The 1-2-3-Toolkit for Building Your Own Balls-into-Bins Algorithm

Bertrand, Pierre; Lenzen, Christoph

doi:10.1137/1.9781611973754.5

Cited by 2 publications

(2 citation statements)

References 12 publications

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“…[2] consider a variant of the balls-into-bins problem, namely, the renaming problem and the setting of synchronous message passing with failureprone servers. Finally, [7] introduced a general framework for parallel balls-into-bins algorithms and generalizes some of the algorithms analyzed in [10].…”

Section: Introductionmentioning

confidence: 99%

Parallel Balanced Allocations

Lenzen

Parter

Yogev

2019

The 31st ACM Symposium on Parallelism in Algorithms and Architectures

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We study parallel algorithms for the classical balls-into-bins problem, in which m balls acting in parallel as separate agents are placed into n bins. Algorithms operate in synchronous rounds, in each of which balls and bins exchange messages once. The goal is to minimize the maximal load over all bins using a small number of rounds and few messages.While the case of m = n balls has been extensively studied, little is known about the heavily loaded case. In this work, we consider parallel algorithms for this somewhat neglected regime of m ≫ n. The naïve solution of allocating each ball to a bin chosen uniformly and independently at random results in maximal load m/n + Θ( m/n • log n) (for m ≥ n log n) with high probability (w.h.p.). In contrast, for the sequential setting Berenbrink et al. [5] showed that letting each ball join the least loaded bin of two randomly selected bins reduces the maximal load to m/n + O(log log m) w.h.p. To date, no parallel variant of such a result is known.We present a simple parallel threshold algorithm that obtains a maximal load of m/n + O(1) w.h.p. within O(log log(m/n) + log * n) rounds. The algorithm is symmetric (balls and bins all "look the same"), and balls send O(1) messages in expectation. The additive term of O(log * n) in the complexity is known to be tight for such algorithms [10]. We also prove that our analysis is tight, i.e., algorithms of the type we provide must run for Ω(min{log log(m/n), n}) rounds w.h.p.Finally, we give a simple asymmetric algorithm (i.e., balls are aware of a common labeling of the bins) that achieves a maximal load of m/n + O(1) in a constant number of rounds w.h.p. Again, balls send only a single message per round, and bins receive (1 + o(1))m/n + O(log n) messages w.h.p. This goes to show that, similar to the case of m = n, asymmetry allows for highly efficient solutions.

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Section: Introductionmentioning

confidence: 99%

Parallel Balanced Allocations

Lenzen

Parter

Yogev

2019

The 31st ACM Symposium on Parallelism in Algorithms and Architectures

Self Cite

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show abstract

“…[ADRS14] consider a variant of the balls-into-bins problem, namely, the renaming problem and the setting of synchronous message passing with failure-prone servers. Finally, [BL14] introduced a general framework for parallel balls-into-bins algorithms and generalizes some of the algorithms analyzed in [LW16].…”

Section: Introductionmentioning

confidence: 99%

Parallel Balanced Allocations: The Heavily Loaded Case

Lenzen,

Parter,

Yogev

2019

Preprint

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We study parallel algorithms for the classical balls-into-bins problem, in which m balls acting in parallel as separate agents are placed into n bins. Algorithms operate in synchronous rounds, in each of which balls and bins exchange messages once. The goal is to minimize the maximal load over all bins using a small number of rounds and few messages.While the case of m = n balls has been extensively studied, little is known about the heavily loaded case. In this work, we consider parallel algorithms for this somewhat neglected regime of m ≫ n. The naïve solution of allocating each ball to a bin chosen uniformly and independently at random results in maximal load m/n + Θ( m/n • log n) (for m ≥ n log n) with high probability (w.h.p.). In contrast, for the sequential setting Berenbrink et al. [BCSV06] showed that letting each ball join the least loaded bin of two randomly selected bins reduces the maximal load to m/n + O(log log m) w.h.p. To date, no parallel variant of such a result is known.We present a simple parallel threshold algorithm that obtains a maximal load of m/n + O(1) w.h.p. within O(log log(m/n) + log * n) rounds. The algorithm is symmetric (balls and bins all "look the same"), and balls send O(1) messages in expectation. The additive term of O(log * n) in the complexity is known to be tight for such algorithms [LW16]. We also prove that our analysis is tight, i.e., algorithms of the type we provide must run for Ω(min{log log(m/n), n}) rounds w.h.p.Finally, we give a simple asymmetric algorithm (i.e., balls are aware of a common labeling of the bins) that achieves a maximal load of m/n + O(1) in a constant number of rounds w.h.p. Again, balls send only a single message per round, and bins receive (1 + o(1))m/n + O(log n) messages w.h.p. This goes to show that, similar to the case of m = n, asymmetry allows for highly efficient solutions.

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The 1-2-3-Toolkit for Building Your Own Balls-into-Bins Algorithm

Cited by 2 publications

References 12 publications

Parallel Balanced Allocations

Parallel Balanced Allocations

Parallel Balanced Allocations: The Heavily Loaded Case

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