Preemptive and non-preemptive on-line algorithms for scheduling with rejection on two uniform machines

G. Dósa, Y. He

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

In this paper, we consider the problem of on-line scheduling a job sequence on two uniform machines. A job can be either rejected, in which case we pay its penalty, or scheduled on machines, in which case it contributes its processing time to the makspan of the constructed schedule. The objective is to minimize the sum of the makespan of the schedule for all accepted jobs and the penalties of all rejected jobs. Both preemptive and non-preemptive versions are considered. For the preemptive version, we present an optimal on-line algorithm with a competitive ratio 1/2 + √1/4 + 1/5 for any s ≥ 1, where s is the machine speed ratio. For the non-preemptive version, we present an improved lower bound. Moreover, as an optimal algorithm for s ≥ 1.6180 is known, we present a modified version of the known algorithm, and show that it becomes optimal for any 1.3852 ≤ s

Original languageEnglish
Pages (from-to)149-164
Number of pages16
JournalComputing
Volume76
Issue number1-2
DOIs
Publication statusPublished - Jan 2006

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Uniform Machines
Optimal Algorithm
Rejection
Penalty
Schedule
Scheduling
Competitive Ratio
Lower bound
Minimise
Processing

Keywords

  • Competitive analysis
  • On-line algorithms
  • Preemption
  • Rejection
  • Scheduling

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

Preemptive and non-preemptive on-line algorithms for scheduling with rejection on two uniform machines. / Dósa, G.; He, Y.

In: Computing, Vol. 76, No. 1-2, 01.2006, p. 149-164.

Research output: Contribution to journalArticle

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