Overcoming Congestion in Distributed Coloring

Halldórsson, Magnús M.; Nolin, Alexandre; Tonoyan, Tigran

doi:10.1145/3519270.3538438

Cited by 6 publications

(13 citation statements)

References 21 publications

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“…As a byproduct, the framework of Halldórsson et al [HKNT22] can be incorporated into a constant-round MPC algorithm assuming the local MPC space is slightly superlinear, i.e., O(n log 4 n) [HKNT22, Corollary 2]. A similar bound has been recently obtained for the CONGEST model in [HNT22], solving D1LC in O(log 5 log n) CONGEST rounds, w.h.p. We make extensive use of the framework laid out by Halldórsson et al [HKNT22] in their algorithm for LOCAL in the design of our D1LC algorithm.…”

Section: Related Workmentioning

confidence: 74%

“…The first advance (in the distributed setting) has come only very recently, when Halldórsson, Kuhn, Nolin, and Tonoyan [HKNT22] presented a randomized O(log 3 log n)-rounds distributed algorithm for D1LC in the LOCAL distributed model, matching the state-of-the art complexity for the simpler (∆ + 1)-coloring problem due to Chang, Li, and Pettie [CLP20]). In another very recent work, Halldórsson, Nolin, and Tonoyan [HNT22] extended the framework and showed that D1LC can be solved in O(log 5 log n)rounds in the distributed CONGEST model, matching the state-of-the-art complexity for the simpler (∆ + 1)coloring problem in CONGEST by Halldórsson, Kuhn, Maus, and Tonoyan [HKMT21]).…”

Section: Introductionmentioning

confidence: 87%

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Fast Parallel Degree+1 List Coloring

Coy¹,

Czumaj²,

Davies³

et al. 2023

Preprint

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Graph coloring problems are arguably among the most fundamental graph problems in parallel and distributed computing with numerous applications. In particular, in recent years the classical (∆ + 1)coloring problem became a benchmark problem to study the impact of local computation for parallel and distributed algorithms. In this work, we study the parallel complexity of a generalization of the (∆ + 1)-coloring problem: the problem of (degree+1)-list coloring (D1LC), where each node has an input palette of acceptable colors, of size one more than its degree, and the objective is to find a proper coloring using these palettes.In a recent work, Halldórsson et al. (STOC'22) presented a randomized O(log 3 log n)-rounds distributed algorithm for D1LC in the LOCAL model, matching for the first time the state-of-the art complexity for (∆ + 1)-coloring due to Chang et al. (SICOMP'20).In this paper, we obtain a similar connection for D1LC in the Massively Parallel Computation (MPC) model with sublinear local space: we present a randomized O(log log log n)-round MPC algorithm for D1LC, matching the state-of-the art MPC algorithm for the (∆ + 1)-coloring problem. We also show that our algorithm can be efficiently derandomized.

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Section: Related Workmentioning

confidence: 74%

Section: Introductionmentioning

confidence: 87%

Fast Parallel Degree+1 List Coloring

Coy¹,

Czumaj²,

Davies³

et al. 2023

Preprint

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show abstract

“…In CONGEST, Halldórsson, Kuhn, Maus, and Tonoyan [HKMT21] gave a O(log 5 log n)-round CONGEST algorithm, later improved to O(log 3 log n) in [HNT22,GK21]. Very recently, Flin, Ghaffari, Kuhn, and Nolin [FGH + 23a] provided a O(log 3 log n)-round algorithm in broadcast CONGEST, in which nodes are restricted to broadcast one O(log n)-bit message per round.…”

Section: Related Workmentioning

confidence: 99%

“…The existing distance-2 algorithm of [HKMN20] uses O(log ∆) rounds and the CONGEST algorithms by [HKMT21] require too much bandwidth at distance-2. We mention that [FGH + 23b] implements [HNT22] without representative hash functions and that it can be done here as well. We discuss the implementation of the algorithm in Appendix D.…”

Section: Sparse-dense Decompositionmentioning

confidence: 99%

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Coloring Fast with Broadcasts

Flin

Ghaffari

Halldórsson

et al. 2023

Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures

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We provide a O(log 6 log n)-round randomized algorithm for distance-2 coloring in CONGEST with ∆ 2 +1 colors. For ∆ ≫ poly log n, this improves exponentially on the O(log ∆+poly log log n) algorithm of [Halldórsson, Kuhn, Maus, Nolin, DISC'20].Our study is motivated by the ubiquity and hardness of local reductions in CONGEST. For instance, algorithms for the Local Lovász Lemma [Moser, Tardos, JACM'10; Fischer, Ghaffari, DISC'17; Davies, SODA'23] usually assume communication on the conflict graph, which can be simulated in LOCAL with only constant overhead, while this may be prohibitively expensive in CONGEST. We hope our techniques help tackle in CONGEST other coloring problems defined by local relations.

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Superfast coloring in CONGEST via efficient color sampling

Halldórsson

Nolin

2023

Theoretical Computer Science

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Overcoming Congestion in Distributed Coloring

Cited by 6 publications

References 21 publications

Fast Parallel Degree+1 List Coloring

Fast Parallel Degree+1 List Coloring

Coloring Fast with Broadcasts

Superfast coloring in CONGEST via efficient color sampling

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