On optimality of a polynomial algorithm for random linear multidimensional assignment problem

We demonstrate that the linear multidimensional assignment problem with iid random costs is polynomially ϵ‐approximable almost surely (a.s.) via a simple greedy heuristic, for a broad range of probability distributions of the assignment costs. Specifically, conditions on discrete and continuous distributions of the cost coefficients, including distributions with unbounded support, have been established that guarantee convergence to unity in the a.s. sense of the cost ratio between the greedy solution and optimal solution. The corresponding convergence rates have been determined.