Better s-t-Tours by Gao Trees

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9682)


We consider the s-t-path TSP: given a finite metric space with two elements s and t, we look for a path from s to t that contains all the elements and has minimum total distance. We improve the approximation ratio for this problem from 1.599 to 1.566. Like previous algorithms, we solve the natural LP relaxation and represent an optimum solution \(x^*\) as a convex combination of spanning trees. Gao showed that there exists a spanning tree in the support of \(x^*\) that has only one edge in each narrow cut (i.e., each cut C with \(x^*(C)<2\)). Our main theorem says that the spanning trees in the convex combination can be chosen such that many of them are such “Gao trees” simultaneously at all sufficiently narrow cuts.


Narrow Cuts Approximation Ratio Main Theorem Says Christofides Algorithm Eulerian Walk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We thank Kanstantsin Pashkovich for allowing us to include his idea described in the second half of Sect. 3.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.RWTH Aachen UniversityAachenGermany
  2. 2.University of BonnBonnGermany

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