Resource augmentation in load balancing

Yossi Azar; Leah Epstein; Rob Van Stee

doi:10.1007/3-540-44985-X_17

Resource augmentation in load balancing

Yossi Azar, Leah Epstein, Rob Van Stee

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

Abstract

We consider load balancing in the following setting. The on-line algorithm is allowed to use n machines, whereas the optimal off-line algorithm is limited to m machines, for some ffixed m < n. We show that while the greedy algorithm has a competitive ratio which decays linearly in the inverse of n=m, the best on-line algorithm has a ratio which decays exponentially in n=m. Specifically, we give an algorithm with competitive ratio of 1 + 1/2^{n/m(1−o(1))}, and a lower bound of 1 + 1/e^n/m(1+o(1)) on the competitive ratio of any randomized algorithm. We also consider the preemptive case.We show an on-line algorithm with a competitive ratio of 1 + 1=e^n/m(1+o(1)). We show that the algorithm is optimal by proving a matching lower bound. We also consider the non-preemptive model with temporary tasks. We prove that for n = m + 1, the greedy algorithm is optimal. (It is not optimal for permanent tasks).

Original language	English
Title of host publication	Algorithm Theory - SWAT 2000 - 7th Scandinavian Workshop on Algorithm Theory, 2000, Proceedings
Editors	Magnús M. Halldórsson
Publisher	Springer Verlag
Pages	189-199
Number of pages	11
ISBN (Print)	3540676902, 9783540676904
DOIs	https://doi.org/10.1007/3-540-44985-X_17
State	Published - 2000
Externally published	Yes
Event	7th Scandinavian Workshop on Algorithm Theory, SWAT 2000 - Bergen, Norway Duration: 5 Jul 2000 → 7 Jul 2000

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1851
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	7th Scandinavian Workshop on Algorithm Theory, SWAT 2000
Country/Territory	Norway
City	Bergen
Period	5/07/00 → 7/07/00

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2000.

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/3-540-44985-X_17

Cite this

Azar, Y., Epstein, L., & Van Stee, R. (2000). Resource augmentation in load balancing. In M. M. Halldórsson (Ed.), Algorithm Theory - SWAT 2000 - 7th Scandinavian Workshop on Algorithm Theory, 2000, Proceedings (pp. 189-199). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1851). Springer Verlag. https://doi.org/10.1007/3-540-44985-X_17

Azar, Yossi ; Epstein, Leah ; Van Stee, Rob. / Resource augmentation in load balancing. Algorithm Theory - SWAT 2000 - 7th Scandinavian Workshop on Algorithm Theory, 2000, Proceedings. editor / Magnús M. Halldórsson. Springer Verlag, 2000. pp. 189-199 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Resource augmentation in load balancing",

abstract = "We consider load balancing in the following setting. The on-line algorithm is allowed to use n machines, whereas the optimal off-line algorithm is limited to m machines, for some ffixed m < n. We show that while the greedy algorithm has a competitive ratio which decays linearly in the inverse of n=m, the best on-line algorithm has a ratio which decays exponentially in n=m. Specifically, we give an algorithm with competitive ratio of 1 + 1/2n/m(1−o(1)), and a lower bound of 1 + 1/en/m(1+o(1)) on the competitive ratio of any randomized algorithm. We also consider the preemptive case.We show an on-line algorithm with a competitive ratio of 1 + 1=en/m(1+o(1)). We show that the algorithm is optimal by proving a matching lower bound. We also consider the non-preemptive model with temporary tasks. We prove that for n = m + 1, the greedy algorithm is optimal. (It is not optimal for permanent tasks).",

author = "Yossi Azar and Leah Epstein and {Van Stee}, Rob",

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year = "2000",

doi = "10.1007/3-540-44985-X_17",

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Azar, Y, Epstein, L & Van Stee, R 2000, Resource augmentation in load balancing. in MM Halldórsson (ed.), Algorithm Theory - SWAT 2000 - 7th Scandinavian Workshop on Algorithm Theory, 2000, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1851, Springer Verlag, pp. 189-199, 7th Scandinavian Workshop on Algorithm Theory, SWAT 2000, Bergen, Norway, 5/07/00. https://doi.org/10.1007/3-540-44985-X_17

Resource augmentation in load balancing. / Azar, Yossi; Epstein, Leah; Van Stee, Rob.
Algorithm Theory - SWAT 2000 - 7th Scandinavian Workshop on Algorithm Theory, 2000, Proceedings. ed. / Magnús M. Halldórsson. Springer Verlag, 2000. p. 189-199 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1851).

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

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AU - Azar, Yossi

AU - Epstein, Leah

AU - Van Stee, Rob

N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2000.

PY - 2000

Y1 - 2000

N2 - We consider load balancing in the following setting. The on-line algorithm is allowed to use n machines, whereas the optimal off-line algorithm is limited to m machines, for some ffixed m < n. We show that while the greedy algorithm has a competitive ratio which decays linearly in the inverse of n=m, the best on-line algorithm has a ratio which decays exponentially in n=m. Specifically, we give an algorithm with competitive ratio of 1 + 1/2n/m(1−o(1)), and a lower bound of 1 + 1/en/m(1+o(1)) on the competitive ratio of any randomized algorithm. We also consider the preemptive case.We show an on-line algorithm with a competitive ratio of 1 + 1=en/m(1+o(1)). We show that the algorithm is optimal by proving a matching lower bound. We also consider the non-preemptive model with temporary tasks. We prove that for n = m + 1, the greedy algorithm is optimal. (It is not optimal for permanent tasks).

AB - We consider load balancing in the following setting. The on-line algorithm is allowed to use n machines, whereas the optimal off-line algorithm is limited to m machines, for some ffixed m < n. We show that while the greedy algorithm has a competitive ratio which decays linearly in the inverse of n=m, the best on-line algorithm has a ratio which decays exponentially in n=m. Specifically, we give an algorithm with competitive ratio of 1 + 1/2n/m(1−o(1)), and a lower bound of 1 + 1/en/m(1+o(1)) on the competitive ratio of any randomized algorithm. We also consider the preemptive case.We show an on-line algorithm with a competitive ratio of 1 + 1=en/m(1+o(1)). We show that the algorithm is optimal by proving a matching lower bound. We also consider the non-preemptive model with temporary tasks. We prove that for n = m + 1, the greedy algorithm is optimal. (It is not optimal for permanent tasks).

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M3 - Conference contribution

AN - SCOPUS:84949815279

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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ER -

Azar Y, Epstein L, Van Stee R. Resource augmentation in load balancing. In Halldórsson MM, editor, Algorithm Theory - SWAT 2000 - 7th Scandinavian Workshop on Algorithm Theory, 2000, Proceedings. Springer Verlag. 2000. p. 189-199. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-44985-X_17

Resource augmentation in load balancing

Abstract

Publication series

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Bibliographical note

ASJC Scopus subject areas

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