A Spatio-Temporally Opportunistic Approach to Best-Start-Time Lagrangian Shortest Path

  • Sarnath RamnathEmail author
  • Zhe Jiang
  • Hsuan-Heng Wu
  • Venkata M. V. Gunturi
  • Shashi Shekhar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9239)


The Best-start-time Lagrangian Shortest Path (BLSP) problem requires choosing the start time that yields the shortest path in a time-dependent graph. The inputs to the problem are a spatio-temporal network, an origin, o, a destination, d, and a discrete interval of possible start times. The solution is a path, P, and a start time, t, such that the total time taken to travel along P, starting at t, is no greater than the time taken to travel along any path from o to d, if we start in the given interval. The problem is important when the traveler is flexible about the start time, but would like to select a start time that minimizes the travel time. Its computational challenges arise from the large number of start time instants, and the manner in which the length of the shortest lagrangian path can vary from one start time instant to the next. Earlier work focused largely on finding the shortest path for a single start time. Researchers recently considered the BLSP problem, and proposed an approach based on finding the shortest lagrangian path for each start time, and then picking the best. Such an approach performs redundant evaluation of common sub-expressions, because time is explored in a sequential manner. We present an algorithm, BESTIMES, and propose an implementation that uses a Temporally Expanded priority queue. Our algorithm is built on the idea of “spatio-temporal opportunism”, which allows us to navigate both space and time simultaneously in a non-sequential manner and appropriately combine sub-paths. Theoretical analysis and experiments on real data show that there is a well-defined range of inputs over which this approach performs significantly better than previous approaches.


Short Path Time Instant Start Time Priority Queue Query Vertex 
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.



We are grateful to the members of the Spatial Database Research Group at the University of Minnesota and Dr Betsy George for their valuable feedback, and Kim Koffolt for editing help. This material is based upon work supported by the National Science Foundation under Grant No. 1029711, IIS-1320580, 0940818 and IIS-1218168, the USDOD under Grant No. HM1582-08-1-0017 and HM0210-13-1-0005, and the University of Minnesota under the OVPR U-Spatial.


  1. 1.
  2. 2.
    Delling, D., Wagner, D.: Landmark-based routing in dynamic graphs. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 52–65. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  3. 3.
    Delling, D., Wagner, D.: Time-dependent route planning. In: Ahuja, R.K., Möhring, R.H., Zaroliagis, C.D. (eds.) Robust and Online Large-Scale Optimization. LNCS, vol. 5868, pp. 207–230. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  4. 4.
    Bauer, R., Delling, D.: Sharc: fast and robust unidirectional routing. J. Exp. Algorithmics 4:2.14, 4:2.4–29 (2010)Google Scholar
  5. 5.
    Chabini, I.: Discrete dynamic shortest path problems in transportation applications: complexity and algorithms with optimal run time. Transp. Res. Rec. 1645, 170–175 (1998)CrossRefGoogle Scholar
  6. 6.
    Cooke, K.L., Halsey, E.: The shortest route through a network with time-dependent internodal transit times. J. Math. Anal. App. 14, 493–498 (1966)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press, Cambridge (2001)zbMATHGoogle Scholar
  8. 8.
    Costa, C.F., Nascimento, M.A., de Macêdo, J.A.F., Machado, J.C.: Nearest neighbor queries with service time constraints in time-dependent road networks. In: Proceedings of 2nd ACM SIGSPATIAL MobiGIS 2013, Orlando, Florida, USA, pp. 22–29 (2013)Google Scholar
  9. 9.
    Dean, B.C.: Shortest paths in fifo time-dependent networks: theory and algorithms. Technical report (2004)Google Scholar
  10. 10.
    Demiryurek, U., Banaei-Kashani, F., Shahabi, C.: A case for time-dependent shortest path computation in spatial networks. In: Proceedings of 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems, GIS 2010, pp. 474–477 (2010)Google Scholar
  11. 11.
    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) CrossRefGoogle Scholar
  12. 12.
    Ding, B., Yu, J.X., Qin, L.: Finding time-dependent shortest paths over large graphs. In: Proceedings of 11th International Conference on Extending Database Technology (EDBT), pp. 205–216 (2008)Google Scholar
  13. 13.
    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: Proceedings of 18th SIGSPATIAL International Conference on Advances in GIS, GIS 2010, pp. 212–221 (2010)Google Scholar
  14. 14.
    Foschini, L., Hershberger, J., Suri, S.: On the complexity of time-dependent shortest paths. In: Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011, pp. 327–341 (2011)Google Scholar
  15. 15.
    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
  16. 16.
    Gunturi, V.M.V., Nunes, E., Yang, K.S., Shekhar, S.: A critical-time-point approach to all-start-time lagrangian shortest paths: a summary of results. In: Pfoser, D., Tao, Y., Mouratidis, K., Nascimento, M.A., Mokbel, M., Shekhar, S., Huang, Y. (eds.) SSTD 2011. LNCS, vol. 6849, pp. 74–91. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  17. 17.
    Jagadeesh, G., Srikanthan, T., Quek, K.: Heuristic techniques for accelerating hierarchical routing on road networks. IEEE Trans. Intell. Transp. Syst. 3(4), 301–309 (2002)CrossRefGoogle Scholar
  18. 18.
    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
  19. 19.
    Kirchler, D., Liberti, L., Calvo, R.W.: Efficient computation of shortest paths in time-dependent multi-modal networks. J. Exp. Algorithmics 19, 1–29 (2015)CrossRefGoogle Scholar
  20. 20.
    Ma, Y., Yang, B., Jensen, C.S.: Enabling time-dependent uncertain eco-weights for road networks. In: Proceedings of Workshop on Managing and Mining Enriched Geo-Spatial Data, SIGMOD 2014, p. 1 (2014)Google Scholar
  21. 21.
    Mouratidis, K., Yiu, M.L., Papadias, D., Mamoulis, N.: Continuous nearest neighbor monitoring in road networks. In: Proceedings of 32nd International Conference on Very Large Data Bases, pp. 43–54, September 2006Google Scholar
  22. 22.
    Nannicini, G., Delling, D., Liberti, L., Schultes, D.: Bidirectional A \(^ \ast \) search for time-dependent fast paths. In: McGeoch, C.C. (ed.) WEA 2008. LNCS, vol. 5038, pp. 334–346. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  23. 23.
    Pinelli, F., Hou, A., Calabrese, F., Nanni, M., Zegras, C., Ratti, C.: Space and time-dependant bus accessibility: a case study in Rome. In: 12th International IEEE Conference on Intelligent Transportation Systems (2009)Google Scholar
  24. 24.
    Yuan, J., Zheng, Y., Zhang, C., Xie, W., Xie, X., Sun, G., Huang, Y.: T-drive: driving directions based on taxi trajectories. In: Proceedings of 18th SIGSPATIAL International Conference on Advances in GIS, GIS 2010 (2010)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Sarnath Ramnath
    • 2
    Email author
  • Zhe Jiang
    • 1
  • Hsuan-Heng Wu
    • 3
  • Venkata M. V. Gunturi
    • 1
  • Shashi Shekhar
    • 1
  1. 1.Computer Science and EngineeringUniversity of MinnesotaMinneapolisUSA
  2. 2.Computer Science and Information TechnologySt. Cloud State UniversitySt. CloudUSA
  3. 3.Department of Computer ScienceNational Tsing Hua UniversityHsinchuTaiwan

Personalised recommendations