The three-dimensional matching problem in Kalmanson matrices

Authors:
Sergey Polyakovskiy;Frits C. Spieksma;Gerhard J. Woeginger
Affiliations:
Operations Research Group, Katholieke Universiteit Leuven, Leuven, Belgium 3000;Operations Research Group, Katholieke Universiteit Leuven, Leuven, Belgium 3000;Department of Mathematics, TU Eindhoven, Eindhoven, The Netherlands 5600 MB
Venue:
Journal of Combinatorial Optimization
Year:
2013

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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).