An improved approximation algorithm for the ATSP with parameterized triangle inequality

In this paper, we consider the asymmetric traveling salesman problem with the γ-parameterized triangle inequality for . That means the edge weights in the given complete graph G=(V,E,ω) satisfy ω(u,w)⩽γ⋅(ω(u,v)+ω(v,w)) for all distinct nodes u,v,w∈V. L.S. Chandran and L.S. Ram gave the first constant factor approximation algorithm with polynomial running time for this problem. They achieve performance ratio . M. Bläser, B. Manthey and J. Sgall obtain a -approximation algorithm. We devise an approximation algorithm with performance ratio , which is better than both and for almost all .