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Approximation Algorithms for Fractional Covering and Packing Problems, and Applications

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Fundamentals of Computation Theory (FCT 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2138))

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Abstract

In this talk we present fast algorithms that find approximate solutions for a general class of problems, which are called fractional packing and covering problems. We describe two main lines of research:

  • algorithms by Plotkin, Shmoys and Tardos [7],

  • algorithms by Grigoriadis, Khachiyan, Porkolab and Villavicencio [1,2]. and new developments.

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References

  1. M.D. Grigoriadis and L.G. Khachiyan, Coordination complexity of parallel pricedirective decomposition, Mathematics of Operations Research 21 (1996), 321–340.

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  2. M.D. Grigoriadis, L.G. Khachiyan, L. Porkolab, and J. Villavicencio: Approximate max-min resource sharing for structured concave optimization, SIAM Journal on Optimization, to appear.

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  3. K. Jansen and L. Porkolab, Linear-time approximation schemes for scheduling malleable parallel tasks, Proceedings of the 10th ACM-SIAM Symposium on Discrete Algorithms (1999), 490–498.

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  4. K. Jansen and L. Porkolab, Improved approximation schemes for scheduling unrelated parallel machines, Proceedings of the 31st ACM Symposium on the Theory of Computing (1999), 408–417.

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  5. K. Jansen and L. Porkolab: On resource constrained scheduling: polynomial time approximation schemes, submitted for publication (2001).

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  6. C. Kenyon, and E. Remila: Approximate strip packing, 37th Annual IEEE Symposium on Foundations of Computer Science, FOCS 96, 31–36, and Mathematics of Operations Research, to appear.

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  7. S.A. Plotkin, D.B. Shmoys, and E. Tardos: Fast approximation algorithms for fractional packing and covering problems, Mathematics of Operations Research 20 (1995), 257–301.

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Author information

Authors and Affiliations

  1. Institut für Informatik und praktische Mathematik, Christian-Albrechts-Universität zu Kiel, 24 098, Kiel, Germany

    Klaus Jansen

Authors
  1. Klaus Jansen
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Editor information

Editors and Affiliations

  1. University of Latvia, Raiņa bulvaris 29, LV-1459, Riga, Latvia

    Rūsiņš Freivalds

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© 2001 Springer-Verlag Berlin Heidelberg

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Jansen, K. (2001). Approximation Algorithms for Fractional Covering and Packing Problems, and Applications. In: Freivalds, R. (eds) Fundamentals of Computation Theory. FCT 2001. Lecture Notes in Computer Science, vol 2138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44669-9_2

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  • DOI: https://doi.org/10.1007/3-540-44669-9_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42487-1

  • Online ISBN: 978-3-540-44669-9

  • eBook Packages: Springer Book Archive

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