# 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} }

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…

## 526 Citations

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

- Computer ScienceProceedings 38th Annual Symposium on Foundations of Computer Science
- 1997

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…

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- 2018

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- Computer Science9th International Conference on Electronics, Circuits and Systems
- 2002

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- 2007

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### ffl)-Approximation Scheme for the Euclidean TSP

- Mathematics
- 1996

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- Computer ScienceNord. J. Comput.
- 1999

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### A linear-time approximation scheme for planar weighted TSP

- Computer Science46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)
- 2005

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- Computer Science48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)
- 2007

For several planar and geometric problems that the best known approximation schemes are essentially optimal with respect to the dependence on epsi, it is shown that if there is a delta 0 such that any of these problems admits a 2-delta O(1/epsi), then ETH fails.

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