The Power of Choice in Priority Scheduling

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

doi:10.1145/3087801.3087810

Cited by 15 publications

(43 citation statements)

References 40 publications

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“…Priority schedulers such as k-LSM [35] enforce these properties deterministically, where k is a tunable parameter. We have shown in previous work that the MultiQueue [29] scheduler ensures these properties both in sequential and concurrent executions [4,2] with parameter k = O(q log q), with exponentially low failure probability in q, the number of queues.…”

Section: F Airness: For Any Taskmentioning

confidence: 99%

“…Specifically, we exhibit instances of incremental algorithms where the overhead of relaxed execution is Ω(log n). Interestingly, this lower bound does not require the scheduler to be adversarial: we show that it holds even in the case of the relatively benign MultiQueue scheduler [29,4].…”

Section: Introductionmentioning

confidence: 97%

“…Relaxation overheads versus relaxation factor/queue multiplier for parallel SSSP Dijkstra's algorithm. The number of queues is the multiplier (x axis) times the number of threads, and is proportional to the average relaxation factor of the queue[4].…”

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confidence: 99%

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Efficiency Guarantees for Parallel Incremental Algorithms under Relaxed Schedulers

Alistarh

Nadiradze

Koval

2019

The 31st ACM Symposium on Parallelism in Algorithms and Architectures

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Several classic problems in graph processing and computational geometry are solved via incremental algorithms, which split computation into a series of small tasks acting on shared state, which gets updated progressively. While the sequential variant of such algorithms usually specifies a fixed (but sometimes random) order in which the tasks should be performed, a standard approach to parallelizing such algorithms is to relax this constraint to allow for out-of-order parallel execution. This is the case for parallel implementations of Dijkstra's single-source shortestpaths (SSSP) algorithm, and for parallel Delaunay mesh triangulation. While many software frameworks parallelize incremental computation in this way, it is still not well understood whether this relaxed ordering approach can still provide any complexity guarantees.In this paper, we address this problem, and analyze the efficiency guarantees provided by a range of incremental algorithms when parallelized via relaxed schedulers. We show that, for algorithms such as Delaunay mesh triangulation and sorting by insertion, schedulers with a maximum relaxation factor of k in terms of the maximum priority inversion allowed will introduce a maximum amount of wasted work of O(log n poly (k)), where n is the number of tasks to be executed. For SSSP, we show that the additional work is O( poly (k) dmax/wmin), where dmax is the maximum distance between two nodes, and wmin is the minimum such distance. In practical settings where n k, this suggests that the overheads of relaxation will be outweighed by the improved scalability of the relaxed scheduler. On the negative side, we provide lower bounds showing that certain algorithms will inherently incur a non-trivial amount of wasted work due to scheduler relaxation, even for relatively benign relaxed schedulers.

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Section: F Airness: For Any Taskmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

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Efficiency Guarantees for Parallel Incremental Algorithms under Relaxed Schedulers

Alistarh

Nadiradze

Koval

2019

The 31st ACM Symposium on Parallelism in Algorithms and Architectures

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“…Parallel scheduling [10,9] is an extremely vast area and a complete survey is beyond our scope. We do wish to emphasize that standard work-stealing schedulers will not provide this type of work bounds, since they do not provide any guarantees in terms of the rank of elements removed: the rank becomes unbounded over long executions, since a single random queue is sampled at every stealing step [2]. To our knowledge, there is only one previous attempt to add priorities to work-stealing schedulers [17], using a multi-level global queue of tasks, partitioned by priority.…”

Section: Introductionmentioning

confidence: 99%

“…This induces a sequential model, 1 where at each step, the scheduler returns a new task: for simplicity, assume for now that the scheduler returns at each step a task chosen uniformly at random among the top-k available tasks, in descending priority order. (We will model realistic relaxed schedulers [21,2] precisely in the following section.) Assume a thread receives a task from the scheduler.…”

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confidence: 99%

Relaxed Schedulers Can Efficiently Parallelize Iterative Algorithms

Alistarh

Brown

Kopinsky

et al. 2018

Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing

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There has been significant progress in understanding the parallelism inherent to iterative sequential algorithms: for many classic algorithms, the depth of the dependence structure is now well understood, and scheduling techniques have been developed to exploit this shallow dependence structure for efficient parallel implementations. A related, applied research strand has studied methods by which certain iterative task-based algorithms can be efficiently parallelized via relaxed concurrent priority schedulers. These allow for high concurrency when inserting and removing tasks, at the cost of executing superfluous work due to the relaxed semantics of the scheduler.In this work, we take a step towards unifying these two research directions, by showing that there exists a family of relaxed priority schedulers that can efficiently and deterministically execute classic iterative algorithms such as greedy maximal independent set (MIS) and matching. Our primary result shows that, given a randomized scheduler with an expected relaxation factor of k in terms of the maximum allowed priority inversions on a task, and any graph on n vertices, the scheduler is able to execute greedy MIS with only an additive factor of poly(k) expected additional iterations compared to an exact (but not scalable) scheduler. This counter-intuitive result demonstrates that the overhead of relaxation when computing MIS is not dependent on the input size or structure of the input graph. Experimental results show that this overhead can be clearly offset by the gain in performance due to the highly scalable scheduler. In sum, we present an efficient method to deterministically parallelize iterative sequential algorithms, with provable runtime guarantees in terms of the number of executed tasks to completion. arXiv:1808.04155v1 [cs.DS] 13 Aug 2018 may only depend on a small subset of other nodes, namely its neighbors which are higher priority in the random order. Blelloch, Fineman and Shun [7] performed an in-depth study of the asymptotic properties of this dependence structure, proving that, for any graph, the maximal depth of a chain of dependences is in fact O(log 2 n) with high probability, where n is the number of nodes in the graph. Recently, an impressive analytic result by Fischer and Noever [13] provided tight Θ(log n) bounds on the maximal dependency depth for greedy sequential MIS, effectively closing this problem for MIS. Beyond greedy MIS, there has been significant progress in analyzing the dependency structure of other fundamental sequential algorithms, such as algorithms for matching [7], list contraction [25], Knuth shuffle [25], linear programming [5], and graph connectivity [5].An alternative approach has been to employ relaxed data structures to schedule task-based programs. Starting with Karp and Zhang [19], the general idea is that, in some applications, the scheduler can relax the strict order induced by following the sequential algorithm, and allow tasks to be processed speculatively ahead of their dependencies, without loss o...

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Balanced Allocations and Global Clock in Population Protocols: An Accurate Analysis

Mocquard

Séricola

Anceaume

2018

Structural Information and Communication Complexity

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The context of this paper is the two-choice paradigm which is deeply used in balanced online resource allocation, priority scheduling, load balancing and more recently in population protocols. The model governing the evolution of these systems consists in throwing balls one by one and independently of each others into n bins, which represent the number of agents in the system. At each discrete instant, a ball is placed in the least filled bin among two bins randomly chosen among the n ones. A natural question is the evaluation of the difference between the number of balls in the most loaded and the one in the least loaded bin. At time t, this difference is denoted by Gap(t). A lot of work has been devoted to the derivation of asymptotic approximations of this gap for large values of n. In this paper we go a step further by showing that for all t ≥ 0, n ≥ 2 and σ > 0, the variable Gap(t) is less than a(1 + σ) ln(n) + b with probability greater than 1 − 1/n σ , where the constants a and b, which are independent of t, σ and n, are optimized and given explicitly, which to the best of our knowledge has never been done before.

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The Power of Choice in Priority Scheduling

Cited by 15 publications

References 40 publications

Efficiency Guarantees for Parallel Incremental Algorithms under Relaxed Schedulers

Efficiency Guarantees for Parallel Incremental Algorithms under Relaxed Schedulers

Relaxed Schedulers Can Efficiently Parallelize Iterative Algorithms

Balanced Allocations and Global Clock in Population Protocols: An Accurate Analysis

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