Skip to main content

Hierarchical Prism Trees for Scalable Time Geographic Analysis

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9927))

Abstract

As location-aware applications and location-based services continue to increase in popularity, data sources describing a range of dynamic processes occurring in near real-time over multiple spatial and temporal scales are becoming the norm. At the same time, existing frameworks useful for understanding these dynamic spatio-temporal data, such as time geography, are unable to scale to the high volume, velocity, and variety of these emerging data sources. In this paper, we introduce a computational framework that turns time geography into a scalable analysis tool that can handle large and rapidly changing datasets. The Hierarchical Prism Tree (HPT) is a dynamic data structure for fast queries on spatio-temporal objects based on time geographic principles and theories, which takes advantage of recent advances in moving object databases and computer graphics. We demonstrate the utility of our proposed HPT using two common time geography tasks (finding similar trajectories and mapping potential space-time interactions), taking advantage of open data on space-time vehicle emissions from the EnviroCar platform.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    Although some parallel versions of kd-trees [35] do show promise.

  2. 2.

    See for example, http://www.realtimerendering.com/intersections.html.

  3. 3.

    https://www.envirocar.org.

  4. 4.

    http://www.obdii.com/background.html.

  5. 5.

    ICARUS analyzes the migratory behavior of animals such as birds and bats:

    http://icarusinitiative.org.

  6. 6.

    Argos is a global, satellite-based platform widely used in animal tracking:

    http://www.argos-system.org/.

References

  1. Batty, M.: Smart cities, big data. Environ. Plan. 39(2), 191–193 (2012)

    Article  MathSciNet  Google Scholar 

  2. Yang, C., Raskin, R., Goodchild, M., Gahegan, M.: Geospatial cyberinfrastructure: past, present and future. Comput. Environ. Urban Syst. 34(4), 264–277 (2010). Geospatial Cyberinfrastructure

    Article  Google Scholar 

  3. Miller, H.J.: A measurement theory for time geography. Geogr. Anal. 37(1), 17–45 (2005)

    Article  Google Scholar 

  4. Hägerstrand, T.: What about people in regional science? Papers Reg. Sci. Assoc. 24, 7–21 (1970)

    Article  Google Scholar 

  5. Miller, H.J.: What about people in geographic information science? In: Fisher, P., Unwin, D. (eds.) Representing GIS, pp. 215–242. Wiley, Hoboken (2005)

    Google Scholar 

  6. Shaw, S.L.: Guest editorial introduction: time geography - its past, present and future. J. Transp. Geogr. 23, 1–4 (2012). Special Issue on Time Geography

    Article  Google Scholar 

  7. Crease, P., Reichenbacher, T.: Linking time geography and activity theory to support the activities of mobile information seekers. Trans. GIS 17(4), 507–525 (2013)

    Article  Google Scholar 

  8. Raubal, M., Miller, H.J., Bridwell, S.: User-centred time geography for location-based services. Geogr. Ann.: Ser. B Hum. Geogr. 86(4), 245–265 (2004)

    Article  Google Scholar 

  9. Kwan, M.P.: Gender and individual access to urban opportunities: a study using space-time measures. Prof. Geogr. 51(2), 210–227 (1999)

    Article  Google Scholar 

  10. Miller, H.J.: Modelling accessibility using space-time prism concepts within geographical information systems. Int. J. Geogr. Inf. Syst. 5(3), 287–301 (1991)

    Article  Google Scholar 

  11. Raubal, M., Winter, S., Teßmann, S., Gaisbauer, C.: Time geography for ad-hoc shared-ride trip planning in mobile geosensor networks. ISPRS J. Photogramm. Remote Sens. 62(5), 366–381 (2007)

    Article  Google Scholar 

  12. Winter, S., Raubal, M.: Time geography for ad-hoc shared-ride trip planning. In: 7th International Conference on Mobile Data Management 2006, MDM 2006 (2006)

    Google Scholar 

  13. Rainham, D., McDowell, I., Krewski, D., Sawada, M.: Conceptualizing the healthscape: contributions of time geography, location technologies and spatial ecology to place and health research. Soc. Sci. Med. 70(5), 668–676 (2010)

    Article  Google Scholar 

  14. Bröring, A., Remke, A., Stasch, C., Autermann, C., Rieke, M., Möllers, J.: EnviroCar: a citizen science platform for analyzing and mapping crowd-sourced car sensor data. Trans. GIS 19(3), 362–376 (2015)

    Article  Google Scholar 

  15. Winter, S., Yin, Z.C.: The elements of probabilistic time geography. GeoInformatica 15(3), 417–434 (2011)

    Article  Google Scholar 

  16. Samet, H.: Applications of Spatial Data Structures. Addison-Wesley, Boston (1990)

    Google Scholar 

  17. Myllymaki, J., Kaufman, J.: High-performance spatial indexing for location-based services. In: Proceedings of 12th International Conference on World Wide Web, WWW 2003, pp. 112–117. ACM, New York (2003)

    Google Scholar 

  18. Gustafsson, T., Hansson, J.: Dynamic on-demand updating of data in real-time database systems. In: Proceedings of 2004 ACM Symposium on Applied Computing, SAC 2004, pp. 846–853. ACM, New York (2004)

    Google Scholar 

  19. Papadias, D., Tao, Y., Kanis, P., Zhang, J.: Indexing spatio-temporal data warehouses. In: Proceedings of 18th International Conference on Data Engineering 2002, pp. 166–175 (2002)

    Google Scholar 

  20. Theodoridis, Y., Sellis, T., Papadopoulos, A., Manolopoulos, Y.: Specifications for efficient indexing in spatiotemporal databases. In: Proceedings of 10th International Conference on Scientific and Statistical Database Management 1998, pp. 123–132, Jul 1998

    Google Scholar 

  21. Wang, W., Yang, J., Muntz, R.: Pk-tree: a spatial index structure for high dimensional point data. In: Tanaka, K., Ghandeharizadeh, S., Kambayashi, Y. (eds.) Information Organization and Databases: Foundations of Data Organization. SISECS, vol. 579. Springer, Berlin (2000)

    Google Scholar 

  22. Tayeb, J., Ulusoy, Ö., Wolfson, O.: A quadtree-based dynamic attribute indexing method. Comput. J. 41(3), 185–200 (1998)

    Article  MATH  Google Scholar 

  23. Navarro, G., Reyes, N.: Dynamic spatial approximation trees for massive data. In: 2nd International Workshop on Similarity Search and Applications, SISAP, pp. 81–88, August 2009

    Google Scholar 

  24. Navarro, G., Reyes, N.: Dynamic spatial approximation trees. J. Exp. Algorithmics 12, 1.5:1–1.5:68 (2008)

    Article  MathSciNet  Google Scholar 

  25. Bo, Z., Fu-ling, B.: Dynamic quadtree spatial index algorithm for mobile GIS. Comput. Eng. 33(15), 86 (2007)

    Google Scholar 

  26. Xia, Y., Prabhakar, S.: Q+rtree: efficient indexing for moving object databases. In: Proceedings of 8th International Conference on Database Systems for Advanced Applications 2003 (DASFAA 2003), pp. 175–182, March 2003

    Google Scholar 

  27. Myllymaki, J., Kaufman, J.H.: DynaMark: a benchmark for dynamic spatial indexing. In: Chen, M.-S., Chrysanthis, P.K., Sloman, M., Zaslavsky, A. (eds.) MDM 2003. LNCS, vol. 2574, pp. 92–105. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  28. Myllymaki, J., Kaufman, J.: Locus: a testbed for dynamic spatial indexing. IEEE Data Eng. Bull. Spec. Issue Index. Mov. Objects 25, 48–55 (2002)

    Google Scholar 

  29. Zhu, Q., Gong, J., Zhang, Y.: An efficient 3D r-tree spatial index method for virtual geographic environments. J. Photogramm. Remote Sens. 62(3), 217–224 (2007)

    Article  Google Scholar 

  30. Ize, T., Wald, I., Parker, S.G.: Asynchronous BVH construction for ray tracing dynamic scenes on parallel multi-core architectures. In: Proceedings of 7th Eurographics Conference on Parallel Graphics and Visualization, EGPGV 2007, pp. 101–108. Eurographics Association, Aire-la-Ville (2007)

    Google Scholar 

  31. Glassner, A.S.: An Introduction to Ray Tracing. Academic Press Ltd., London (1989)

    MATH  Google Scholar 

  32. Stich, M., Friedrich, H., Dietrich, A.: Spatial splits in bounding volume hierarchies. In: Proceedings of Conference on High Performance Graphics 2009, HPG 2009, pp. 7–13. ACM, New York (2009)

    Google Scholar 

  33. Maneewongvatana, S., Mount, D.M.: Analysis of approximate nearest neighbor searching with clustered point sets. CoRR cs.CG/9901013 (1999)

    Google Scholar 

  34. Vinkler, M., Havran, V., Bittner, J.: Bounding volume hierarchies versus kd-trees on contemporary many-core architectures. In: Proceedings of 30th Spring Conference on Computer Graphics. SCCG 2014, pp. 29–36. ACM, New York (2014)

    Google Scholar 

  35. Shevtsov, M., Soupikov, A., Kapustin, A.: Highly parallel fast kd-tree construction for interactive ray tracing of dynamic scenes. Comput. Graph. Forum 26(3), 395–404 (2007)

    Article  Google Scholar 

  36. He, L., Ortiz, R., Enquobahrie, A., Manocha, D.: Interactive continuous collision detection for topology changing models using dynamic clustering. In: Proceedings of 19th Symposium on Interactive 3D Graphics and Games, i3D 2015, pp. 47–54. ACM, New York (2015)

    Google Scholar 

  37. Stein, C., Limper, M., Kuijper, A.: Spatial data structures for accelerated 3D visibility computation to enable large model visualization on the web. In: Proceedings of 19th International ACM Conference on 3D Web Technologies, Web3D 2014, pp. 53–61. ACM, New York (2014)

    Google Scholar 

  38. Kopta, D., Ize, T., Spjut, J., Brunvand, E., Davis, A., Kensler, A.: Fast, effective BVH updates for animated scenes. In: Proceedings of ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games, I3D 2012, pp. 197–204. ACM, New York (2012)

    Google Scholar 

  39. Yoon, S.E., Curtis, S., Manocha, D.: Ray tracing dynamic scenes using selective restructuring. In: Proceedings of 18th Eurographics Conference on Rendering Techniques, EGSR 2007, pp. 73–84. Eurographics Association, Aire-la-Ville (2007)

    Google Scholar 

  40. Karras, T., Aila, T.: Fast parallel construction of high-quality bounding volume hierarchies. In: Proceedings of 5th High-Performance Graphics Conference, HPG 2013, pp. 89–99. ACM, New York (2013)

    Google Scholar 

  41. Miller, H., Raubal, M., Jaegal, Y.: Measuring space-time prism similarity through temporal profile curves. In: 19th AGILE Conference on Geographic Information Science - Geospatial Data in a Changing World, p. 19 (2016)

    Google Scholar 

  42. Keßler, C., Farmer, C.J.Q.: Querying and integrating spatial-temporal information on the web of data via time geography. Web Semant.: Sci. Serv. Agents World Wide Web 35(1), 25–34 (2015)

    Article  Google Scholar 

  43. Schwesinger, U., Siegwart, R., Furgale, P.: Fast collision detection through bounding volume hierarchies in workspace-time space for sampling-based motion planners. In: 2015 IEEE International Conference on Robotics and Automation (ICRA), pp. 63–68, May 2015

    Google Scholar 

  44. Long, J., Nelson, T.: Home range and habitat analysis using dynamic time geography. J. Wildl. Manag. 79(3), 481–490 (2015)

    Article  Google Scholar 

  45. Long, J.A., Nelson, T.A.: Measuring dynamic interaction in movement data. Trans. GIS 17(1), 62–77 (2013)

    Article  Google Scholar 

  46. Larsson, T., Akenine-Möller, T.: A dynamic bounding volume hierarchy for generalized collision detection. Comput. Graph. 30(3), 450–459 (2006)

    Article  Google Scholar 

  47. Sinha, G., Mark, D.M.: Measuring similarity between geospatial lifelines in studies of environmental health. J. Geogr. Syst. 7(1), 115–136 (2005)

    Article  Google Scholar 

  48. Gao, P., Kupfer, J.A., Zhu, X., Guo, D.: Quantifying animal trajectories using spatial aggregation and sequence analysis: a case study of differentiating trajectories of multiple species. Geogr. Anal. 48, 275–291 (2016)

    Article  Google Scholar 

  49. Demšar, U., Virrantaus, K.: Space-time density of trajectories: exploring spatio-temporal patterns in movement data. Int. J. Geogr. Inf. Sci. 24(10), 1527–1542 (2010)

    Article  Google Scholar 

  50. Long, J.A., Webb, S.L., Nelson, T.A., Gee, K.L.: Mapping areas of spatial-temporal overlap from wildlife tracking data. Mov. Ecol. 3(1), 1–14 (2015)

    Article  Google Scholar 

  51. Ram, P., Lee, D., March, W., Gray, A.G.: Linear-time algorithms for pairwise statistical problems. In: Advances in Neural Information Processing Systems (NIPS), December 2009, vol. 22. MIT Press (2010)

    Google Scholar 

  52. Gray, A.G., Moore, A.W.: \(N\)-body problems in statistical learning. In: Leen, T.K., Dietterich, T.G., Tresp, V. (eds.) Advances in Neural Information Processing Systems (NIPS), December 2000, vol. 13. MIT Press (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Carson J. Q. Farmer .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Farmer, C.J.Q., Keßler, C. (2016). Hierarchical Prism Trees for Scalable Time Geographic Analysis. In: Miller, J., O'Sullivan, D., Wiegand, N. (eds) Geographic Information Science. GIScience 2016. Lecture Notes in Computer Science(), vol 9927. Springer, Cham. https://doi.org/10.1007/978-3-319-45738-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-45738-3_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45737-6

  • Online ISBN: 978-3-319-45738-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics