Time-Aggregated Graphs for Modeling Spatio-temporal Networks

  • Betsy George
  • Shashi Shekhar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4231)


Given applications such as location based services and the spatio-temporal queries they may pose on a spatial network (eg. road networks), the goal is to develop a simple and expressive model that honors the time dependence of the road network. The model must support the design of efficient algorithms for computing the frequent queries on the network. This problem is challenging due to potentially conflicting requirements of model simplicity and support for efficient algorithms. Time expanded networks which have been used to model dynamic networks employ replication of the network across time instants, resulting in high storage overhead and algorithms that are computationally expensive. In contrast, the proposed time-aggregated graphs do not replicate nodes and edges across time; rather they allow the properties of edges and nodes to be modeled as a time series. Since the model does not replicate the entire graph for every instant of time, it uses less memory and the algorithms for common operations (e.g. connectivity, shortest path) are computationally more efficient than the time expanded networks.


Time-aggregated graphs shortest paths spatio-temporal data-bases location based services 


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  1. 1.
    Dean, B.C.: Algorithms for minimum-cost paths in time-dependent networks. Networks 44 (August 2004)Google Scholar
  2. 2.
    Ding, Z., Guting, R.H.: Modeling temporally variable transportation networks. In: Proc. 16th Intl. Conf. on Database Systems for Advanced Applications, pp. 154–168 (2004)Google Scholar
  3. 3.
    Hall, R.: The fastest path through a network with random time-dependent travel times. Transportation Science 20, 182–188 (1986)CrossRefGoogle Scholar
  4. 4.
    Kaufman, D.E., Smith, R.L.: Fastest paths in time-dependent networks for intelligent vehicle highway systems applications. IVHS Journal 1(1), 1–11 (1993)Google Scholar
  5. 5.
    Kohler, E., Langtau, 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
  6. 6.
    Lu, Q., George, B., Shekhar, S.: Capacity Constrained Routing Algorithms for Evacuation Planning: A Summary of Results. In: Bauzer Medeiros, C., Egenhofer, M.J., Bertino, E. (eds.) SSTD 2005. LNCS, vol. 3633, pp. 291–307. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Miller-Hooks, E., Mahmassani, H.S.: Least possible time paths in stochastic time-varying networks. Computers and Operations Research 25(12), 1107–1125 (1998)zbMATHCrossRefGoogle Scholar
  8. 8.
    Miller-Hooks, E., Mahmassani, H.S.: Path comparisons for a priori and time-adaptive decisions in stochastic, time-varying networks. European Journal of Operational Research 146, 67–82 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Pallottino, S., Scuttella, M.G.: Shortest path algorithms in tranportation models: Classical and innovative aspects. Equilibrium and Advanced transportation Modelling (Kluwer), 245–281 (1998)Google Scholar
  10. 10.
    Shekhar, S., Chawla, S.: Spatial Databases: Tour. Prentice-Hall, Englewood Cliffs (2003)Google Scholar
  11. 11.
    Shekhar, S., Chawla, S., Vatsavai, R., Ma, X., Yoo, J.S.: Location Based Services. In: Schiller, J., Voisard, A. (eds.) Morgan Kaufmann, San Francisco (2004)Google Scholar
  12. 12.
    Sawitzki, D.: Implicit Maximization of Flows over Time. Technical report, University of Dortmund (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Betsy George
    • 1
  • Shashi Shekhar
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity of MinnesotaMinneapolisUSA

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