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Between a rock and a hard place: the two-to-one assignment problem

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  • Dries Goossens
  • Sergey Polyakovskiy
  • Frits Spieksma
  • Gerhard Woeginger

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 $${\frac{3}{2}}$$ -approximation. Moreover, we further show that the best of these two solutions is a $${\frac{4}{3}}$$ -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. Finally, we report on some computational experiments showing the performance of the described heuristics. Copyright Springer-Verlag 2012

Suggested Citation

  • Dries Goossens & Sergey Polyakovskiy & Frits Spieksma & Gerhard Woeginger, 2012. "Between a rock and a hard place: the two-to-one assignment problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(2), pages 223-237, October.
    • Handle: RePEc:spr:mathme:v:76:y:2012:i:2:p:223-237
    DOI: 10.1007/s00186-012-0397-2
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    References listed on IDEAS

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    1. Urban, Timothy L. & Russell, Robert A., 2003. "Scheduling sports competitions on multiple venues," European Journal of Operational Research, Elsevier, vol. 148(2), pages 302-311, July.
    2. Crama, Yves & Spieksma, Frits C. R., 1992. "Approximation algorithms for three-dimensional assignment problems with triangle inequalities," European Journal of Operational Research, Elsevier, vol. 60(3), pages 273-279, August.
    3. Spieksma, Frits C. R. & Woeginger, Gerhard J., 1996. "Geometric three-dimensional assignment problems," European Journal of Operational Research, Elsevier, vol. 91(3), pages 611-618, June.
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    1. Zamorano, Emilio & Stolletz, Raik, 2017. "Branch-and-price approaches for the Multiperiod Technician Routing and Scheduling Problem," European Journal of Operational Research, Elsevier, vol. 257(1), pages 55-68.

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