Optimal non-preemptive semi-online scheduling on two related machines

Leah Epstein; Lene M. Favrholdt

doi:10.1007/3-540-45687-2_20

Optimal non-preemptive semi-online scheduling on two related machines

Leah Epstein, Lene M. Favrholdt

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Weconsider the following non-preemptive semi-online scheduling problem. Jobs with non-increasing sizes arrive one by one to be scheduled on two uniformly related machines, with the goal of minimizing the makespan. We analyze both the optimal overall competitive ratio, and the optimal competitive ratio as a function of the speed ratio (q ≥ 1) between the two machines. We show that the greedy algorithm LPT has optimal competitive ratio ¼ (1 + √17) ≈ 1.28 overall, but does not have optimal competitive ratio for every value of q. Wedetermine the intervals of q where LPT is an algorithm of optimal competitive ratio, and design different algorithms of optimal competitive ratio for the intervals where it fails to be the best algorithm. As a result, we give a tight analysis of the competitive ratio for every speed ratio.

Original language	English
Title of host publication	Mathematical Foundations of Computer Science 2002 - 27th International Symposium, MFCS 2002, Proceedings
Editors	Krzysztof Diks, Wojciech Rytter, Wojciech Rytter
Publisher	Springer Verlag
Pages	245-256
Number of pages	12
ISBN (Print)	3540440402, 9783540440406
DOIs	https://doi.org/10.1007/3-540-45687-2_20
State	Published - 2002
Externally published	Yes
Event	27th International Symposium on Mathematical Foundations of Computer Science, MFCS 2002 - Warsaw, Poland Duration: 26 Aug 2002 → 30 Aug 2002

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2420
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	27th International Symposium on Mathematical Foundations of Computer Science, MFCS 2002
Country/Territory	Poland
City	Warsaw
Period	26/08/02 → 30/08/02

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/3-540-45687-2_20

Cite this

Epstein, L., & Favrholdt, L. M. (2002). Optimal non-preemptive semi-online scheduling on two related machines. In K. Diks, W. Rytter, & W. Rytter (Eds.), Mathematical Foundations of Computer Science 2002 - 27th International Symposium, MFCS 2002, Proceedings (pp. 245-256). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2420). Springer Verlag. https://doi.org/10.1007/3-540-45687-2_20

Epstein, Leah ; Favrholdt, Lene M. / Optimal non-preemptive semi-online scheduling on two related machines. Mathematical Foundations of Computer Science 2002 - 27th International Symposium, MFCS 2002, Proceedings. editor / Krzysztof Diks ; Wojciech Rytter ; Wojciech Rytter. Springer Verlag, 2002. pp. 245-256 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Weconsider the following non-preemptive semi-online scheduling problem. Jobs with non-increasing sizes arrive one by one to be scheduled on two uniformly related machines, with the goal of minimizing the makespan. We analyze both the optimal overall competitive ratio, and the optimal competitive ratio as a function of the speed ratio (q ≥ 1) between the two machines. We show that the greedy algorithm LPT has optimal competitive ratio ¼ (1 + √17) ≈ 1.28 overall, but does not have optimal competitive ratio for every value of q. Wedetermine the intervals of q where LPT is an algorithm of optimal competitive ratio, and design different algorithms of optimal competitive ratio for the intervals where it fails to be the best algorithm. As a result, we give a tight analysis of the competitive ratio for every speed ratio.",

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Epstein, L & Favrholdt, LM 2002, Optimal non-preemptive semi-online scheduling on two related machines. in K Diks, W Rytter & W Rytter (eds), Mathematical Foundations of Computer Science 2002 - 27th International Symposium, MFCS 2002, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2420, Springer Verlag, pp. 245-256, 27th International Symposium on Mathematical Foundations of Computer Science, MFCS 2002, Warsaw, Poland, 26/08/02. https://doi.org/10.1007/3-540-45687-2_20

Optimal non-preemptive semi-online scheduling on two related machines. / Epstein, Leah; Favrholdt, Lene M.
Mathematical Foundations of Computer Science 2002 - 27th International Symposium, MFCS 2002, Proceedings. ed. / Krzysztof Diks; Wojciech Rytter; Wojciech Rytter. Springer Verlag, 2002. p. 245-256 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2420).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Epstein, Leah

AU - Favrholdt, Lene M.

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N2 - Weconsider the following non-preemptive semi-online scheduling problem. Jobs with non-increasing sizes arrive one by one to be scheduled on two uniformly related machines, with the goal of minimizing the makespan. We analyze both the optimal overall competitive ratio, and the optimal competitive ratio as a function of the speed ratio (q ≥ 1) between the two machines. We show that the greedy algorithm LPT has optimal competitive ratio ¼ (1 + √17) ≈ 1.28 overall, but does not have optimal competitive ratio for every value of q. Wedetermine the intervals of q where LPT is an algorithm of optimal competitive ratio, and design different algorithms of optimal competitive ratio for the intervals where it fails to be the best algorithm. As a result, we give a tight analysis of the competitive ratio for every speed ratio.

AB - Weconsider the following non-preemptive semi-online scheduling problem. Jobs with non-increasing sizes arrive one by one to be scheduled on two uniformly related machines, with the goal of minimizing the makespan. We analyze both the optimal overall competitive ratio, and the optimal competitive ratio as a function of the speed ratio (q ≥ 1) between the two machines. We show that the greedy algorithm LPT has optimal competitive ratio ¼ (1 + √17) ≈ 1.28 overall, but does not have optimal competitive ratio for every value of q. Wedetermine the intervals of q where LPT is an algorithm of optimal competitive ratio, and design different algorithms of optimal competitive ratio for the intervals where it fails to be the best algorithm. As a result, we give a tight analysis of the competitive ratio for every speed ratio.

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Epstein L, Favrholdt LM. Optimal non-preemptive semi-online scheduling on two related machines. In Diks K, Rytter W, Rytter W, editors, Mathematical Foundations of Computer Science 2002 - 27th International Symposium, MFCS 2002, Proceedings. Springer Verlag. 2002. p. 245-256. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45687-2_20

Optimal non-preemptive semi-online scheduling on two related machines

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Bibliographical note

ASJC Scopus subject areas

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