The maximum traveling salesman problem with submodular rewards

In this paper we extend the classic problem of finding the maximum weight Hamiltonian cycle in a graph to the case where the reward is a submodular function of the edges. We propose a greedy algorithm and a 2-matching based algorithm, and we show that they have approximation factors of 1/2+k and max {2/3(2+k) , 2/3 (1 - k)} respectively, where k is the curvature of the function. Both algorithms run in time cubic to the number of vertices. We provide simulation results to empirically evaluate the performance of the algorithms.