A primal-dual approximation algorithm for the Asymmetric Prize-Collecting TSP

We present a primal-dual ⌈log( n )⌉-approximation algorithm for the version of the asymmetric prize collecting traveling salesman problem, where the objective is to find a directed tour that visits a subset of vertices such that the length of the tour plus the sum of penalties associated with vertic...

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Bibliographic Details
Published in:Journal of combinatorial optimization Vol. 25; no. 2; pp. 265 - 278
Main Author: Nguyen, Viet Hung
Format: Journal Article
Language:English
Published: Boston Springer US 01.02.2013
Springer Science + Business Media
Springer Verlag
Subjects:
Combinatorics
Computer Science
Convex and Discrete Geometry
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
Approximation algorithm
Prize collecting Traveling Salesman
Primal-dual algorithm
ISSN:1382-6905, 1573-2886
Online Access:Get full text
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Summary:We present a primal-dual ⌈log( n )⌉-approximation algorithm for the version of the asymmetric prize collecting traveling salesman problem, where the objective is to find a directed tour that visits a subset of vertices such that the length of the tour plus the sum of penalties associated with vertices not in the tour is as small as possible. The previous algorithm for the problem (V.H. Nguyen and T.T Nguyen in Int. J. Math. Oper. Res. 4(3):294–301, 2012 ) which is not combinatorial, is based on the Held-Karp relaxation and heuristic methods such as the Frieze et al.’s heuristic (Frieze et al. in Networks 12:23–39, 1982 ) or the recent Asadpour et al.’s heuristic for the ATSP (Asadpour et al. in 21st ACM-SIAM symposium on discrete algorithms, 2010 ). Depending on which of the two heuristics is used, it gives respectively 1+⌈log( n )⌉ and as an approximation ratio. Our algorithm achieves an approximation ratio of ⌈log( n )⌉ which is weaker than but represents the first combinatorial approximation algorithm for the Asymmetric Prize-Collecting TSP.
ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-012-9501-z