Nearly linear time approximation schemes for Euclidean TSP and other geometric problems

  title={Nearly linear time approximation schemes for Euclidean TSP and other geometric problems},
  author={Sanjeev Arora},
  journal={Proceedings 38th Annual Symposium on Foundations of Computer Science},
  • Sanjeev Arora
  • Published 11 July 1997
  • Computer Science
  • Proceedings 38th Annual Symposium on Foundations of Computer Science
We present a randomized polynomial time approximation scheme for Euclidean TSP in R/sup 2/ that is substantially more efficient than our earlier scheme (1996) (and the scheme of Mitchell (1996)). For any fixed c>1 and any set of n nodes in the plane, the new scheme finds a (1+1/c)-approximation to the optimum traveling salesman tour in O(n(logn)/sup O(c)/) time. (Our earlier scheme ran in n/sup O(C)/ time.) For points in R/sup d/ the algorithm runs in O(n(logn)/sup (O(/spl radic/dc)/d-1)) time… 

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