A Critical-Time-Point Approach to All-Start-Time Lagrangian Shortest Paths: A Summary of Results

  • Venkata M. V. Gunturi
  • Ernesto Nunes
  • KwangSoo Yang
  • Shashi Shekhar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6849)


Given a spatio-temporal network, a source, a destination, and a start-time interval, the All-start-time Lagrangian Shortest Paths (ALSP) problem determines a path set which includes the shortest path for every start time in the given interval. ALSP is important for critical societal applications related to air travel, road travel, and other spatio-temporal networks. However, ALSP is computationally challenging due to the non-stationary ranking of the candidate paths, meaning that a candidate path which is optimal for one start time may not be optimal for others. Determining a shortest path for each start-time leads to redundant computations across consecutive start times sharing a common solution. The proposed approach reduces this redundancy by determining the critical time points at which an optimal path may change. Theoretical analysis and experimental results show that this approach performs better than naive approaches particularly when there are few critical time points.


Short Path Time Instant Start Time Priority Queue Total Travel Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Delta airlines,
  2. 2.
  3. 3.
  4. 4.
    Batchelor, G.K.: An introduction to fluid dynamics. Cambridge Univ. Press, Cambridge (1973)zbMATHGoogle Scholar
  5. 5.
    Chabini, I., Lan, S.: Adaptations of the a* algorithm for the computation of fastest paths in deterministic discrete-time dynamic networks. IEEE Transactions on Intelligent Transportation Systems 3(1), 60–74 (2002)CrossRefGoogle Scholar
  6. 6.
    Demiryurek, U., Banaei-Kashani, F., Shahabi, C.: A case for time-dependent shortest path computation in spatial networks. In: Proc. of the SIGSPATIAL Intl. Conf. on Advances in GIS, GIS 2010, pp. 474–477 (2010)Google Scholar
  7. 7.
    Deutsch, C.: Ups embraces high-tech delivery methods. NY Times (July 12, 2007),
  8. 8.
    Ding, B., Yu, J.X., Qin, L.: Finding time-dependent shortest paths over large graphs. In: Proc. of the Intl. Conf. on Extending Database Technology (EDBT), pp. 205–216 (2008)Google Scholar
  9. 9.
    Evans, M.R., Yang, K., Kang, J.M., Shekhar, S.: A lagrangian approach for storage of spatio-temporal network datasets: a summary of results. In: Proc. of the SIGSPATIAL Intl. Conf. on Advances in GIS, GIS 2010, pp. 212–221 (2010)Google Scholar
  10. 10.
    Foschini, L., Hershberger, J., Suri, S.: On the complexity of time-dependent shortest paths. In: SODA. pp. 327–341 (2011)Google Scholar
  11. 11.
    George, B., Shekhar, S.: Time-aggregated graphs for modelling spatio-temporal networks. J. Semantics of Data XI, 191 (2007)Google Scholar
  12. 12.
    George, B., Shekhar, S., Kim, S.: Spatio-temporal network databases and routing algorithms. Tech. Rep. 08-039, Univ. of Minnesota - Comp. Sci. and Engg. (2008)Google Scholar
  13. 13.
    George, B., Kim, S., Shekhar, S.: Spatio-temporal network databases and routing algorithms: A summary of results. In: Papadias, D., Zhang, D., Kollios, G. (eds.) SSTD 2007. LNCS, vol. 4605, pp. 460–477. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Gunturi, V., Shekhar, S., Bhattacharya, A.: Minimum spanning tree on spatio-temporal networks. In: Bringas, P.G., Hameurlain, A., Quirchmayr, G. (eds.) DEXA 2010. LNCS, vol. 6262, pp. 149–158. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  15. 15.
    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), p. 10 (2006)Google Scholar
  16. 16.
    Kaufman, D.E., Smith, R.L.: Fastest paths in time-dependent networks for intelligent vehicle-highway systems application. I V H S Journal 1(1), 1–11 (1993)CrossRefGoogle Scholar
  17. 17.
    Köhler, E., Langkau, K., Skutella, M.: Time-expanded graphs for flow-dependent transit times. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 599–611. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  18. 18.
    Kleinberg, J., Tardos, E.: Algorithm Design. Pearson Education, London (2009)Google Scholar
  19. 19.
    Lovell, J.: Left-hand-turn elimination. NY Times (December 9, 2007),
  20. 20.
    Orda, A., Rom, R.: Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length. J. ACM 37(3), 607–625 (1990)CrossRefzbMATHGoogle Scholar
  21. 21.
    Yuan, J., Zheng, Y., Zhang, C., Xie, W., Xie, X., Sun, G., Huang, Y.: T-drive: driving directions based on taxi trajectories. In: Proc. of the SIGSPATIAL Intl. Conf. on Advances in GIS, GIS 2010, pp. 99–108 (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Venkata M. V. Gunturi
    • 1
  • Ernesto Nunes
    • 1
  • KwangSoo Yang
    • 1
  • Shashi Shekhar
    • 1
  1. 1.Computer Science and EngineeringUniversity of MinnesotaUSA

Personalised recommendations