Asymptotic Moments of the Bottleneck Assignment Problem

One of the most important variants of the standard linear assignment problem is the bottleneck assignment problem. In this paper we give a method by which one can find all of the asymptotic moments of a random bottleneck assignment problem in which costs (independent and identically distributed) are chosen from a wide variety of continuous distributions. Our method is obtained by determining the asymptotic moments of the time to first complete matching in a random bipartite graph process and then transforming those, via a Maclaurin series expansion for the inverse cumulative distribution function, into the desired moments for the bottleneck assignment problem. Our results improve on the previous best-known expression for the expected value of a random bottleneck assignment problem, yield the first results on moments other than the expected value, and produce the first results on the moments for the time to first complete matching in a random bipartite graph process.