An improved approximation algorithm for the asymmetric TSP with strengthened triangle inequality

Abstract

We consider the asymmetric traveling salesperson problem with γ-parameterized triangle inequality for γ ∈ [ 1 / 2 , 1 ) . That means, the edge weights fulfill w ( u , v ) ⩽ γ ⋅ ( w ( u , x ) + w ( x , v ) ) for all nodes u , v , x . Chandran and Ram [L.S. Chandran, L.S. Ram, Approximations for ATSP with parametrized triangle inequality, in: Proc. 19th Int. Symp. on Theoret. Aspects of Comput. Sci. (STACS), in: Lecture Notes in Comput. Sci., vol. 2285, Springer, Berlin, 2002, pp. 227–237] gave the first constant factor approximation algorithm with polynomial running time for this problem. They achieve performance ratio γ / ( 1 − γ ) . We devise an approximation algorithm with performance ratio ( 1 + γ ) / ( 2 − γ − γ 3 ) , which is better for γ ∈ [ 0.5437 , 1 ) , that is, for the particularly interesting large values of γ.