An Approximation Algorithm for the Clustered Path Travelling Salesman Problem
Authors: 
Jiaxuan Zhang, Suogang Gao, Bo Hou, Wen LiuAuthors Info & Claims
Jiaxuan Zhang, Suogang Gao, Bo Hou, Wen LiuAuthors Info & ClaimsPages 15 - 27
Abstract
In this paper, we consider the clustered path travelling salesman problem. In this problem, we are given a complete graph with edge weight satisfying the triangle inequality. In addition, the vertex set V is partitioned into clusters . The objective of the problem is to find a minimum Hamiltonian path in G, and in the path all vertices of each cluster are visited consecutively. We provide a polynomial-time approximation algorithm for the problem.
References
[1]
An H-C, Kleinberg R, and Shmoys DB Improving Christofide’ algorithm for the s-t path TSP J. ACM 2015 62 5 1-28
[2]
Anily S, Bramel J, and Hertz A A 5/3-approximation algorithm for the clustered traveling salesman tour and path problems Oper. Res. Lett. 1999 24 29-35
[3]
Arkin EM, Hassin R, and Klein L Restricted delivery problems on a network Networks 1994 29 205-216
[4]
Bland RG and Shallcross DF Large travelling salesman problems arising from experiments in X-ray crystallography: a preliminary report on computation Oper. Res. Lett. 1989 8 3 125-128
[5]
Chisman JA The clustered traveling salesman problem Comput. Oper. Res. 1975 2 115-119
[6]
Christofides, N.: Worst-case analysis of a new heuristic for the Travelling Salesman Problem. Technical report 388, Graduate School of Industrial Administration, Carnegie Mellon University (1976)
[7]
Diestel R Graph Theory 2017 New York Springer
[8]
Edmonds J Paths, trees and flowers Can. J. Math. 1965 17 449-467
[9]
Gendreau M, Hertz A, and Laporte G The traveling salesman problem with backhauls Comput. Oper. Res. 1996 23 501-508
[10]
Grinman, A.: The Hungarian algorithm for weighted bipartite graphs. Seminar in Theoretical Computer Science (2015)
[11]
Grötschel M and Holland O Solution of large-scale symmetric traveling salesman problems Math. Program. 1991 51 141-202
[12]
Gottschalk C and Vygen J Better s-t-tours by Gao trees Math. Program. 2018 172 191-207
[13]
Guttmann-Beck N, Hassin R, Khuller S, and Raghavachari B Approximation algorithms with bounded performance guarantees for the clustered traveling salesman problem Algorithmica 2000 28 422-437
[14]
Hong YM, Lai HJ, and Liu QH Supereulerian digraphs Discrete Math. 2014 330 87-95
[15]
Hoogeveen JA Analysis of Christofides’ heuristic: some paths are more difficult than cycles Oper. Res. Lett. 1991 10 291-295
[16]
Jongens K and Volgenant T The symmetric clustered traveling salesman problem Eur. J. Oper. Res. 1985 19 68-75
[17]
Kawasaki M and Takazawa T Improving approximation ratios for the clustered travelling salesman problem J. Oper. Res. Soc. Jpn. 2020 63 2 60-70
[18]
Plante RD, Lowe TJ, and Chandrasekaran R The product matrix travelling salesman problem: an application and solution heuristics Oper. Res. 1987 35 772-783
[19]
Sebő, A., van Zuylen, A.: The salesman’s improved paths: a 3/2+1/34 approximation. In: Proceedings of 57th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 118–127 (2016)
[20]
Traub V and Vygen J Approaching 3/2 for the s-t path TSP J. ACM 2019 66 2 1-17
[21]
Yao A An O algorithm for finding minimum spanning trees Inf. Process. Lett. 1975 4 21-23
[22]
Zenklusen, R.: A 1.5-approximation for path TSP. In: Proceedings of the 30th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1539–1549 (2019)
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Published: 13 August 2022
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