Distributed Symmetry-Breaking Algorithms for Congested Cliques

Barenboim, Leonid; Khazanov, V. B.

doi:10.1007/978-3-319-90530-3_5

Cited by 7 publications

(7 citation statements)

References 22 publications

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“…In this paper, our new distributed result is an improvement for coloring in the CONGESTED-CLIQUE model. It is worth noting that the CONGESTED-CLIQUE model has been receiving extensive attention recently, see e.g., [PST11, DLP12, BHP12, Len13, DKO14, Nan14, HPS14, HP15, CHKK + 16, HPP + 15, BKKL17, Gal16, CLT18, Gha16, Gha17, GGK + 18, PS18,Par18,BK18].…”

Section: Congested Clique Model Of Distributed Computingmentioning

confidence: 99%

The Complexity of (Δ+1) Coloring in Congested Clique, Massively Parallel Computation, and Centralized Local Computation

Chang

Fischer

Ghaffari

et al. 2019

Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing

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In this paper, we present new randomized algorithms that improve the complexity of the classic (∆+1)-coloring problem, and its generalization (∆+1)-list-coloring, in three well-studied models of distributed, parallel, and centralized computation:Congested Clique: We present an O(1)-round randomized algorithm for (∆ + 1)-list coloring in the congested clique model of distributed computing. This settles the asymptotic complexity of this problem. It moreover improves upon the O(log * ∆)-round randomized algorithms of Parter and Su [DISC'18] and O((log log ∆) · log * ∆)-round randomized algorithm of Parter [ICALP'18]. Massively Parallel Computation: We present a (∆ + 1)-list coloring algorithm with round complexity O( √ log log n) in the Massively Parallel Computation (MPC) model with strongly sublinear memory per machine. This algorithm uses a memory of O(n α ) per machine, for any desirable constant α > 0, and a total memory of O(m), where m is the size of the graph. Notably, this is the first coloring algorithm with sublogarithmic round complexity, in the sublinear memory regime of MPC. For the quasilinear memory regime of MPC, an O(1)-round algorithm was given very recently by Assadi et al. [SODA'19]. Centralized Local Computation: We show that (∆ + 1)-list coloring can be solved with ∆ O(1) ·O(log n) query complexity, in the centralized local computation model. The previous state-of-the-art for (∆ + 1)-list coloring in the centralized local computation model are based on simulation of known LOCAL algorithms. The deterministic O( √ ∆poly log ∆ + log * n)-round LOCAL algorithm of Fraigniaud et al. [FOCS'16] can be implemented in the centralized local computation model with query complexity ∆ O( √ ∆poly log ∆) ·O(log * n); the randomized O(log * ∆) + 2 O( √ log log n) -round LOCAL algorithm of Chang et al. [STOC'18] can be implemented in the centralized local computation model with query complexity ∆ O(log * ∆) · O(log n). a significantly more relaxed problem in comparison to ∆ + 1 coloring. For instance, we have long known a very simple O(∆)-coloring algorithm in LOCAL-model algorithm with round complexity 2 O( √ log log n) [BEPS16], but only recently such a round complexity was achieved for ∆ + 1 coloring [CLP18, HSS18]. Our focus is on the much more stringent ∆ + 1 coloring problem. For this problem, the LOCAL model algorithms of [CLP18, HSS18] need messages of O(∆ 2 log n) bits, and thus do not extend to CONGEST or CONGESTED-CLIQUE. For CONGESTED-CLIQUE model, the main challenge is when ∆ > √ n, as otherwise, one can simulate the algorithm of [CLP18] by leveraging the all-toall communication in CONGESTED-CLIQUE which means each vertex in each round is capable of communicating O(n log n) bits of information. Parter [Par18] designed the first sublogarithmic-time (∆+1) coloring algorithm for CONGESTED-CLIQUE, which runs in O(log log ∆ log * ∆) rounds. The algorithm of [Par18] is able to reduce the maximum degree to O( √ n) in O(log log ∆) iterations, and each iteration invokes the algorithm of [CLP18] on instances...

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Section: Congested Clique Model Of Distributed Computingmentioning

confidence: 99%

The Complexity of (Δ+1) Coloring in Congested Clique, Massively Parallel Computation, and Centralized Local Computation

Chang

Fischer

Ghaffari

et al. 2019

Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing

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“…Parameterized distributed algorithms have appeared implicitly in many of the above-mentioned subgraph detection works, and recently Ben-Basat et al [10] and Siebertz and Vigny [43] have explicitly studied aspects of distributed parameterized complexity. In terms of structural parameters, maximum degree is a standard parameter in distributed setting, and algorithms parameterized degeneracy has been studied for various problems and models [7,9,31]. Recently, Li [35] has show that the treewidth of the input graph can be approximated in Õ(D) rounds in CONGEST, and many classical optimization problems that are fixed-parameter tractable wrt.…”

Section: Additional Related Workmentioning

confidence: 99%

Beyond Distributed Subgraph Detection: Induced Subgraphs, Multicolored Problems and Graph Parameters

Korhonen¹,

Amir²

2021

Preprint

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Subgraph detection has recently been one of the most studied problems in the CONGEST model of distributed computing. In this work, we study the distributed complexity of problems closely related to subgraph detection, mainly focusing on induced subgraph detection. The main line of this work presents lower bounds and parameterized algorithms w.r.t structural parameters of the input graph:-On general graphs, we give unconditional lower bounds for induced detection of cycles and patterns of treewidth 2 in CONGEST. Moreover, by adapting reductions from centralized parameterized complexity, we prove lower bounds in CONGEST for detecting patterns with a 4-clique, and for induced path detection conditional on the hardness of triangle detection in the congested clique.-On graphs of bounded degeneracy, we show that induced paths can be detected fast in CONGEST using techniques from parameterized algorithms, while detecting cycles and patterns of treewidth 2 is hard.-On graphs of bounded vertex cover number, we show that induced subgraph detection is easy in CONGEST for any pattern graph. More specifically, we adapt a centralized parameterized algorithm for a more general maximum common induced subgraph detection problem to the distributed setting.In addition to these induced subgraph detection results, we study various related problems in the CONGEST and congested clique models, including for multicolored versions of subgraph-detection-like problems.

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“…Via a reduction to the maximal independent set (MIS) problem, they gave a (Δ + 1)-coloring algorithm that runs in (log Δ) rounds provided that Δ = ( 1/3 ). Parter [18] showed a deterministic (Δ + 1)-coloring in (log Δ) rounds, that works for any value of Δ. Barenboim and Khazanov [2] presented improved deterministic local algorithms as a function of the graph's arboricity. Finally, concurrently with our work, Bamberger et al [1] give (deg +1)-list coloring algorithms requiring (log Δ log log Δ) rounds in CONGESTED CLIQUE, (log 2 Δ) in linear-space MPC, and (log 2 Δ + log ) in low-space MPC.…”

Section: Related Workmentioning

confidence: 99%