George Markowsky
J. Math. Anal. Appl.
The random assignment problem is to choose a minimum-cost perfect matching in a complete n × n bipartite graph, whose edge weights are chosen randomly from some distribution such as the exponential distribution with mean 1. In this case it is known that the expectation does not grow unboundedly with n, but approaches some limiting value c* between 1.51 and 2. The limit is conjectured to be π2/6, while a recent conjecture is that for finite n, the expected cost is ∑ni=11/i2. This paper contains two principal results. First, by defining and analyzing a constructive algorithm, we show that the limiting expectation is c* < 1.94. Second, we extend the finite-n conjecture to partial assignments on complete m × n bipartite graphs and prove it in some limited cases. © 1999 John Wiley & Sons, Inc.
George Markowsky
J. Math. Anal. Appl.
Corneliu Constantinescu
SPIE Optical Engineering + Applications 2009
J. LaRue, C. Ting
Proceedings of SPIE 1989
A.R. Conn, Nick Gould, et al.
Mathematics of Computation