The traveling salesman problem, conformal invariance, and dense polymers
J.L. Jacobsen, N. Read, and H. Saleur
TL;DR
This paper suggests that the optimal tour in the planar random Euclidean traveling salesman problem exhibits conformal invariance at large scales, linking it to dense polymers and minimal spanning trees, supported by numerical tests.
Contribution
It introduces the idea that the TSP's optimal tour statistics are conformally invariant and connects this to dense polymers and minimal spanning trees, supported by numerical evidence.
Findings
Power-law behavior in zigzag probabilities
Subleading corrections to tour length
Numerical tests support conformal invariance hypothesis
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.