The Power of Choice in Priority Scheduling

Alistarh, Dan; Kopinsky, Justin; Li, Jerry; Nadiradze, Giorgi

doi:10.48550/arxiv.1706.04178

Cited by 4 publications

(34 citation statements)

References 26 publications

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“…Analysis Overview. Our analysis generalizes the argument of [5] to the more intricate variant of the Multi-Queue process which we consider. Due to space constraints, we only sketch the argument here, and provide the full proof as supplementary material.…”

Section: Analysis Of the Stealing Multi-queuementioning

confidence: 71%

“…We now provide rank bounds for the above algorithm, in a simplified analytical model. As in [5], we assume that all element insertions occur initially and in increasing rank order. Additionally, we assume that tasks are inserted at random among the queues, and that extractTopB() operations occur atomically, so that we can analyze a sequential "linearized" version of the process.…”

Section: Analysis Of the Stealing Multi-queuementioning

confidence: 99%

“…We would like to apply a similar approach for deletions. Yet, allowing fully-local removals would perturb the twochoice process, and cause divergence [21,5]. Nevertheless, we show that the process can be adapted as follows: to remove, with probability p steal the thread considers stealing tasks from a randomly chosen other queue, comparing the top element of a local queue with that on top of a globally-chosen random queue, and removing the higherpriority element.…”

Section: Introductionmentioning

confidence: 99%

“…(For simplicity, we discuss concurrencyrelated details in the later sections.) Alistarh et al [5] showed that a sequential variant of the Multi-Queue ensures that the rank of an element removed is always O(m), in expectation, and O(m log m), with high probability in the number of queues m. Follow-up work showed that similar guarantees can be extended to concurrent executions [3], and gave work bounds for some task-based algorithms when executed via Multi-Queue-like priority schedulers [4,7,2]. Despite their guarantees, Multi-Queue schedulers are known to have lower overall performance relative to efficient scheduling heuristics [17,27].…”

Section: Introductionmentioning

confidence: 99%

“…Our theoretical contribution is a generalization of the Multi-Queue analysis of [5] showing that, under assumptions, the above process, which we call the stealing Multi-Queue (SMQ), induces a non-trivial trade-off between the stealing probability, the scheduling properties, and the average rank of elements removed. For instance, assuming a Multi-Queue formed of m = n queues (one queue per thread), with task batches of size O(B), and a balanced thread scheduling distribution, we show that the expected rank removed at a step is O(Bm), and O(Bm log(Bm)) with high probability.…”

Section: Introductionmentioning

confidence: 99%

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Multi-Queues Can Be State-of-the-Art Priority Schedulers

Postnikova¹,

Koval²,

Nadiradze³

et al. 2021

Preprint

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Designing and implementing efficient parallel priority schedulers is an active research area. An intriguing proposed design is the Multi-Queue: given n threads and m ≥ n distinct priority queues, task insertions are performed uniformly at random, while, to delete, a thread picks two queues uniformly at random, and removes the observed task of higher priority. This approach scales well, and has probabilistic rank guarantees: roughly, the rank of each task removed, relative to remaining tasks in all other queues, is O(m) in expectation. Yet, the performance of this pattern is below that of well-engineered schedulers, which eschew theoretical guarantees for practical efficiency. We investigate whether it is possible to design and implement a Multi-Queue-based task scheduler that is both highly-efficient and has analytical guarantees. We propose a new variant called the Stealing Multi-Queue (SMQ), a cache-efficient variant of the Multi-Queue, which leverages both queue affinity-each thread has a local queue, from which tasks are usually removed; but, with some probability, threads also attempt to steal higher-priority tasks from the other queues-and task batching, that is, the processing of several tasks in a single insert / remove step. These ideas are well-known for task scheduling without priorities; our theoretical contribution is showing that, despite relaxations, this design can still provide rank guarantees, which in turn implies bounds on total work performed. We provide a general SMQ implementation which can surpass state-of-the-art schedulers such as Galois and PMOD in terms of performance on popular graph-processing benchmarks. Notably, the performance improvement comes mainly from the superior rank guarantees provided by our scheduler, confirming that analytically-reasoned approaches can still provide performance improvements for priority task scheduling.

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Section: Analysis Of the Stealing Multi-queuementioning

confidence: 71%

Section: Analysis Of the Stealing Multi-queuementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multi-Queues Can Be State-of-the-Art Priority Schedulers

Postnikova¹,

Koval²,

Nadiradze³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

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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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