The price of bounded preemption

Noga Alon, Yossi Azar, Mark Berlin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In this paper we provide a tight bound for the price of preemption for scheduling jobs on a single machine (or multiple machines). The input consists of a set of jobs to be scheduled and of an integer parameter k ≥ 1. Each job has a release time, deadline, length (also called processing time) and value associated with it. The goal is to feasibly schedule a subset of the jobs so that their total value is maximal; while preemption of a job is permitted, a job may be preempted no more than k times. The price of preemption is the worst possible (i.e., largest) ratio of the optimal non-bounded-preemptive scheduling to the optimal k-bounded-preemptive scheduling. Our results show that allowing at most k preemptions suffices to guarantee a Θ(min{logk+1 n, logk+1 P}) fraction of the total value achieved when the number of preemptions is unrestricted (where n is the number of the jobs and P the ratio of the maximal length to the minimal length), giving us an upper bound for the price; a specific scenario serves to prove the tightness of this bound. We further show that when no preemptions are permitted at all (i.e., k = 0), the price is Θ(min{n, log P}). As part of the proof, we introduce the notion of the Bounded-Degree Ancestor-Free Sub-Forest (BAS). We investigate the problem of computing the maximal-value BAS of a given forest and give a tight bound for the loss factor, which is Θ(logk+1 n) as well, where n is the size of the original forest and k is the bound on the degree of the sub-forest.

Original languageEnglish
Title of host publicationSPAA 2018 - Proceedings of the 30th ACM Symposium on Parallelism in Algorithms and Architectures
PublisherAssociation for Computing Machinery
Pages301-310
Number of pages10
ISBN (Electronic)9781450357999
DOIs
StatePublished - 11 Jul 2018
Event30th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2018 - Vienna, Austria
Duration: 16 Jul 201818 Jul 2018

Publication series

NameAnnual ACM Symposium on Parallelism in Algorithms and Architectures

Conference

Conference30th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2018
Country/TerritoryAustria
CityVienna
Period16/07/1818/07/18

Funding

FundersFunder number
German-Israeli Foundation for Scientific Research and Development
Israel Science Foundation1506/16

    Keywords

    • Bounded preemptions
    • Bounded-degree sub-forest
    • Multiple machines
    • Scheduling jobs

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