Abstract
The Prize-Collecting Traveling Salesman Problem is a class of generalizations of the classic Traveling Salesman Problem (TSP) where it is not necessary to visit all the vertices. Given the edge costs and a certain profit associated with each vertex, the goal is to find a route which satisfies maximum collected profit and minimum traveling costs constraints. We show polynomial-time approximation algorithms for two variants of the problem and establish conditions under which the presented algorithms are asymptotically optimal on random inputs.
Supported by the program of fundamental scientific researches of the SB RAS, project 0314-2019-0014, and by the Ministry of Science and Higher Education of the Russian Federation under the 5-100 Excellence Programme.
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Gimadi, E.K., Tsidulko, O. (2020). Asymptotically Optimal Algorithms for the Prize-Collecting Traveling Salesman Problem on Random Inputs. In: Matsatsinis, N., Marinakis, Y., Pardalos, P. (eds) Learning and Intelligent Optimization. LION 2019. Lecture Notes in Computer Science(), vol 11968. Springer, Cham. https://doi.org/10.1007/978-3-030-38629-0_16
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DOI: https://doi.org/10.1007/978-3-030-38629-0_16
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