Improved algorithms for stretch scheduling

Michael A. Bender, Shanmugavelayutham Muthukrishnan, Rajmohan Rajaraman

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    We study the basic problem of preemptive scheduling of an online stream of jobs on a single processor. The ith job arrives at time r(t) and has processing time p(i) that is known at the time of its arrival. If C(i) is the completion time of job t, then the flow time is C(i) -r(i) and stretch of a job is the ratio of its flow time to its processing time; that is, c(i)-r(i)/p(i) Flow time considers the time a job is in the system regardless of the service it requested; the stretch measure relies on the intuition that a job that requested long service must be prepared to wait longer than the small jobs. In this paper, we present improved algorithmic results in stretch scheduling. We first show that a simple online algorithm that takes amortized O(l) time per job arrival is 0(A1/a)-competitive with respect to maximum stretch, where A is the ratio of the largest processing time to the smallest processing time. This is significantly more efficient than the best known online algorithm for this problem which takes ft(n2) per scheduling step (n is the number of jobs seen thus far). We next present a polynomial time approximation scheme for average stretch scheduling. The previous best polynomial-time algorithm is the shortest remaining processing time algorithm, which achieves a 2-approximation. Finally, we consider the impact of incomplete knowledge of job sizes on the average stretch performance of scheduling algorithms. We show that a constant-factor competitive ratio tor average stretch is achievable even if the processing times (or remaining processing times) of jobs are known only to within a constant factor of accuracy.

    Original languageEnglish (US)
    Title of host publicationProceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002
    PublisherAssociation for Computing Machinery
    Pages762-771
    Number of pages10
    ISBN (Electronic)089871513X
    StatePublished - Jan 1 2002
    Event13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002 - San Francisco, United States
    Duration: Jan 6 2002Jan 8 2002

    Publication series

    NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
    Volume06-08-January-2002

    Other

    Other13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002
    CountryUnited States
    CitySan Francisco
    Period1/6/021/8/02

    Fingerprint

    Stretch
    Scheduling
    Processing
    Flow Time
    Online Algorithms
    Polynomials
    Scheduling algorithms
    Preemptive Scheduling
    Polynomial Time Approximation Scheme
    Time of Arrival
    Competitive Ratio
    Completion Time
    Scheduling Algorithm
    Polynomial-time Algorithm
    Approximation

    ASJC Scopus subject areas

    • Software
    • Mathematics(all)

    Cite this

    Bender, M. A., Muthukrishnan, S., & Rajaraman, R. (2002). Improved algorithms for stretch scheduling. In Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002 (pp. 762-771). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 06-08-January-2002). Association for Computing Machinery.

    Improved algorithms for stretch scheduling. / Bender, Michael A.; Muthukrishnan, Shanmugavelayutham; Rajaraman, Rajmohan.

    Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002. Association for Computing Machinery, 2002. p. 762-771 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 06-08-January-2002).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Bender, MA, Muthukrishnan, S & Rajaraman, R 2002, Improved algorithms for stretch scheduling. in Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 06-08-January-2002, Association for Computing Machinery, pp. 762-771, 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002, San Francisco, United States, 1/6/02.
    Bender MA, Muthukrishnan S, Rajaraman R. Improved algorithms for stretch scheduling. In Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002. Association for Computing Machinery. 2002. p. 762-771. (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).
    Bender, Michael A. ; Muthukrishnan, Shanmugavelayutham ; Rajaraman, Rajmohan. / Improved algorithms for stretch scheduling. Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002. Association for Computing Machinery, 2002. pp. 762-771 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).
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