Abstract
We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges to make a given graph Eulerian, whereas our approach also allows for the removal of certain edges leading to a decreased cost. For the TSP on graphic metrics (graph-TSP), we show that the approach gives a 1.461-approximation algorithm with respect to the Held-Karp lower bound. For graph-TSP restricted either to half-integral solutions to the Held-Karp relaxation or to a class of graphs that contains subcubic and claw-free graphs, we show that the integrality gap of the Held-Karp relaxation matches the conjectured ratio 4/3. The framework also allows for generalizations in a natural way and leads to analogous results for the s , t -path traveling salesman problem on graphic metrics where the start and end vertices are prespecified.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
