Multi-index assignment problem: an asymptotically optimal approach

The multi-index axial assignment problem is considered. It is known to be NP-hard in general case. In the paper a sublinear approximation algorithm is proposed. Performance and probability-of-failure bounds of the algorithm are established, and conditions of asymptotical optimality of the algorithm described are proved in the case of matrices with random elements distributed independently with a common distribution function which is minorised by the uniform distribution.