#5467. Many-visits TSP revisited

August 2026publication date
Proposal available till 19-05-2025
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Journal’s subject area:
Applied Mathematics;
Computational Theory and Mathematics;
Theoretical Computer Science;
Computer Networks and Communications;
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Abstract:
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 each city v exactly k(v) times. The currently fastest algorithm is due to Berger, Kozma, Mnich and Vincze [SODA 20XX, TALG 20XX] and runs in time and space O?(5n). They also show a polynomial-space algorithm running in time O(16n+o(n)). In this work, we show three main results: • A randomized polynomial-space algorithm running in time O?(2nD), where D is the maximum distance between two cities. By using standard methods, this results in a (1+?)-approximation running in time O?(2n??1). • A tight analysis of Berger et al.s exponential-space algorithm, resulting in an O?(4n) running time bound. • A new polynomial-space algorithm, running in time O(7.88n).
Keywords:
Exponential algorithm; Many-visits traveling salesman problem

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