Abstract
We present an exact algorithm for the Minimum Duration Time-Dependent Shortest Path Problem with piecewise linear arc travel time functions. The algorithm iteratively refines a time-expanded network model, which allows for the computation of a lower and an upper bound, until - in a finite number of iterations - an optimal solution is obtained.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Chabini, I.: Discrete dynamic shortest path problems in transportation applications: complexity and algorithms with optimal run time. Transp. Res. Rec. 1645, 170–175 (1998)
Dean, B.C.: Shortest paths in FIFO time-dependent networks: theory and algorithms. Rapport technique, Massachusetts Institute of Technology (2004)
Demiryurek, U., Banaei-Kashani, F., Shahabi, C., Ranganathan, A.: Online computation of fastest path in time-dependent spatial networks. In: Pfoser, D., Tao, Y., Mouratidis, K., Nascimento, M.A., Mokbel, M., Shekhar, S., Huang, Y. (eds.) SSTD 2011. LNCS, vol. 6849, pp. 92–111. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22922-0_7
Gunturi, V.M., Joseph, K., Shekhar, S., Carley, K.M.: Information lifetime aware analysis for dynamic social networks. Technical report, University of Minnesota (2012)
Foschini, L., Hershberger, J., Suri, S.: On the complexity of time-dependent shortest paths. Algorithmica 68(4), 1075–1097 (2014)
Orda, A., Rom, R.: Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length. J. ACM (JACM) 37(3), 607–625 (1990)
Nachtigall, K.: Time depending shortest-path problems with applications to railway networks. Eur. J. Oper. Res. 83(1), 154–166 (1995)
Ding, B., Yu, J.X., Qin, L.: Finding time-dependent shortest paths over large graphs. In: Proceedings of the 11th International Conference on Extending Database Technology: Advances in Database Technology, pp. 205–216. ACM (2008)
Kanoulas, E., Du, Y., Xia, T., Zhang, D.: Finding fastest paths on a road network with speed patterns. In: Proceedings of the 22nd International Conference on Data Engineering, ICDE 2006, p. 10. IEEE (2006)
Boland, N., Hewitt, M., Marshall, L., Savelsbergh, M.: The continuous-time service network design problem. Oper. Res. 65(5), 1303–1321 (2017)
Acknowledgements
This material is based upon work supported by the National Science Foundation under Grant No. 1662848.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
He, E., Boland, N., Nemhauser, G., Savelsbergh, M. (2018). A Dynamic Discretization Discovery Algorithm for the Minimum Duration Time-Dependent Shortest Path Problem. In: van Hoeve, WJ. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2018. Lecture Notes in Computer Science(), vol 10848. Springer, Cham. https://doi.org/10.1007/978-3-319-93031-2_21
Download citation
DOI: https://doi.org/10.1007/978-3-319-93031-2_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-93030-5
Online ISBN: 978-3-319-93031-2
eBook Packages: Computer ScienceComputer Science (R0)