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  1. Home > Articles & Issues >
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  3. New bounds and algor ...
Article

New bounds and algorithms for on-line scheduling: two identical processors, known sum and upper bound on the tasks

Enrico Angelelli ORCID (1), Maria Grazia Speranza ORCID (1), Zsolt Tuza (2) (3)
(1) Department of Quantitative Methods [Brescia]
(2) Computer and Automation Research Institute [Budapest]
(3) Department of Computer Science and Systems Technology [Veszprem]
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Imported on
March 26, 2015
Published on
January 1, 2006
Last modified on
March 31, 2025
Volume 8
vol. 8
DOI
10.46298/dmtcs.367
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https://about.hal.science/hal-authorisation-v1
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New bounds and algorithms for on-line scheduling: two identical processors, known sum and upper bound on the tasks

Enrico Angelelli ORCID (1), Maria Grazia Speranza ORCID (1), Zsolt Tuza (2) (3)
(1) Department of Quantitative Methods [Brescia]
(2) Computer and Automation Research Institute [Budapest]
(3) Department of Computer Science and Systems Technology [Veszprem]
Abstract
In this paper we study a semi on-line version of the classical multiprocessor scheduling problem on two identical processors. We assume that the sum of the tasks and an upper bound gamma on the size of each task are known. Each task has to be assigned upon arrival and the assignment cannot be changed later. The objective is the minimization of the maximum completion time on the processors. In this paper we propose new algorithms and improve known lower and upper bounds on the competitive ratio. Algorithms and bounds depend on the value of gamma. An optimal algorithm is obtained for gamma in the interval [ 1/n,2(n+1)/n(2n+1) ] and gamma = (2n-1)/2n(n-1), where n is any integer value larger or equal 2.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • semi on-line scheduling
  • parallel processors
  • competitive analysis
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