Spatio-temporal Networks: Modeling, Storing, and Querying Temporally-Detailed Roadmaps

  • Michael R. Evans
  • KwangSoo Yang
  • Viswanath Gunturi
  • Betsy George
  • Shashi Shekhar
Chapter

Abstract

Given spatio-temporal networks (e.g., roadmaps with traffic speed reported as a time-series in 5 min increments over a typical day for each road-segment) and operators (e.g., network snapshot, shortest path or path evaluation), a spatio-temporal network model provides a computer representation to facilitate reasoning, analysis and algorithm design for important societal applications. For example, next generation routing services are estimated to save consumers hundreds of billions of dollars in terms of time and fuel saved by 2020. Developing a model for spatio-temporal networks is challenging due to potentially conflicting requirements of expressiveness and model simplicity. Related work in Time Geography models spatio-temporal movement and relationships via dimension-based representations such as space-time prisms and space-time trajectories. These representations are not adequate for many STN use-cases, such as spatio-temporal routing queries. To address these limitations, we discuss a novel model called time-aggregated graph (TAG) that allows the properties of the network to be modeled as a time series. This model retains spatial network information while reducing the temporal replication needed in other models, thus resulting in a much more efficient model for several computational techniques for routing problems. In this chapter, we discuss spatio-temporal networks as represented by time-aggregated graphs at a conceptual, logical, and physical level. This chapter also focuses on shortest path algorithms for spatio-temporal networks. We develop the topics via case studies using TAGs in context of Lagrangian shortest-path queries and evacuation route planning.

References

  1. Abou-Rjeili, A., & Karypis, G. (2006). Multilevel algorithms for partitioning power-law graphs. In 20th international parallel and distributed processing symposium, 2006. IPDPS 2006 (p. 10). IEEE.Google Scholar
  2. Ahuja, R. K., Magnanti, T. L., & Orlin, J. B. (1993). Network flows. Englewood Cliffs: Prentice Hall.Google Scholar
  3. Batty, M. (2005). Agents, cells, and cities: New representational models for simulating multiscale urban dynamics. Environment and Planning A, 37, 1373–1394.CrossRefGoogle Scholar
  4. Ben-Akiva, M. (2002). Development of a deployable real-time dynamic traffic assignment system: Dynamit and dynamit-p user’s guide. Technical Report. Cambridge: Massachusetts Institute of Technology.Google Scholar
  5. Bertsekas, D. P. (1987). Dynamic programming: Deterministic and stochastic models. Englewood Cliffs: Prentice-Hall.Google Scholar
  6. Burns, L. (1979). Transportation, temporal, and spatial components of accessibility. Lexington: Lexington Books.Google Scholar
  7. Chabini, I. (1998). Discrete dynamic shortest path problems in transportation applications: Complexity and algorithms with optimal run time. Transportation Research Record: Journal of the Transportation Research Board, 1645(-1), 170–175.CrossRefGoogle Scholar
  8. Chabini, I., & Lan, S. (2002). 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.CrossRefGoogle Scholar
  9. Christakos, G., Bogaert, P., & Serre, M. (2001). Temporal GIS: Advanced functions for field-based applications. New York: Springer.CrossRefGoogle Scholar
  10. Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2001). Introduction to algorithms. Cambridge, MA: MIT Press.Google Scholar
  11. Dehne, F., Omran, M. T., & Sack, J.-R. (2009). Shortest paths in time-dependent FIFO networks using edge load forecasts. In Proceedings of the second international workshop on computational transportation science, IWCTS’09 (pp. 1–6). New York, NY: ACM.Google Scholar
  12. Delling, D. (2008). Time-dependent SHARC-routing. In Proceedings of the 16th annual European symposium on algorithms, ESA’08 (pp. 332–343). Berlin/Heidelberg: Springer.Google Scholar
  13. Delling, D., & Wagner, D. (2007). Landmark-based routing in dynamic graphs. In Experimental algorithms (pp. 52–65). Berlin/Heidelberg: Springer.Google Scholar
  14. Demiryurek, U., Banaei-Kashani, F., & Shahabi, C. (2010). A case for time-dependent shortest path computation in spatial networks. In Proc. of the ACM SIGSPATIAL Intl. Conf. on Advances in GIS, GIS’10 (pp. 474–477).Google Scholar
  15. Demiryurek, U., Banaei-Kashani, F., Shahabi, C., & Ranganathan, A. (2011). Online computation of fastest path in time-dependent spatial networks. In Advances in spatial and temporal databases. LNCS 6849 (pp. 92–111). Berlin/Heidelberg: Springer.Google Scholar
  16. Deutsch, C. (2007). UPS embraces high-tech delivery methods. www.nytimes.com/2007/07/12/business/12ups.html
  17. DiBiase, D., MacEachren, A., Krygier, J., & Reeves, C. (1992). Animation and the role of map design in scientific visualization. Cartography and Geographic Information Science, 19(4), 201–214.CrossRefGoogle Scholar
  18. Dijkstra, E. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1(1), 269–271.CrossRefGoogle Scholar
  19. Ding, B., Yu, J., & Qin, L. (2008). 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). New York: ACM.Google Scholar
  20. Dreyfus, S. (1969). An appraisal of some shortest path algorithms. Operations Research, 17, 395–412.CrossRefGoogle Scholar
  21. Egenhofer, M., & Golledge, R. (1998). Spatial and temporal reasoning in geographic information systems. New York: Oxford University Press.Google Scholar
  22. Ford, L., & Fulkerson, D. (1958). Constructing maximal dynamic flows from static flows. Operations Research, 6(3), 419–433.CrossRefGoogle Scholar
  23. Ford, L., & Fulkerson, D. (1962). Flows in networks. Princeton: Princeton University Press.Google Scholar
  24. Francis, R. L., & Chalmet, L. G. (1984). A negative exponential solution to an evacuation problem (Technical Report Research Report No. 84–86) Washington, DC: National Bureau Of Standards, Center for Fire Research.Google Scholar
  25. Frank, A. (2003). 2: Ontology for spatio-temporal databases. Lecture Notes in Computer Science, 2520, 9.CrossRefGoogle Scholar
  26. Frank, A., Grumbach, S., Güting, R., Jensen, C., Koubarakis, M., Lorentzos, N., Manolopoulos, Y., Nardelli, E., Pernici, B., Schek, H., et al. (1999). Chorochronos: A research network for spatiotemporal database systems. ACM SIGMOD Record, 28(3), 12–21.CrossRefGoogle Scholar
  27. Galton, A., & Worboys, M. (2005). Processes and events in dynamic geo-networks. Lecture Notes in Computer Science, 3799, 45.CrossRefGoogle Scholar
  28. George, B. & Shekhar, S. (2006). Time-aggregated graphs for modeling spatio-temporal networks. In Advances in conceptual modeling – Theory and practice (pp. 85–99). Berlin/Heidelberg: Springer.Google Scholar
  29. George, B., & Shekhar, S. (2007a, November). Modeling spatio-temporal network computations – A summary of results. In Proceedings of second international conference on GeoSpatial Semantics (GeoS 2007), Mexico City, Mexico.Google Scholar
  30. George, B., & Shekhar, S. (2007b). Time-aggregated graphs for modeling spatio-temporal networks – An extended abstract. Journal on Data Semantics, XI. 191–212. Berlin/Heidelberg: Springer.Google Scholar
  31. George, B., Kang, J., & Shekhar, S. (2007a, August). Spatio-temporal sensor graphs: A data model for discovery of patterns in sensor data. In Proceedings of first international workshop on knowledge discovery in Sensor Data (SensorKDD) in connection with KDD’07.Google Scholar
  32. George, B., Kim, S., & Shekhar, S. (2007b, July). Spatio-temporal network databases and routing algorithms: A summary of results. In Proceedings of international symposium on Spatial and Temporal Databases (SSTD’07), Boston, MA.Google Scholar
  33. George, B., Shekhar, S., & Kim, S. (2008). Spatio-temporal network databases and routing algorithms (Technical Report 08–039). Minneapolis: University of Minnesota – Computer Science and Engineering.Google Scholar
  34. Goodchild, M., Yuan, M., & Cova, T. (2007). Towards a general theory of geographic representation in GIS. International Journal of Geographical Information Science, 21(3), 239–260.CrossRefGoogle Scholar
  35. Gunturi, V., Shekhar, S., & Bhattacharya, A. (2010). Minimum spanning tree on spatio-temporal networks. In Proceedings of the 21st international conference on database and expert systems applications: Part II, DEXA’10 (pp. 149–158). Berlin/Heidelberg: Springer.Google Scholar
  36. Gunturi, V. M. V., Nunes, E., Yang, K., & Shekhar, S. (2011). A critical-time-point approach to all-start-time Lagrangian shortest paths: A summary of results. Advances in spatial and temporal databases. LNCS 6849 (pp. 74–91). Berlin/Heidelberg: Springer.Google Scholar
  37. Guttman, A. (1984). R-trees: A dynamic index structure for spatial searching. In Proceedings of the 1984 ACM SIGMOD international conference on management of data (pp. 47–57). New York: ACM.Google Scholar
  38. Hägerstrand, T. (1970). What about people in regional science? Papers in Regional Science, 24(1), 6–21.CrossRefGoogle Scholar
  39. Hamacher, H., & Tjandra, S. (2002). Mathematical modeling of evacuation problems: A state of the art. In Pedestrian and evacuation dynamics (pp. 227–266). Berlin/Heidelberg: Springer.Google Scholar
  40. Harrower, M. (2004). A look at the history and future of animated maps. Cartographica: The International Journal for Geographic Information and Geovisualization, 39(3), 33–42.CrossRefGoogle Scholar
  41. Herrera, J., & Bayen, A. (2009). Incorporation of Lagrangian measurements in freeway traffic state estimation. Transportation Research Part B: Methodological, 44, 460–481.CrossRefGoogle Scholar
  42. Hoppe, B., & Tardos, E. (1994). Polynomial time algorithms for some evacuation problems. In Proceedings of the fifth annual ACM-SIAM symposium on discrete algorithms, SODA’94 (pp. 433–441). Society for Industrial and Applied Mathematics. Philadelphia, PA.Google Scholar
  43. Janelle, D. (2004). Impact of information technologies. In The geography of urban transportation (p. 86). New York, NY: Addison-Wesley.Google Scholar
  44. Joel Lovell (December 9, 2007). Left-hand-turn elimination. New York Times. http://goo.gl/3bkPb
  45. Kanoulas, E., Du, Y., Xia, T., & Zhang, D. (2006). Finding fastest paths on a road network with speed patterns. In Proceedings of the 22nd International Conference on Data Engineering (ICDE) (p. 10). IEEE.Google Scholar
  46. Kaufman, D., & Smith, R. (1993). Fastest paths in time-dependent networks for intelligent vehicle highway systems applications. IVHS Journal, 1(1), 1–11.Google Scholar
  47. Kim, S., George, B., & Shekhar, S. (2007). Evacuation route planning: Scalable heuristics. In Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems (ACM-GIS) (pp. 1–8). New York, NY: ACM.Google Scholar
  48. Kisko, T. M., & Francis, R. L. (1985). Evacnet+: A computer program to determine optimal building evacuation plans. Fire Safety Journal, 9(2), 211–220.CrossRefGoogle Scholar
  49. Kisko, T., Francis, R., & Nobel, C. (1998). EVACNET4 user’s guide. University of Florida.Google Scholar
  50. Kohler, E., Langtau, K., & Skutella, M. (2002). Time-expanded graphs for flow-dependent transit times. In Proceedings 10th annual European symposium on algorithms (pp. 599–611). Berlin/Heidelberg: Springer.Google Scholar
  51. Kriegel, H.-P., Renz, M., & Schubert, M. (2010). Route skyline queries: A multi-preference path planning approach. In 26th international conference on data engineering (ICDE), 2010 IEEE (pp. 261–272). IEEE. Long Beach, CA.Google Scholar
  52. Kwan, M. (2004). GIS methods in time-geographic research: Geocomputation and geovisualization of human activity patterns. Geografiska Annaler: Series B, Human Geography, 86(4), 267–280.CrossRefGoogle Scholar
  53. Langran, G. (1992). Time in geographic information systems. London: Taylor & Francis.Google Scholar
  54. Langran, G., & Chrisman, N. (1988). A framework for temporal geographic information. Cartographica: The International Journal for Geographic Information and Geovisualization, 25(3), 1–14.CrossRefGoogle Scholar
  55. Lenntorp, B. (1977). Paths in space-time environments: A time-geographic study of movement possibilities of individuals. Environment and Planning A, 9, 961–972.CrossRefGoogle Scholar
  56. Lu, Q., Huang, Y., & Shekhar, S. (2003). Evacuation planning: A capacity constrained routing approach. In First NSF/NIJ symposium on intelligence and security informatics (pp. 111–125). Berlin/Heidelberg: Springer.Google Scholar
  57. Lu, Q., George, B., & Shekhar, S. (2005). Capacity constrained routing algorithms for evacuation planning: A summary of results. In Proceedings of 9th International Symposium on Spatial and Temporal Databases (SSTD™05) (pp. 22–24). Berlin/Heidelberg: Springer.Google Scholar
  58. Lu, Q., George, B., & Shekhar, S. (2007). Evacuation route planning: A case study in semantic computing. International Journal of Semantic Computing, 1(2), 249. World Scientific Publishing.CrossRefGoogle Scholar
  59. Luenberger, D. (1973). Introduction to linear and nonlinear programming. Reading: Addison-Wesley.Google Scholar
  60. Mahmassani, H. S., Sbayti, H., & Zhou, X. (2004). Dynasmart-p version 1.0 user’s guide. (Technical Report). Maryland Transportation Initiative, University of Maryland.Google Scholar
  61. McIntosh, J., & Yuan, M. (2005). Assessing similarity of geographic processes and events. Transactions in GIS, 9(2), 223–245.CrossRefGoogle Scholar
  62. Miller, H. (1999). Measuring space-time accessibility benefits within transportation networks: Basic theory and computational procedures. Geographical Analysis, 31(2), 187–212.CrossRefGoogle Scholar
  63. Miller, H. (2005). A measurement theory for time geography. Geographical Analysis, 37(1), 17–45.CrossRefGoogle Scholar
  64. Monmonier, M. (1990). Strategies for the visualization of geographic time-series data. Cartographica: The International Journal for Geographic Information and Geovisualization, 27(1), 30–45.CrossRefGoogle Scholar
  65. O’Sullivan, D. (2005). Geographical information science: Time changes everything. Progress in Human Geography, 29(6), 749.CrossRefGoogle Scholar
  66. Orda, A., & Rom, R. (1990). Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length. Journal of the ACM (JACM), 37(3), 607–625.CrossRefGoogle Scholar
  67. Orda, A., & Rom, R. (1991). Minimum weight paths in time-dependent networks. Networks, 21, 295–319.CrossRefGoogle Scholar
  68. Pallottino, S., & Scuttella, M. G. (1998). Shortest path algorithms in transportation models: Classical and innovative aspects. In Equilibrium and advanced transportation modelling (pp. 245–281). Kluwer. Springer US.Google Scholar
  69. Peuquet, D., & Duan, N. (1995). An event-based spatiotemporal data model (ESTDM) for temporal analysis of geographical data. International Journal of Geographical Information Science, 9(1), 7–24.CrossRefGoogle Scholar
  70. Pred, A. (1977). The choreography of existence: Comments on Hagerstrand’s time-geography and its usefulness. Economic Geography, 53, 207–221.CrossRefGoogle Scholar
  71. Russel, S., & Norwig, P. (1995). Artificial intelligence: A modern approach. Upper Saddle River: Prentice-Hall.Google Scholar
  72. Samet, H. (1995). Spatial data structures. In Modern database systems, the object model, interoperability and beyond (pp. 361–385). New York, NY: Addison-Wesley.Google Scholar
  73. Shekhar, S., & Liu, D.-R. (1997). CCAM: A connectivity-clustered access method for networks and network computations. IEEE Transactions on Knowledge and Data Engineering, 9(1), 102–119.CrossRefGoogle Scholar
  74. Shekhar, S., & Xiong, H. (2007). Encyclopedia of GIS. Berlin: Springer.Google Scholar
  75. Timmermans, H., Arentze, T., & Joh, C. (2002). Analysing space-time behaviour: New approaches to old problems. Progress in Human Geography, 26(2), 175.CrossRefGoogle Scholar
  76. Torrens, P. (2006). Simulating sprawl. Annals of the Association of American Geographers, 96(2), 248–275.CrossRefGoogle Scholar
  77. USA-Today. (2011, June). Evacuation plans age as population near nuclear plants soars.Google Scholar
  78. Vasconez, K., & Kehrli, M. (2010). Highway evacuations in selected metropolitan areas: Assessment of impediments (Technical Report FHWA-HOP-10-059). Washington, DC: Federal Highway Administration, Office of Transportation Operations.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht. 2015

Authors and Affiliations

  • Michael R. Evans
    • 1
  • KwangSoo Yang
    • 1
  • Viswanath Gunturi
    • 1
  • Betsy George
    • 1
  • Shashi Shekhar
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity of MinnesotaMinneapolisUSA

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