Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
The hardness of approximation: gap location
Computational Complexity
Three-dimensional axial assignment problems with decomposable cost coefficients
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Joint Classification and Pairing of Human Chromosomes
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
An adaptive hybrid genetic algorithm for the three-matching problem
IEEE Transactions on Evolutionary Computation
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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.