 OF 56 REFERENCES
Improved Distributed Lower Bounds for MIS and Bounded (Out-)Degree Dominating Sets in Trees
• Computer Science, Mathematics
PODC
• 2021
This work proves lower bounds for a much more relaxed family of distributed symmetry breaking problems and provides a novel way to do simplifications for round elimination, which is expected to be of independent interest.
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.
Deterministic Distributed Vertex Coloring: Simpler, Faster, and without Network Decomposition
• Computer Science
2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
• 2022
An improved deterministic algorithm based on an improved variant of the network decomposition of Rozhoň and Ghaffari leads to an improvement in the complexity of randomized algorithms for ($\Delta +1$)-coloring, now reaching the bound of $O(\text{log}^{3}\text{ log}\ n)$ rounds.
Local Conflict Coloring Revisited: Linial for Lists
• Computer Science
DISC
• 2020
The state-of-the-art truly local $(deg+1)$-list coloring algorithm from Barenboim et al. [PODC'18] is improved by slightly reducing the runtime to $O(\sqrt{\Delta\log\Delta})+\log^* n$ and significantly reducing the message size (from huge to roughly $\Delta$).
Improved Deterministic Network Decomposition
• Computer Science
SODA
• 2021
A modified version of the CONGEST network decomposition algorithm is presented, constructing a decomposition whose quality does not depend on the identifiers, and thus improves the randomized round complexity for various problems.
Distributed Lower Bounds for Ruling Sets
• Computer Science
2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
• 2020
Lower bounds for distributedly computing ruling sets are presented, for the problem of computing a (2, 1)-ruling set in the LOCAL model of distributed computing.
The Topology of Local Computing in Networks
• Computer Science
ICALP
• 2020
This paper reformulates the celebrated lower bound of $\Omega(\log^*n)$ rounds for 3-coloring the $n$-node ring, in the algebraic topology framework, and presents "compact" protocol complexes, whose sizes do not depend on the size of the network.
Truly Tight-in-Δ Bounds for Bipartite Maximal Matching and Variants
• Computer Science
PODC
• 2020
This work provides truly tight bounds in Δ for the complexity of bipartite maximal matching and many natural variants, up to and including the additive constant in the LOCAL model.
Classification of distributed binary labeling problems
• Computer Science
DISC
• 2020
We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees. These are locally checkable problems that can
Distributed Edge Coloring and a Special Case of the Constructive Lovász Local Lemma
• Computer Science
ACM Trans. Algorithms
• 2020
A new distributed Lovász local lemma algorithm for tree-structured dependency graphs, which arise naturally from O(1)-round probabilistic algorithms run on trees, is developed and shown that the Ω (logΔ log n) lower bound can be nearly matched on trees.