Abstract
We investigate the computational complexity of several special cases of the three-dimensional matching problem where the costs are decomposable and determined by a so-called Kalmanson matrix. For the minimization version we develop an efficient polynomial time algorithm that is based on dynamic programming. For the maximization version, we show that there is a universally optimal matching (whose structure is independent of the particular Kalmanson matrix).
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Polyakovskiy, S., Spieksma, F.C.R. & Woeginger, G.J. The three-dimensional matching problem in Kalmanson matrices. J Comb Optim 26, 1–9 (2013). https://doi.org/10.1007/s10878-011-9426-y
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DOI: https://doi.org/10.1007/s10878-011-9426-y