Many-visits TSP revisited

We study the Many-Visits Traveling Salesman Problem, where given a number k(v) for each of n cities and pairwise (possibly asymmetric) integer distances, one has to find an optimal tour that visits city v exactly times. The currently fastest algorithm is due Berger, Kozma, Mnich Vincze [SODA 2019, TALG 2020] runs in time space O⁎(5n). They also show polynomial-space running O(16n+o(n)). In this work, we three main results: A randomized O⁎(2nD), D maximum distance between two cities. By using standard methods, results (1+ϵ)-approximation O⁎(2nϵ−1). tight analysis Berger et al.'s exponential-space algorithm, resulting O⁎(4n) bound. new O(7.88n).