An improved approximation algorithm for the maximum TSP

Abstract

In this paper, we consider the maximum traveling salesman problem with γ -parameterized triangle inequality for γ ∈ [ 1 2 , 1 ) , which means that the edge weights in the given complete graph G = ( V , E , w ) satisfy w ( u v ) ≤ γ ⋅ ( w ( u x ) + w ( x v ) ) for all distinct nodes u , x , v ∈ V . For the maximum traveling salesman problem with γ -parameterized triangle inequality, R. Hassin and S. Rubinstein gave a constant factor approximation algorithm with polynomial running time, they achieved a performance ratio γ only for γ ∈ [ 1 2 , 5 7 ) in [8], which is the best known result. We design a k γ + 1 − 2 γ k γ -approximation algorithm for the maximum traveling salesman problem with γ -parameterized triangle inequality by using a similar idea but very different method to that in [11], where k = min { | C i | ∣ i = 1 , 2 , … , m } , C 1 , C 2 , … , C m is an optimal solution of the minimum cycle cover in G , which is better than the γ -approximation algorithm for almost all γ ∈ [ 1 2 , 1 ) .