Constant-Factor Approximation Algorithms for a Series of Combinatorial Routing Problems Based on the Reduction to the Asymmetric Traveling Salesman Problem

For the first time, algorithms with constant performance guarantees are substantiated for a series of asymmetric routing problems of combinatorial optimization: the Steiner cycle problem (SCP), the generalized traveling salesman problem (GTSP), the capacitated vehicle routing problem with unsplittab...

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Bibliographic Details
Published in:Proceedings of the Steklov Institute of Mathematics Vol. 319; no. Suppl 1; pp. S140 - S155
Main Authors: Khachay, M. Yu, Neznakhina, E. D., Ryzhenko, K. V.
Format: Journal Article Conference Proceeding
Language:English
Published: Moscow Pleiades Publishing 01.12.2022
Springer Nature B.V
Subjects:
Algorithms
Approximation
Asymmetry
Combinatorial analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
Optimization
Polynomials
Route planning
Traveling salesman problem
Vehicle routing
prize collecting traveling salesman problem
polynomial-time reduction
asymmetric traveling salesman problem
generalized traveling salesman problem
vehicle routing problem
constant-factor approximation algorithm
Steiner cycle problem
ISSN:0081-5438, 1531-8605
Online Access:Get full text
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Summary:For the first time, algorithms with constant performance guarantees are substantiated for a series of asymmetric routing problems of combinatorial optimization: the Steiner cycle problem (SCP), the generalized traveling salesman problem (GTSP), the capacitated vehicle routing problem with unsplittable customer demands (CVRP-UCD), and the prize collecting traveling salesman problem (PCTSP). The presented results are united by the property that they all rely on polynomial cost-preserving reduction to appropriate instances of the asymmetric traveling salesman problem (ATSP) and on the 22 𝜀 -approximation algorithm for this classical problem proposed by O. Svensson and V. Traub in 2019.
Bibliography:ObjectType-Article-1
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SourceType-Conference Papers & Proceedings-1
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ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543822060128