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

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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 \({\frac{3}{2}}\) -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.

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Correspondence to Frits C. R. Spieksma.

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This research has been supported by the Netherlands Organisation for Scientific Research (NWO) under grant 639.033.403, by BSIK grant 03018 (BRICKS: Basic Research in Informatics for Creating the Knowledge Society), and by OT Grant OT/07/015. An earlier version of this work appeared in the Proceedings of the 7th Workshop on Approximation and Online Algorithms (WAOA 2009).

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Goossens, D., Polyakovskiy, S., Spieksma, F.C.R. et al. Between a rock and a hard place: the two-to-one assignment problem. Math Meth Oper Res 76, 223–237 (2012). https://doi.org/10.1007/s00186-012-0397-2

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  • DOI: https://doi.org/10.1007/s00186-012-0397-2

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