New Bounds for the Traveling Salesman Constant

@article{Steinerberger2015NewBF,
  title={New Bounds for the Traveling Salesman Constant},
  author={Stefan Steinerberger},
  journal={Advances in Applied Probability},
  year={2015},
  volume={47},
  pages={27 - 36}
}
  • S. Steinerberger
  • Published 25 November 2013
  • Mathematics
  • Advances in Applied Probability
Let X 1, X 2, …, X n be independent and uniformly distributed random variables in the unit square [0, 1]2, and let L(X 1, …, X n ) be the length of the shortest traveling salesman path through these points. In 1959, Beardwood, Halton and Hammersley proved the existence of a universal constant β such that lim n→∞ n −1/2 L(X 1, …, X n ) = β almost surely. The best bounds for β are still those originally established by Beardwood, Halton and Hammersley, namely 0.625 ≤ β ≤ 0.922. We slightly improve… 
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