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Between a Rock and a Hard Place: The Two-to-One Assignment Problem

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Approximation and Online Algorithms (WAOA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5893))

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Abstract

We describe the two-to-one assignment problem, a problem in between the axial three-index assignment problem and the three-dimensional matching problem, having applications in various domains. For the (relevant) case of decomposable costs satisfying the triangle inequality we provide, on the positive side, two constant factor approximation algorithms. These algorithms involve solving minimum weight matching problems and transportation problems, leading to a 2-approximation, and a \(\frac32\)-approximation. Moreover, we further show that the best of these two solutions is a \(\frac43\)-approximation for our problem. On the negative side, we show that the existence of a polynomial time approximation scheme for our problem would imply P=NP.

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Author information

Authors and Affiliations

  1. Operations Research Group, Katholieke Universiteit Leuven, Naamsestraat 69, B-3000, Leuven, Belgium

    Dries Goossens, Sergey Polyakovskiy & Frits C. R. Spieksma

  2. Department of Mathematics, TU Eindhoven, P.O. Box 513, 5600, MB Eindhoven, The Netherlands

    Gerhard J. Woeginger

Authors
  1. Dries Goossens
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  2. Sergey Polyakovskiy
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  3. Frits C. R. Spieksma
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  4. Gerhard J. Woeginger
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Editor information

Editors and Affiliations

  1. IBISC, CNRS FRE 3190, Université d’Evry Val d’Essonne, Place des Terasses, Tour Evry 2, 91000, Evry Cedex, France

    Evripidis Bampis

  2. Institute for Computer Science and Applied Mathematics, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

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© 2010 Springer-Verlag Berlin Heidelberg

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Goossens, D., Polyakovskiy, S., Spieksma, F.C.R., Woeginger, G.J. (2010). Between a Rock and a Hard Place: The Two-to-One Assignment Problem. In: Bampis, E., Jansen, K. (eds) Approximation and Online Algorithms. WAOA 2009. Lecture Notes in Computer Science, vol 5893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12450-1_15

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  • DOI: https://doi.org/10.1007/978-3-642-12450-1_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12449-5

  • Online ISBN: 978-3-642-12450-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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