Abstract
We introduce the Train Scheduling Problem which can be described as follows: Given m trains via their tracks, i.e., curves in the plane, and the trains’ lengths, we want to compute a schedule that moves collision-free and with limited speed the trains along their tracks such that the maximal travel time is minimized. We prove that there is no FPTAS for the Train Scheduling Problem unless P = NP. Furthermore, we provide near-optimal runtime algorithms extending existing schedules.
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References
Akella, S., Hutchinson, S.: Coordinating the motions of multiple robots with specified trajectories. In: Proceedings of the 2002 IEEE International Conference on Robotics and Automation, ICRA 2002, Washington, DC, USA, 11–15 May 2002, pp. 624–631 (2002)
Cole, R.: Slowing down sorting networks to obtain faster sorting algorithms. J. ACM 34(1), 200–208 (1987)
Hopcroft, J.E., Schwartz, J.T., Sharir, M.: On the complexity of motion planning for multiple independent objects; PSPACE-hardness of the warehouseman’s problem. Int. J. Rob. Res. 3(4), 76–88 (1984)
Kant, K., Zucker, S.W.: Toward efficient trajectory planning: the path-velocity decomposition. Int. J. Rob. Res. 5(3), 72–89 (1986)
Kavraki, L.E., LaValle, S.M.: Motion planning. In: Siciliano, B., Khatib, O. (eds.) Springer Handbook of Robotics, pp. 139–162. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-32552-1_7
Latombe, J.C.: Robot Motion Planning. Kluwer Academic Publishers, Norwell (1991)
LaValle, S.M.: Planning Algorithms. Cambridge University Press, Cambridge (2006)
O’Donnell, P.A., Lozano-Pérez, T.: Deadlock-free and collision-free coordination of two robot manipulators. In: Proceedings of the 1989 IEEE International Conference on Robotics and Automation, Scottsdale, Arizona, USA, 14–19 May 1989, pp. 484–489 (1989)
Reif, J.H., Sharir, M.: Motion planning in the presence of moving obstacles. J. ACM 41(4), 764–790 (1994)
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Scheffer, C. (2020). Train Scheduling: Hardness and Algorithms. In: Rahman, M., Sadakane, K., Sung, WK. (eds) WALCOM: Algorithms and Computation. WALCOM 2020. Lecture Notes in Computer Science(), vol 12049. Springer, Cham. https://doi.org/10.1007/978-3-030-39881-1_30
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DOI: https://doi.org/10.1007/978-3-030-39881-1_30
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