Abstract
In this paper, the first fixed-ratio approximation algorithms are proposed for a series of asymmetric settings of well-known combinatorial routing problems. Among them are the Steiner cycle problem, the prize-collecting traveling salesman problem, the minimum cost cycle cover problem by a bounded number of cycles, etc. Almost all of the proposed algorithms rely on original reductions of the considered problems to auxiliary instances of the asymmetric traveling salesman problem and employ the breakthrough approximation results for this problem obtained recently by O. Svensson, J. Tarnawski, L. Végh, V. Traub, and J. Vygen. On the other hand, approximation of the cycle cover problem was proved by applying a deeper extension of their approach.
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Notes
A family of subsets \(\mathcal{L}\) is called laminar if for arbitrary \(A,B \in \mathcal{L}\) one of the following three alternatives holds: \(A \subseteq B\), \(B \subset A\), or \(A \cap B = \emptyset \).
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Funding
This research was supported by the Russian Science Foundation, grant no. 22-21-00672, https://rscf.ru/project/22-21-00672/.
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Translated by I. Ruzanova
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Neznakhina, E.D., Ogorodnikov, Y.Y., Rizhenko, K.V. et al. Approximation Algorithms with Constant Factors for a Series of Asymmetric Routing Problems. Dokl. Math. 108, 499–505 (2023). https://doi.org/10.1134/S1064562423701454
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DOI: https://doi.org/10.1134/S1064562423701454