2025/08/30 by Morteza Alimi, Niklas Dahlmeier, Alimi, Morteza +7
Computer Science · Engineering · #68R05 (Primary) #90C27 (Secondary) #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Data Structures and Algorithms (cs.DS) #E.1 #F.2.2 #FOS: Computer and information sciences #G.2.1 #Vehicle Routing Optimization Methods
paper · pdf · doi:10.48550/arxiv.2509.00448
openalex publication_date 2025/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The path version of the Traveling Salesman Problem is one of the most well-studied variants of the ubiquitous TSP. Its generalization, the Multi-Path TSP, has recently been used in the best known algorithm for path TSP by Traub and Vygen [Cambridge University Press, 2024]. The best known approximation factor for this problem is 2.214 by Böhm, Friggstad, Mömke and Spoerhase [SODA 2025]. In this paper we show that for the case of graphic metrics, a significantly better approximation guarantee of 2 can be attained. Our algorithm is based on sampling paths from a decomposition of the flow corresponding to the optimal solution to the LP for the problem, and connecting the left-out vertices with doubled edges. The cost of the latter is twice the optimum in the worst case; we show how the cost of the sampled paths can be absorbed into it without increasing the approximation factor. Furthermore, we prove that any below-2 approximation algorithm for the special case of the problem where each source is the same as the corresponding sink yields a below-2 approximation algorithm for Graphic Multi-Path TSP. We also show that our ideas can be utilized to give a factor 1.791-approximation algorithm for Ordered TSP in graphic metrics, for which the aforementioned paper [SODA 2025] and Armbruster, Mnich and Nägele [APPROX 2024] give a 1.868-approximation algorithm in general metrics.