2011 IEEE 52nd Annual Symposium on Foundations of Computer Science (2011)

Palm Springs, California USA

Oct. 22, 2011 to Oct. 25, 2011

ISSN: 0272-5428

ISBN: 978-0-7695-4571-4

pp: 560-569

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FOCS.2011.56

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 in order 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), the approach yields a 1.461-approximation algorithm with respect to the Held-Karp lower bound. For graph-TSP restricted to a class of graphs that contains degree three bounded and claw-free graphs, we show that the integrality gap of the Held-Karp relaxation matches the conjectured ratio 4/3. The framework allows for generalizations in a natural way and also leads to a 1.586-approximation algorithm for the traveling salesman path problem on graphic metrics where the start and end vertices are prespecified.

INDEX TERMS

approximation, TSP, linear programming

CITATION

T. Möemke and O. Svensson, "Approximating Graphic TSP by Matchings,"

*2011 IEEE 52nd Annual Symposium on Foundations of Computer Science(FOCS)*, Palm Springs, California USA, 2011, pp. 560-569.

doi:10.1109/FOCS.2011.56

CITATIONS