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oai:drops-oai.dagstuhl.de:3402 2024-03-06T10:34:08Z ddc:004 open_access

13/9-approximation for Graphic TSP Mucha, Marcin approximation algorithms travelling salesman problem The Travelling Salesman Problem is one of the most fundamental and most studied problems in approximation algorithms. For more than 30 years, the best algorithm known for general metrics has been Christofides's algorithm with approximation factor of 3/2, even though the so-called Held-Karp LP relaxation of the problem is conjectured to have the integrality gap of only 4/3. Very recently, significant progress has been made for the important special case of graphic metrics, first by Oveis Gharan et al. (2011), and then by Momke and Svensson (2011). In this paper, we provide an improved analysis of the approach used by the latter, yielding a bound of 13/9 on the approximation factor, as well as a bound of 19/12+epsilon for any epsilon>0 for a more general Travelling Salesman Path Problem in graphic metrics. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Marcin Mucha 2012 Is Part Of LIPIcs, Volume 14, 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2012.30 urn:nbn:de:0030-drops-34025 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.30 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode