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Approximation schemes for covering and scheduling in related machines

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Approximation Algorithms for Combinatiorial Optimization (APPROX 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1444))

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.

Research supported in part by the Israel Science Foundation and by the United States-Israel Binational Science Foundation (BSF).

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Authors and Affiliations

  1. Dept. of Computer Science, Tel-Aviv University, Israel

    Yossi Azar & Leah Epstein

Authors
  1. Yossi Azar
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  2. Leah Epstein
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Klaus Jansen José Rolim

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© 1998 Springer-Verlag Berlin Heidelberg

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Azar, Y., Epstein, L. (1998). Approximation schemes for covering and scheduling in related machines. In: Jansen, K., Rolim, J. (eds) Approximation Algorithms for Combinatiorial Optimization. APPROX 1998. Lecture Notes in Computer Science, vol 1444. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0053962

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  • DOI: https://doi.org/10.1007/BFb0053962

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  • Print ISBN: 978-3-540-64736-2

  • Online ISBN: 978-3-540-69067-2

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