@article{Forlizzi_Hromkovič_Proietti_Seibert_2006, title={On the Stability of Approximation for Hamiltonian Path Problems}, volume={1}, url={https://journals.lib.unb.ca/index.php/AOR/article/view/95}, abstractNote={We consider the problem of finding a cheapest Hamiltonian path of a complete graph satisfying a relaxed triangle inequality, i.e., such that for some parameter β > 1, the edge costs satisfy the inequality c({x, y}) ≤β (c({x, z}) + c({z, y})) for every triple of vertices x, y, z. There are three variants of this problem, depending on the number of prespecified endpoints: zero, one, or two. For metric graphs there exist approximation algorithms, with approximation ratio 3/2 for the first two variants and 5/3 for the latter one. Using results on the approximability of the Travelling Salesman Problem with input graphs satisfying the relaxed triangle inequality, we obtain for our problem approximation algorithms with ratio in(β <sup>2</sup> + β,3/2 β <sup>2</sup>) for zero or one respecified endpoints, and 5/3 β<sup>2</sup> for two endpoints.}, number={1}, journal={Algorithmic Operations Research}, author={Forlizzi, Luca and Hromkovič, Juraj and Proietti, Guido and Seibert, Sebastian}, year={2006}, month={Jan.} }