Leo Liberti, James Ostrowski
Journal of Global Optimization
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.
Leo Liberti, James Ostrowski
Journal of Global Optimization
Corneliu Constantinescu
SPIE Optical Engineering + Applications 2009
L Auslander, E Feig, et al.
Advances in Applied Mathematics
T. Graham, A. Afzali, et al.
Microlithography 2000