Abstract
We study an online scheduling problem that is motivated by applications such as car-sharing for trips among a number of locations. Users submit ride requests, and the scheduler aims to accept as many requests as k servers (cars) could. Each ride request specifies the pick-up time, the pick-up location, and the drop-off location. A request can be submitted at any time during a certain time interval that precedes the pick-up time. The scheduler has to decide whether or not to accept a request immediately at the time when the request is submitted (booking time). For the general case in which requests may have arbitrary lengths, L, the ratio of the longest to the shortest request, is an important parameter. We give an algorithm with competitive ratio O(L), where the ratio L is known in advance. It is shown that no \(O(L^{\alpha })\)-competitive algorithm exists for the fixed booking variant, where \(0<\alpha <1\). It is also proved that no O(L)-competitive algorithm exists for the variable booking variant.
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References
The future of driving: Seeing the back of the car. The Economist (2012)
Ascheuer, N., Krumke, S.O., Rambau, J.: Online dial-a-ride problems: minimizing the completion time. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 639–650. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-46541-3_53
Bjelde, A., et al.: Tight bounds for online TSP on the line. In: Proceedings of the 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017), pp. 994–1005. SIAM (2017). https://doi.org/10.1137/1.9781611974782.63
Böhmová, K., Disser, Y., Mihalák, M., Šrámek, R.: Scheduling transfers of resources over time: towards car-sharing with flexible drop-offs. In: Kranakis, E., Navarro, G., Chávez, E. (eds.) LATIN 2016. LNCS, vol. 9644, pp. 220–234. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49529-2_17
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)
Krumke, S.O., de Paepe, W.E., Poensgen, D., Lipmann, M., Marchetti-Spaccamela, A., Stougie, L.: On minimizing the maximum flow time in the online dial-a-ride problem. In: Erlebach, T., Persinao, G. (eds.) WAOA 2005. LNCS, vol. 3879, pp. 258–269. Springer, Heidelberg (2006). https://doi.org/10.1007/11671411_20
Christman, A., Forcier, W., Poudel, A.: From theory to practice: maximizing revenues for on-line dial-a-ride. J. Comb. Optim. 35(2), 512–529 (2018)
Lipton, R.J., Tomkins, A.: Online interval scheduling. In: Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, 23–25 January 1994, Arlington, Virginia, USA, pp. 302–311 (1994). http://dl.acm.org/citation.cfm?id=314464.314506
Luo, K., Erlebach, T., Xu, Y.: Car-sharing between two locations: online scheduling with flexible advance bookings. In: Wang, L., Zhu, D. (eds.) COCOON 2018. LNCS, vol. 10976, pp. 242–254. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94776-1_21
Luo, K., Erlebach, T., Xu, Y.: Car-sharing between two locations: online scheduling with two servers. In: 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018, 27–31 August 2018, Liverpool, UK. LIPIcs, vol. 117, pp. 50:1–50:14. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2018). https://doi.org/10.4230/LIPIcs.MFCS.2018.50
Luo, K., Erlebach, T., Xu, Y.: Online scheduling of car-sharing requests between two locations with many cars and flexible advance bookings. In: ISAAC 2018: The 29th International Symposium on Algorithms and Computation. LIPIcs, vol. 123. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2018, to appear)
Luo, K., Erlebach, T., Xu, Y.: Car-sharing on a star network: on-line scheduling with k servers. In: 36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019, 13–16 March 2019, Berlin, Germany, pp. 51:1–51:14 (2019). https://doi.org/10.4230/LIPIcs.STACS.2019.51
Acknowledgments
This work was partially supported by the China Postdoctoral Science Foundation (Grant No. 2016M592811), and the National Nature Science Foundation of China (Grant No. 71701048).
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Liu, H., Luo, K., Xu, Y., Zhang, H. (2019). Car-Sharing Problem: Online Scheduling with Flexible Advance Bookings. In: Li, Y., Cardei, M., Huang, Y. (eds) Combinatorial Optimization and Applications. COCOA 2019. Lecture Notes in Computer Science(), vol 11949. Springer, Cham. https://doi.org/10.1007/978-3-030-36412-0_27
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DOI: https://doi.org/10.1007/978-3-030-36412-0_27
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