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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