AbstractWe consider the assignment problem between two sets of N random points on a smooth, two-dimensional manifold $$\Omega $$
Ω
of unit area. It is known that the average cost scales as $$E_{\Omega }(N)\sim {1}/{2\pi }\ln N$$
E
Ω
(
N
)
∼
1
/
2
π
ln
N
with a correction that is at most of order $$\sqrt{\ln N\ln \ln N}$$
ln
N
ln
ln
N
. In this paper, we show that, within the linearization approximation of the field-theoretical formulation of the problem, the first $$\Omega $$
Ω
-dependent correction is on the constant term, and can be exactly computed from the spectrum of the Laplace–Beltrami operator on $$\Omega $$
Ω
. We perform the explicit calculation of this constant for various families of surfaces, and compare our predictions with extensive numerics.
ANALYSIS OF LABOR EMPLOYMENT ASSESMENT ON PRODUCTION MACHINE TO MINIMIZE TIME PRODUCTION
