A (Slightly) Improved Approximation Algorithm for Metric TSP

In “An Improved Approximation Algorithm for TSP,” Karlin, Klein, and Oveis Gharan design the first improvement over classical 1.5 approximation algorithm of Christofides-Serdyukov after more than 40 years. Their chooses a random spanning tree from maximum entropy distribution trees with marginals equal to optimum LP solution TSP, then, similar Christofides’ algorithm, it adds minimum cost matching on odd degree vertices tree. To analyze their simple algorithms, they prove exploit new tools theory strongly Rayleigh distributions.