The random linear bottleneck assignment problem

Abstract

In this contribution asymptotic properties of the linear bottleneck assignment problem LBAP are investigated. It is shown that the expected value of the optimal solution of an n x n LBAP with independently and identically distributed costs tends towards the infimum of the cost range as n tends to infinity. Furthermore, explicit upper and lower bounds for the uniform cost distribution are given as functions in n. Exploiting results from evolutionary random graph theory an algorithm with O(n2) expected running time is presented.