Polynomial time approximation schemes for Euclidean TSP and other geometric problems

@article{Arora1996PolynomialTA,
  title={Polynomial time approximation schemes for Euclidean TSP and other geometric problems},
  author={Sanjeev Arora},
  journal={Proceedings of 37th Conference on Foundations of Computer Science},
  year={1996},
  pages={2-11}
}
  • Sanjeev Arora
  • Published 14 October 1996
  • Computer Science
  • Proceedings of 37th Conference on Foundations of Computer Science
We present a polynomial time approximation scheme for Euclidean TSP in /spl Rfr//sup 2/. Given any n nodes in the plane and /spl epsiv/>0, the scheme finds a (1+/spl epsiv/)-approximation to the optimum traveling salesman tour in time n/sup 0(1//spl epsiv/)/. When the nodes are in /spl Rfr//sup d/, the running time increases to n(O/spl tilde/(log/sup d-2/n)//spl epsiv//sup d-1/) The previous best approximation algorithm for the problem (due to Christofides (1976)) achieves a 3/2-approximation… 

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