Finding Least On-Road Travel Time on Road Network

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9877)

Abstract

Shortest path and fastest path query on time-dependent road network are widely used nowadays, but none of them can answer a least on-road travel time query, which aims to find a path between two vertices on a time-dependent road network that has the minimum on-road travel time(waiting on any vertex is allowed). In this paper, we propose a cheapest path algorithm which expands Dijkstra’s Algorithm to solve this problem. The time complexity of it is \(O(|V|\log |V|+|V|T+|E|T^2)\), where T is the number of the involving time unit, |V| is the number of vertices and |E| is the number of edges. Extensive experiments are conducted on the two different speed profiles to test the performance of our cheapest path algorithm. The results validate the effectiveness of our work.

References

  1. 1.
    Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Math. 1(1), 269–271 (1959)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Goldberg, A.V., Harrelson, C.: Computing the shortest path: a search meets graph theory. In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 156–165. Society for Industrial and Applied Mathematics (2005)Google Scholar
  3. 3.
    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)Google Scholar
  4. 4.
    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: Advancesin Database Technology, pp. 205–216. ACM (2008)Google Scholar
  5. 5.
    Chabini, I.: Discrete dynamic shortest path problems in transportation applications: Complexity and algorithms with optimal run time. Trans. Res. Record: J. Transp. Res. Board 1645, 170–175 (1998)CrossRefGoogle Scholar
  6. 6.
    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)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    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). doi:10.1007/978-3-642-22922-0_7 CrossRefGoogle Scholar
  8. 8.
    Lu, E.H.-C., Lee, W.-C., Tseng, V.S.: Mining fastest path from trajectories with multiple destinations in road networks. Knowl. Inf. Syst. 29(1), 25–53 (2011)CrossRefGoogle Scholar
  9. 9.
    Cai, X., Kloks, T., Wong, C.: Time-varying shortest path problems with constraints. Networks 29(3), 141–150 (1997)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Wang, X., Zhou, X., Lu, S.: Spatiotemporal data modelling, management: a survey. In: Proceedings of the 36th International Conference on Technology of Object-Oriented Languages and Systems, TOOLS-Asia 2000, pp. 202–211. IEEE (2000)Google Scholar
  11. 11.
    Deng, K., Zhou, X., Shen, H.T., Sadiq, S., Li, X.: Instance optimal query processing in spatial networks. VLDB J. 18(3), 675–693 (2009)CrossRefGoogle Scholar
  12. 12.
    Zheng, K., Fung, P.C., Zhou, X.: K-nearest neighbor search for fuzzy objects. In: Proceedings of the 2010 ACM SIGMOD International Conference on Management of Data, pp. 699–710. ACM (2010)Google Scholar
  13. 13.
    Wu, H., Cheng, J., Huang, S., Ke, Y., Lu, Y., Xu, Y.: Path problems in temporal graphs. Proc. VLDB Endowment 7(9), 721–732 (2014)CrossRefGoogle Scholar
  14. 14.
    Wang, S., Lin, W., Yang, Y., Xiao, X., Zhou, S.: Efficient route planning on public transportation networks: a labelling approach. In: Proceedings of the 2015 ACM SIGMOD International Conference on Management of Data, pp. 967–982. ACM (2015)Google Scholar
  15. 15.
    Fratta, L., Gerla, M., Kleinrock, L.: The flow deviation method: An approach to store-and-forward communication network design. Networks 3(2), 97–133 (1973)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Cooke, K.L., Halsey, E.: The shortest route through a network with time-dependent internodal transit times. J. Math. Anal. Appl. 14(3), 493–498 (1966)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Batz, G.V., Delling, D., Sanders, P., Vetter, C.: Time-dependent contraction hierarchies. In: Proceedings of the Meeting on Algorithm Engineering and Expermiments, pp. 97–105. Society for Industrial and Applied Mathematics (2009)Google Scholar
  18. 18.
    Delling, D.: Time-dependent sharc-routing. Algorithmica 60(1), 60–94 (2011)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Dibbelt, J., Pajor, T., Strasser, B., Wagner, D.: Intriguingly simple and fast transit routing. In: Bonifaci, V., Demetrescu, C., Marchetti-Spaccamela, A. (eds.) SEA 2013. LNCS, vol. 7933, pp. 43–54. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  20. 20.
    Geisberger, R.: Contraction of timetable networks with realistic transfers. In: Festa, P. (ed.) SEA 2010. LNCS, vol. 6049, pp. 71–82. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  21. 21.
    Dreyfus, S.E.: An appraisal of some shortest-path algorithms. Oper. Res. 17(3), 395–412 (1969)CrossRefMATHGoogle Scholar
  22. 22.
    Halpern, J.: Shortest route with time dependent length of edges and limited delay possibilities in nodes. Z. fuer Oper. Res. 21(3), 117–124 (1977)MathSciNetMATHGoogle Scholar
  23. 23.
    Orda, A., Rom, R.: Minimum weight paths in time-dependent networks. Networks 21(3), 295–319 (1991)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.School of ITEEThe University of QueenslandBrisbaneAustralia

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