Approximation schemes for covering and scheduling in related machines

Yossi Azar; Leah Epstein

doi:10.1007/BFb0053962

Approximation schemes for covering and scheduling in related machines

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

Abstract

We consider the problem of assigning a set of jobs to m parallel related machines so as to maximize the minimum load over the machines. This situation corresponds to a case that a system which consists of the m machines is alive (i.e. productive) only when all machines are alive, and the system should be maintained alive as long as possible. The above problem is called related machines covering problem and is different from the related machines scheduling problem in which the goal is to minimize the maximum load. Our main result is a polynomial approximation scheme for this covering problem. To the best of our knowledge the previous best approximation algorithm has a performance ratio of 2. Also, an approximation scheme for the special case of identical machines was given by [14]. Some of our techniques are built on ideas of Hochbaum and Shmoys [12]. They provided an approximation scheme for the well known related machines scheduling. In fact, our algorithm can be adapted to provide a simpler approximation scheme for the related machines scheduling as Well.

Original language	English
Title of host publication	Approximation Algorithms for Combinatorial Optimization - International Workshop, APPROX 1998, Proceedings
Editors	José Rolim, Klaus Jansen
Publisher	Springer Verlag
Pages	39-47
Number of pages	9
ISBN (Print)	3540647368, 9783540647362
DOIs	https://doi.org/10.1007/BFb0053962
State	Published - 1998
Externally published	Yes
Event	International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 1998 - Aalborg, Denmark Duration: 18 Jul 1998 → 19 Jul 1998

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1444
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 1998
Country/Territory	Denmark
City	Aalborg
Period	18/07/98 → 19/07/98

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1998.

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/BFb0053962

Cite this

Azar, Y., & Epstein, L. (1998). Approximation schemes for covering and scheduling in related machines. In J. Rolim, & K. Jansen (Eds.), Approximation Algorithms for Combinatorial Optimization - International Workshop, APPROX 1998, Proceedings (pp. 39-47). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1444). Springer Verlag. https://doi.org/10.1007/BFb0053962

Azar, Yossi ; Epstein, Leah. / Approximation schemes for covering and scheduling in related machines. Approximation Algorithms for Combinatorial Optimization - International Workshop, APPROX 1998, Proceedings. editor / José Rolim ; Klaus Jansen. Springer Verlag, 1998. pp. 39-47 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We consider the problem of assigning a set of jobs to m parallel related machines so as to maximize the minimum load over the machines. This situation corresponds to a case that a system which consists of the m machines is alive (i.e. productive) only when all machines are alive, and the system should be maintained alive as long as possible. The above problem is called related machines covering problem and is different from the related machines scheduling problem in which the goal is to minimize the maximum load. Our main result is a polynomial approximation scheme for this covering problem. To the best of our knowledge the previous best approximation algorithm has a performance ratio of 2. Also, an approximation scheme for the special case of identical machines was given by [14]. Some of our techniques are built on ideas of Hochbaum and Shmoys [12]. They provided an approximation scheme for the well known related machines scheduling. In fact, our algorithm can be adapted to provide a simpler approximation scheme for the related machines scheduling as Well.",

author = "Yossi Azar and Leah Epstein",

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Azar, Y & Epstein, L 1998, Approximation schemes for covering and scheduling in related machines. in J Rolim & K Jansen (eds), Approximation Algorithms for Combinatorial Optimization - International Workshop, APPROX 1998, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1444, Springer Verlag, pp. 39-47, International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 1998, Aalborg, Denmark, 18/07/98. https://doi.org/10.1007/BFb0053962

Approximation schemes for covering and scheduling in related machines. / Azar, Yossi; Epstein, Leah.
Approximation Algorithms for Combinatorial Optimization - International Workshop, APPROX 1998, Proceedings. ed. / José Rolim; Klaus Jansen. Springer Verlag, 1998. p. 39-47 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1444).

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

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N2 - We consider the problem of assigning a set of jobs to m parallel related machines so as to maximize the minimum load over the machines. This situation corresponds to a case that a system which consists of the m machines is alive (i.e. productive) only when all machines are alive, and the system should be maintained alive as long as possible. The above problem is called related machines covering problem and is different from the related machines scheduling problem in which the goal is to minimize the maximum load. Our main result is a polynomial approximation scheme for this covering problem. To the best of our knowledge the previous best approximation algorithm has a performance ratio of 2. Also, an approximation scheme for the special case of identical machines was given by [14]. Some of our techniques are built on ideas of Hochbaum and Shmoys [12]. They provided an approximation scheme for the well known related machines scheduling. In fact, our algorithm can be adapted to provide a simpler approximation scheme for the related machines scheduling as Well.

AB - We consider the problem of assigning a set of jobs to m parallel related machines so as to maximize the minimum load over the machines. This situation corresponds to a case that a system which consists of the m machines is alive (i.e. productive) only when all machines are alive, and the system should be maintained alive as long as possible. The above problem is called related machines covering problem and is different from the related machines scheduling problem in which the goal is to minimize the maximum load. Our main result is a polynomial approximation scheme for this covering problem. To the best of our knowledge the previous best approximation algorithm has a performance ratio of 2. Also, an approximation scheme for the special case of identical machines was given by [14]. Some of our techniques are built on ideas of Hochbaum and Shmoys [12]. They provided an approximation scheme for the well known related machines scheduling. In fact, our algorithm can be adapted to provide a simpler approximation scheme for the related machines scheduling as Well.

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Azar Y, Epstein L. Approximation schemes for covering and scheduling in related machines. In Rolim J, Jansen K, editors, Approximation Algorithms for Combinatorial Optimization - International Workshop, APPROX 1998, Proceedings. Springer Verlag. 1998. p. 39-47. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/BFb0053962

Approximation schemes for covering and scheduling in related machines

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Bibliographical note

ASJC Scopus subject areas

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