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All-Norm Approximation Algorithms

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Book cover Algorithm Theory — SWAT 2002 (SWAT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2368))

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Abstract

A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different ℓ p norms. We address this problem by introducing the concept of an All-norm ρ-approximation algorithm, which supplies one solution that guarantees ρ-approximation to all ℓ p norms simultaneously. Specifically, we consider the problem of scheduling in the restricted assignment model, where there are m machines and n jobs, each is associated with a subset of the machines and should be assigned to one of them. Previous work considered approximation algorithms for each norm separately. Lenstra et al. [12] showed a 2-approximation algorithm for the problem with respect to the ℓ∞ norm. For any fixed ℓ p norm the previously known approximation algorithm has a performance of θ(p). We provide an all-norm 2-approximation polynomial algorithm for the restricted assignment problem. On the other hand, we show that for any given l p norm (p > 1) there is no PTAS unless P=NP by showing an APX-hardness result. We also show for any given ℓ p norm a FPTAS for any fixed number of machines.

Research supported in part by the Israeli Ministry of industry and trade and by the Israel Science Foundation.

Research supported in part by the Israel Science Foundation (grant no. 250/01).

Research supported in part by the Israeli Ministry of industry and trade.

Supported by the START program Y43-MAT of the Austrian Ministry of Science.

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Author information

Authors and Affiliations

  1. School of Computer Science, Tel-Aviv University, Tel-Aviv, 69978, Israel

    Yossi Azar

  2. School of Computer and Media Sciences, The Interdisciplinary Center, P.O.B 167, 46150, Herzliya, Israel

    Leah Epstein

  3. School of Computer Science, Tel-Aviv University, Tel-Aviv, 69978, Israel

    Yossi Richter

  4. Department of Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Gerhard J. Woeginger

  5. Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-010, Graz, Austria

    Gerhard J. Woeginger

Authors
  1. Yossi Azar
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  2. Leah Epstein
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  3. Yossi Richter
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  4. Gerhard J. Woeginger
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Applied Mathematics, University of Kuopio, P.O. Box 1627, 70211, Kuopio, Finland

    Martti Penttonen

  2. BRICS, University of Aarhus, Department of Computer Science, NY Munkegade, 8000, Aarhus C, Denmark

    Erik Meineche Schmidt

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© 2002 Springer-Verlag Berlin Heidelberg

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Azar, Y., Epstein, L., Richter, Y., Woeginger, G.J. (2002). All-Norm Approximation Algorithms. In: Penttonen, M., Schmidt, E.M. (eds) Algorithm Theory — SWAT 2002. SWAT 2002. Lecture Notes in Computer Science, vol 2368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45471-3_30

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  • DOI: https://doi.org/10.1007/3-540-45471-3_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43866-3

  • Online ISBN: 978-3-540-45471-7

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