The traveling salesman problem, conformal invariance, and dense polymers

Details The traveling salesman problem, conformal invariance, and dense polymers The traveling salesman problem, conformal invariance, and dense polymers

2004-03-10

arxiv.org/abs/cond-mat/0403277v3

Phys. Rev. Lett. 93, 038701 (2004)

Physics

Condensed Matter

Statistical Mechanics

4 pages. v2: small revisions, improved argument about dimensions d>2. v3: Final version, with a correction to the form of the

Scientific paper

10.1103/PhysRevLett.93.038701

We propose that the statistics of the optimal tour in the planar random Euclidean traveling salesman problem is conformally invariant on large scales. This is exhibited in power-law behavior of the probabilities for the tour to zigzag repeatedly between two regions, and in subleading corrections to the length of the tour. The universality class should be the same as for dense polymers and minimal spanning trees. The conjectures for the length of the tour on a cylinder are tested numerically.

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