The mean field traveling salesman and related problems
Journal article, 2010
The edges of a complete graph on n vertices are assigned i.i.d. random costs from a distribution for which the interval [0, t] has probability asymptotic to t as t -> 0 through positive values. In this so called pseudo-dimension 1 mean field model, we study several optimization problems, of which the traveling salesman is the best known. We prove that, as n -> a, the cost of the minimum traveling salesman tour converges in probability to a certain number, approximately 2.0415, which is characterized analytically.
model
asymptotics
random assignment problem
finite-size
expected value
exact expectations
spin-glass
statistical-mechanics
combinatorial optimization
minimum assignment
Author
Johan Wästlund
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
Acta Mathematica
0001-5962 (ISSN)
Vol. 204 1 91-150Subject Categories
Mathematics
DOI
10.1007/s11511-010-0046-7