# Approaching 3/2 for the s-t-path TSP

@article{Traub2019Approaching3F, title={Approaching 3/2 for the s-t-path TSP}, author={Vera Traub and Jens Vygen}, journal={Journal of the ACM (JACM)}, year={2019}, volume={66}, pages={1 - 17} }

We show that there is a polynomial-time algorithm with approximation guarantee 3/2+ε for the s-t-path TSP, for any fixed ε > 0. It is well-known that Wolsey’s analysis of Christofide algorithm also works for the s-t-path TSP with its natural LP relaxation, except for the narrow cuts (in which the LP solution has a value less than two). A fixed optimum tour has either a single edge in a narrow cut (then call the edge and the cut lonely) or at least three (then call the cut busy). Our algorithm…

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## 25 Citations

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