Distributed $(\Delta+1)$-Coloring via Ultrafast Graph Shattering

Chang, Yi‐Jun; Li, Wenzheng; Pettie, Seth

doi:10.1137/19m1249527

Cited by 23 publications

(94 citation statements)

References 21 publications

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“…In the description below, we focus on the main randomized part (a.k.a the pre-shattering part) of the CLP algorithm [12], that runs in (log * Δ) rounds. We start by providing useful definitions, originally introduced by Harris, Schneider and Su [26].…”

Section: Algorithm Descriptions 21 Terminology and A Quick Exposition Of The Clp Algorithmmentioning

confidence: 99%

“…The next lemma (Lemma 3.1 of [12]) summarizes the key properties of the almost-cliques. Throughout, assume that < 1/5 and let , be the subsets of -dense ( -sparse) nodes.…”

Section: Algorithm Descriptions 21 Terminology and A Quick Exposition Of The Clp Algorithmmentioning

confidence: 99%

“…Harris, Schneider and Su [26] presented a new graph decomposition technique that provided the first sublogarithmic solution for the problem. Finally, in a subsequent remarkable breakthrough result, Chang, Li and Pettie (CLP) [10,12] presented an ( (poly log ))-round solution for the problem, where ( ′ ) is the deterministic complexity of the (deg +1)-list coloring problem on an ′ -vertex graph. In the latter problem, every vertex has a palette of only deg( ) + 1 colors.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Improved Deterministic (Δ+1) Coloring in Low-Space MPC

Czumaj

Davies

Parter

2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

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We present a deterministic (log log log )-round low-space Massively Parallel Computation (MPC) algorithm for the classical problem of (Δ + 1)-coloring on -vertex graphs. In this model, every machine has sublinear local space of size for any arbitrary constant ∈ (0, 1). Our algorithm works under the relaxed setting where each machine is allowed to perform exponential local computations, while respecting the space and bandwidth limitations. Our key technical contribution is a novel derandomization of the ingenious (Δ + 1)-coloring local algorithm by Chang-Li-Pettie (STOC 2018, SIAM J. Comput. 2020). The Chang-Li-Pettie algorithm runs in = (log log ) rounds, which sets the state-ofthe-art randomized round complexity for the problem in the local model. Our derandomization employs a combination of tools, notably pseudorandom generators (PRG) and bounded-independence hash functions.The achieved round complexity of (log log log ) rounds matches the bound of log(), which currently serves an upper bound barrier for all known randomized algorithms for locally-checkable problems in this model. Furthermore, no deterministic sublogarithmic low-space MPC algorithms for the (Δ + 1)-coloring problem have been known before. CCS CONCEPTS• Computing methodologies → Distributed algorithms; • Mathematics of computing → Graph algorithms; • Theory of computation → Pseudorandomness and derandomization.

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Section: Algorithm Descriptions 21 Terminology and A Quick Exposition Of The Clp Algorithmmentioning

confidence: 99%

“…The next lemma (Lemma 3.1 of [12]) summarizes the key properties of the almost-cliques. Throughout, assume that < 1/5 and let , be the subsets of -dense ( -sparse) nodes.…”

Section: Algorithm Descriptions 21 Terminology and A Quick Exposition Of The Clp Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Improved Deterministic (Δ+1) Coloring in Low-Space MPC

Czumaj

Davies

Parter

2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

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“…algorithms, we need to understand and improve deterministic algorithms. See [13,15,45] for quantitative statements for various problems.…”

Section: Motivationsmentioning

confidence: 99%

“…Both of these have terms that are clearly remnants of the 2 O( √ log n) -complexity network decomposition [23,43]. And they have clear gaps to the corresponding LOCAL-model bounds, which are O(log Δ + poly(log log n)) [22] and poly(log log n) [14,15], respectively. ?…”

Section: Open Problems: Congest Modelmentioning

confidence: 99%

Network Decomposition and Distributed Derandomization (Invited Paper)

Ghaffari

2020

Structural Information and Communication Complexity

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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) graph problem that admits an efficient randomized distributed algorithm also admits an efficient deterministic distributed algorithm, thereby resolving several central and decades-old open problems in distributed graph algorithms. We present a short and self-contained version of the proofs, and conclude by discussing several related questions that remain open.This article accompanies a keynote talk of the author at the International Colloquium on Structural Information and Communication Complexity (SIROCCO) 2020. The writing is based on [24,28,45] and primarily targets non-experts.

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Superfast Coloring in CONGEST via Efficient Color Sampling

Halldórsson

Nolin

2021

Structural Information and Communication Complexity

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Distributed $(\Delta+1)$-Coloring via Ultrafast Graph Shattering

Cited by 23 publications

References 21 publications

Improved Deterministic (Δ+1) Coloring in Low-Space MPC

Improved Deterministic (Δ+1) Coloring in Low-Space MPC

Network Decomposition and Distributed Derandomization (Invited Paper)

Superfast Coloring in CONGEST via Efficient Color Sampling

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