Advertisement

Algorithmica

, Volume 20, Issue 1, pp 101–118 | Cite as

Minimizing Mean Flow Time with Error Constraint

  • J. Y. -T. Leung
  • T. W. Tam
  • C. S. Wong
  • G. H. Young

Abstract.

We consider the problem of minimizing mean flow time for the Imprecise Computation Model introduced by Lin et al. A task system TS=({T i },{r(T i )},{d(T i )},{m(T i )},{o(T i )}) consists of a set of n independent tasks, where r(T i ),d(T i ),m(T i ) , and o(T i ) denote the ready time, deadline, execution time of the mandatory part, and execution time of the optional part of T i , respectively. Given a task system TS and an error threshold K , our goal is to find a preemptive schedule on one processor such that the average error is no more than K and the mean flow time of the schedule is minimized. Such a schedule is called an optimal schedule. In this article we show that the problem of finding an optimal schedule is NP-hard, even if all tasks have identical ready times and deadlines. A pseudopolynomial-time algorithm is given for a set of tasks with identical ready times and deadlines, and oppositely ordered mandatory execution times and total execution times (i.e., there is a labeling of tasks such that m(T i )≤ m(T i+1 ) and m(T i )+o(T i )≥ m(T i+1 )+o(T i+1 ) for each 1≤ i<n ). Finally, polynomial-time algorithms are given for (1) a set of tasks with identical ready times, and similarly ordered mandatory execution times and total execution times and (2) a set of tasks with similarly ordered ready times, deadlines, mandatory execution times, and total execution times.

Key words. Real-time system, NP-hard, Pseudopolynomial time, Polynomial time, Ready time, Deadline, Imprecise computation, Mean flow time, Average error, Nonpreemptive scheduling, Preemptive scheduling. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York Inc. 1998

Authors and Affiliations

  • J. Y. -T. Leung
    • 1
  • T. W. Tam
    • 1
  • C. S. Wong
    • 1
  • G. H. Young
    • 1
  1. 1.Department of Computer Science and Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588-0115, USA.US

Personalised recommendations