The power of choice in priority scheduling Conference Paper

Author(s): Alistarh, Dan; Kopinsky, Justin; Li, Jerry; Nadiradze, Giorgi
Title: The power of choice in priority scheduling
Abstract: Consider the following random process: we are given n queues, into which elements of increasing labels are inserted uniformly at random. To remove an element, we pick two queues at random, and remove the element of lower label (higher priority) among the two. The cost of a removal is the rank of the label removed, among labels still present in any of the queues, that is, the distance from the optimal choice at each step. Variants of this strategy are prevalent in state-of-the-art concurrent priority queue implementations. Nonetheless, it is not known whether such implementations provide any rank guarantees, even in a sequential model. We answer this question, showing that this strategy provides surprisingly strong guarantees: Although the single-choice process, where we always insert and remove from a single randomly chosen queue, has degrading cost, going to infinity as we increase the number of steps, in the two choice process, the expected rank of a removed element is O(n) while the expected worst-case cost is O(n log n). These bounds are tight, and hold irrespective of the number of steps for which we run the process. The argument is based on a new technical connection between "heavily loaded" balls-into-bins processes and priority scheduling. Our analytic results inspire a new concurrent priority queue implementation, which improves upon the state of the art in terms of practical performance.
Conference Title: PODC: Principles of Distributed Computing
Volume: Part F129314
Conference Dates: July 25 -27, 2017
Conference Location: Washingon, DC, USA
ISBN: 978-145034992-5
Publisher: ACM  
Date Published: 2017-07-26
Start Page: 283
End Page: 292
DOI: 10.1145/3087801.3087810
Notes: We would like to thank James Aspnes, Thomas Sauerwald, Nir Shavit, Milan Vojnovic, and Udi Wieder for useful discussions. Dan Alistarh and Giorgi Nadiradze were supported by the Swiss National Fund Ambizione Project PZ00P2 161375. Justin Kopinsky was supported by the NSF under grants IIS-1447786 and CCF-1563880. Jerry Li was supported by NSF CAREER Award CCF-1453261, a Google Faculty Research Award, and an NSF Fellowship.
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