Improved Analysis for Graphic TSP Approximation via Matchings

The Travelling Salesman Problem is one 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 HeldKarp 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. [3], and then by Mömke and Svensson [8]. In this paper, we provide an improved analysis for the approach presented in [8] yielding a bound of 35 24 on the approximation factor, as well as a bound of 19 12 + ε for any ε > 0 for a more general Travelling Salesman Path Problem in graphic metrics.