Approximation Algorithms with Constant Factors for a Series of Asymmetric Routing Problems

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 nu...

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Bibliographic Details
Published in:Doklady. Mathematics Vol. 108; no. 3; pp. 499 - 505
Main Authors: Neznakhina, E. D., Ogorodnikov, Yu. Yu, Rizhenko, K. V., Khachay, M. Yu
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.12.2023
Springer Nature B.V
Subjects:
Accuracy
Algorithms
Approximation
Asymmetry
Combinatorial analysis
Costs
Customers
Fines & penalties
Graphs
Linear programming
Mathematics
Mathematics and Statistics
Traveling salesman problem
Vehicles
approximation algorithm
constant ratio
asymmetric traveling salesman problem
cycle cover problem
vehicle routing problem
Steiner cycle problem
ISSN:1064-5624, 1531-8362
Online Access:Get full text
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Summary: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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ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562423701454