 
Summary: Probab. Theory Relat. Fields 93, 507534
Probability
Theory
9 SpringerVerlag1992
Asymptotics in the random assignment problem
David Aldous*
Department of Statistics, University of California, Berkeley,CA 94720,USA
Received October 17, 1991;in revised form March 24, 1992
Summary. We show that, in the usual probabilistic model for the random assign
ment problem, the optimal cost tends to a limit constant in probability and
in expectation. The method involves construction of an infinite limit structure,
in terms of which the limit constant is defined. But we cannot improve on
the known numerical bounds for the limit.
Mathematics Subject Classification: 60C05
1 Introduction
In the deterministic assignment problem, there are n jobs, n machines and a
n x n nonnegative matrix (tj,,,) representing the cost of performing job j on
machine m. An assignment is a permutation ~ of {1, ..., n}, indicating that job
j is assigned to machine ~(j). The optimal assignment has cost min~tj,~(j),
j
