# Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems

@article{Arora1998PolynomialTA, title={Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems}, author={Sanjeev Arora}, journal={J. ACM}, year={1998}, volume={45}, pages={753-782} }

We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed <italic>c</italic> > 1 and given any <italic>n</italic> nodes in <inline-equation><f><sc>R</sc></f> </inline-equation><supscrpt>2</supscrpt>, a randomized version of the scheme finds a (1 + 1/<italic>c</italic>)-approximation to the optimum traveling salesman tour in <italic>O(n</italic>(log <italic>n</italic>)<supscrpt><italic>O(c)</italic>)</supscrpt> time. When the nodes are in <inline…

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