TY - JOUR
T1 - Between a rock and a hard place : the two-to-one assignment problem
AU - Goossens, D.
AU - Polyakovskiy, S.
AU - Spieksma, F.C.R.
AU - Woeginger, G.J.
PY - 2012
Y1 - 2012
N2 - 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 3/2-approximation. Moreover, we further show that the best of these two solutions is a 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.
AB - 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 3/2-approximation. Moreover, we further show that the best of these two solutions is a 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.
U2 - 10.1007/s00186-012-0397-2
DO - 10.1007/s00186-012-0397-2
M3 - Article
SN - 1432-2994
VL - 79
SP - 223
EP - 237
JO - Mathematical Methods of Operations Research
JF - Mathematical Methods of Operations Research
IS - 2
ER -