• 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}
}
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… 

Figures and Tables from this paper

References

SHOWING 1-10 OF 56 REFERENCES
Improved Distributed Lower Bounds for MIS and Bounded (Out-)Degree Dominating Sets in Trees
TLDR
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.
Distributed Graph Coloring Made Easy
TLDR
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
  • M. Ghaffari, F. Kuhn
  • Computer Science
    2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
  • 2022
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
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
TLDR
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.
...
...