Random assignment and shortest path problems

The purpose of this article is to bring together some results on random assignment and shortest path problems, and to clarify how they relate to each other. In particular, we investigate the consequences of the two very different and hard proofs of the ζ(2) limit theorem for the random assignment problem given by David Aldous [1] and by Chandra Nair, Balaji Prabhakar and Mayank Sharma [11]. The random shortest path problem had already been investigated by Svante Janson [6] (and has recently been further studied by R. Van der Hofstad, G. Hooghiemstra and P. Van Mieghem [4; 5]). By putting the papers [11] and [6] side by side, one can see that there is a close connection between these two random optimization problems. By establishing this connection we show that some results of Aldous [1] must hold also for the shortest path problem. Actually these properties are easier to establish directly for the shortest path problem, and by doing so we obtain, via the results of [11], new independent proofs of Aldous’ results.