An asymptotically exact algorithm for one modification of planar three-index assignment problem

Abstract

An m-layer three-index assignment problem is considered which is a modification of the classical planar three-index assignment problem. This problem is NP-hard for m ⩾ 2. An approximate algorithm, solving this problem for 1 an > 0. The time complexity of the algorithm is O(mn2 + m7/2). It is shown that in the case of a uniform distribution (and also a distribution of minorized type) the algorithm is asymptotically exact if m = Θ(n1 − θ) and bn/an = o(nθ) for every constant θ, 0 < θ < 1.