Preemptive scheduling algorithms with nested processing set restriction

Document Type

Conference Proceeding

Publication Date

12-1-2009

Abstract

We consider the problem of preemptively scheduling n independent jobs {J1, J2, ..., Jn} on m parallel machines {M1, M2, ..., Mm}, where each job Jj can only be processed on a prespecified subset Mj of machines called its processing set. The machines are linearly ordered, and the processing set of Jj is specified by two machine indexes aj and b j; i.e., Mj = { Maj, Maj + 1, ... Mb j}. The processing sets are nested; i.e., for i ≠ j, we have Mi⊆Mj, or Mj ⊆Mi, or Mj ∩ Mi = 0. Our goal is to minimize the makespan. We first give an O(n log n)-time algorithm to find an optimal schedule. We then give an O(mn + n log n)-time algorithm to find a maximal schedule, where a schedule is said to be maximal if it processes as much work as any other schedule in any time interval [0, t], t > 0. © 2009 World Scientific Publishing Company.

Identifier

70749161398 (Scopus)

Publication Title

International Journal of Foundations of Computer Science

External Full Text Location

https://doi.org/10.1142/S012905410900708X

ISSN

01290541

First Page

1147

Last Page

1160

Issue

6

Volume

20

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