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arXiv · 2504.10657

Balanced TSP partitioning

Benjamin Aram Berendsohn·Hwi Kim·László Kozma
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Abstract

The traveling salesman problem (TSP) famously asks for a shortest tour that a salesperson can take to visit a given set of cities in any order. In this paper, we ask how much faster $k \ge 2$ salespeople can visit the cities if they divide the task among themselves. We show that, in the two-dimensional Euclidean setting, two salespeople can always achieve a speedup of at least $\frac12 + \frac1\pi \approx 0.818$, for any given input, and there are inputs where they cannot do better. We also give (non-matching) upper and lower bounds for $k \geq 3$.

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Benjamin Aram Berendsohn, Hwi Kim, László Kozma. 2025-04-14. Balanced TSP partitioning. https://arxiv.org/abs/2504.10657

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