Abstract
The stacker crane problem is treated as one modified arc routing problem. This problem is to find some route for stacker cranes on a construction site such that all arcs in a mixed graph \(G=(V,E\cup A;w)\) must be traversed at least once. In the real literature, since many different building materials must be handled, we consider the generalized stacker crane (GSC) problem, and the objective of this new problem is to determine a minimum weighted tour C traversing each arc e (in A) a number of times between the lower demand and upper demand.
In this paper, we design two approximation algorithms for the GSC problem. The first algorithm uses some exact algorithm to solve the integral circulation problem, and the second algorithm uses some approximation algorithm to solve the metric traveling salesman problem. Combining these two approximation algorithms, we can design a 9/5-approximation algorithm to solve the GSC problem.
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References
Edmonds, J., Johnson, E.L.: Matching, Euler tours and the Chinese postman. Math. Program. 5, 88–124 (1973)
Frederickson, G.N., Hecht, M.S., Kim, C.E.: Approximation algorithms for some routing problems. SIAM J. Comput. 7(2), 178–193 (1978)
Frederickson, G.N.: Approximation algorithms for some postman problems. J. ACM 26, 538–554 (1979)
Guan, M.G.: Graphic programming using odd and even points (in Chinese). Acta Mathematica Sinica 10, 263–266 (1960). [English translation: Chinese Mathematics, 1, 273–277 (1962)]
Lenstra, J.K., Rinnooy Kan, A.H.G.: On general routing problems. Networks 6, 273–280 (1976)
Orloff, C.S.: A fundamental problem in vehicle routing. Networks 4, 35–64 (1974)
Papadimitriou, C.H.: On the complexity of edge traversing. J. ACM 23(3), 544–554 (1976)
Raghavachari, B., Veerasamy, J.: A 3/2-approximation algorithm for the mixed postman problem. SIAM J. Discrete Math. 12(4), 425–433 (1999)
Acknowledgments
The work is supported in part by the National Natural Science Foundation of China [Nos. 11461081, 61662088, 11761078] and the Natural Science Foundation of Education Department of Yunnan Province [No. 2017ZZX235].
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Li, J., Liu, X., Li, W., Guan, L., Lichen, J. (2017). Approximation Algorithms for the Generalized Stacker Crane Problem. In: Gao, X., Du, H., Han, M. (eds) Combinatorial Optimization and Applications. COCOA 2017. Lecture Notes in Computer Science(), vol 10627. Springer, Cham. https://doi.org/10.1007/978-3-319-71150-8_8
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