Multiple-Choice Balanced Allocation in (Almost) Parallel

Berenbrink, Petra; Czumaj, Artur; Englert, Matthias; Friedetzky, Tom; Nagel, Lars

doi:10.1007/978-3-642-32512-0_35

Cited by 22 publications

(54 citation statements)

References 17 publications

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“…The key difference between these models and the one we consider is that our model is completely asynchronous, and in fact the interleavings are chosen adversarially. The technique we employ is fundamentally different from those of [22,8]. In particular, we believe our techniques could be adapted to re-derive the main result of [8], albeit with worse constants.…”

Section: Related Workmentioning

confidence: 99%

Distributionally Linearizable Data Structures

Alistarh

Brown

Kopinsky

et al. 2018

Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures

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Relaxed concurrent data structures have become increasingly popular, due to their scalability in graph processing and machine learning applications ([24, 14]). Despite considerable interest, there exist families of natural, high performing randomized relaxed concurrent data structures, such as the popular MultiQueue [27] pattern for implementing relaxed priority queue data structures, for which no guarantees are known in the concurrent setting [3].Our main contribution is in showing for the first time that, under a set of analytic assumptions, a family of relaxed concurrent data structures, including variants of MultiQueues, but also a new approximate counting algorithm we call the MultiCounter, provides strong probabilistic guarantees on the degree of relaxation with respect to the sequential specification, in arbitrary concurrent executions. We formalize these guarantees via a new correctness condition called distributional linearizability, tailored to concurrent implementations with randomized relaxations. Our result is based on a new analysis of an asynchronous variant of the classic powerof-two-choices load balancing algorithm, in which placement choices can be based on inconsistent, outdated information (this result may be of independent interest). We validate our results empirically, showing that the MultiCounter algorithm can implement scalable relaxed timestamps, which in turn can improve the performance of the classic TL2 transactional algorithm by up to 3×, for some settings of parameters.

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Section: Related Workmentioning

confidence: 99%

Distributionally Linearizable Data Structures

Alistarh

Brown

Kopinsky

et al. 2018

Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures

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“…By finding a lower bound on the difference B 1 −B γ 0 for some γ 0 , we complete Theorem 1. If d k ≥ e (ln ln n) 3 , then the lower bound on B γ * presented in Theorem 6 is an asymptotically tight lower bound on the maximum load B 1 . Therefore, we assume that d k ≤ e (ln ln n) 3 throughout this section.…”

Section: Lower Bound Onmentioning

confidence: 97%

“…the number of choices made by each ball varies depending on the load of the chosen bins) that achieves O(ln ln n/ ln d) maximum load with (1 + o(1))n message cost. 1 Parallel versions [1,16,11,10,3] of balanced allocation have been studied. Recent works addressed near optimal adaptive algorithms: a constant maximum bin load using an average of O(1) bin choices per ball [10,6].…”

Section: Introductionmentioning

confidence: 99%

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A Generalization of Multiple Choice Balls-into-Bins: Tight Bounds

Park

2016

Algorithmica

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This paper investigates a general version of the multiple choice model called the (k, d)-choice process in which n balls are assigned to n bins. In the process, k < d balls are placed into the k least loaded out of d bins chosen independently and uniformly at random in each of n k rounds. The primary goal is to derive tight bounds on the maximum bin load for (k, d)-choice for any 1 ≤ k < d ≤ n. Our results enable one to choose suitable parameters k and d for which the (k, d)-choice process achieves the optimal tradeoff between the maximum bin load and message cost: a constant maximum load and O(n) messages. The maximum load for a heavily loaded case where m > n balls are placed into n bins is also presented for the case d ≥ 2k. Potential applications are discussed such as distributed storage as well as parallel job scheduling in a cluster.

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“…Relationship to balanced allocations. Scalable backoff is closely related to balls-and-bins games [3,[6][7][8]16,41,54,57]. Bins correspond to time slots and balls correspond to packets.…”

Section: Introductionmentioning

confidence: 99%

How to Scale Exponential Backoff: Constant Throughput, Polylog Access Attempts, and Robustness

Bender¹,

Fineman²,

Gilbert³

et al. 2015

Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms

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Randomized exponential backoff is a widely deployed technique for coordinating access to a shared resource. A good backoff protocol should, arguably, satisfy three natural properties: (i) it should provide constant throughput, wasting as little time as possible; (ii) it should require few failed access attempts, minimizing the amount of wasted effort; and (iii) it should be robust, continuing to work efficiently even if some of the access attempts fail for spurious reasons. Unfortunately, exponential backoff has some well-known limitations in two of these areas: it provides poor (sub-constant) throughput (in the worst case), and is not robust (to adversarial disruption).The goal of this paper is to "fix" exponential backoff by making it scalable, particularly focusing on the case where processes arrive in an on-line, worst-case fashion. We present a relatively simple backoff protocol, Re-Backoff, that has, at its heart, a version of exponential backoff. It guarantees expected constant throughput with dynamic process arrivals and requires only an expected polylogarithmic number of access attempts per process.Re-Backoff is also robust to periods where the shared resource is unavailable for a period of time. If it is unavailable for D time slots, Re-Backoff provides the following guarantees. When the number of packets is a finite n, the average expected number of access attempts for successfully sending a packet is O(log 2 (n + D)). In the infinite case, the average expected number of access attempts for successfully sending a packet is O(log 2 (η + D)) where η is the maximum number of processes that are ever in the system concurrently.

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Multiple-Choice Balanced Allocation in (Almost) Parallel

Cited by 22 publications

References 17 publications

Distributionally Linearizable Data Structures

Distributionally Linearizable Data Structures

A Generalization of Multiple Choice Balls-into-Bins: Tight Bounds

How to Scale Exponential Backoff: Constant Throughput, Polylog Access Attempts, and Robustness

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