The mean field traveling salesman and related problems
Artikel i vetenskaplig tidskrift, 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

Författare

Johan Wästlund

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Acta Mathematica

0001-5962 (ISSN)

Vol. 204 91-150

Ämneskategorier

Matematik

DOI

10.1007/s11511-010-0046-7