GraCT: A Grammar Based Compressed Representation of Trajectories

  • Nieves R. Brisaboa
  • Adrián Gómez-Brandón
  • Gonzalo Navarro
  • José R. ParamáEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9954)


We present a compressed data structure to store free trajectories of moving objects (ships over the sea, for example) allowing spatio-temporal queries. Our method, GraCT, uses a \(k^2\)-tree to store the absolute positions of all objects at regular time intervals (snapshots), whereas the positions between snapshots are represented as logs of relative movements compressed with Re-Pair. Our experimental evaluation shows important savings in space and time with respect to a fair baseline.


Compression Ratio Time Instant Absolute Position Candidate Object Object Identifier 
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.


  1. 1.
    Brisaboa, N., Ladra, S., Navarro, G.: DACs: bringing direct access to variable-length codes. Inf. Process. Manag. 49(1), 392–404 (2013)CrossRefGoogle Scholar
  2. 2.
    Brisaboa, N.R., Fariña, A., Navarro, G., Param, J.R.: Lightweight natural language text compression. Inf. Retrieval 10(1), 1–33 (2007)CrossRefGoogle Scholar
  3. 3.
    Brisaboa, N.R., Ladra, S., Navarro, G.: Compact representation of web graphs with extended functionality. Inf. Syst. 39(1), 152–174 (2014)CrossRefGoogle Scholar
  4. 4.
    Chakka, V.P., Everspaugh, A., Patel, J.M.: Indexing large trajectory data sets with SETI. In: Proceedings of the conference on innovative data systems research, CIDR 2003 (2003).
  5. 5.
    Gutiérrez, G.A., Navarro, G., Rodríguez, M.A., González, A.F., Orellana, J.: A spatio-temporal access method based on snapshots and events. In: GIS, pp. 115–124. ACM (2005)Google Scholar
  6. 6.
    Hadjieleftheriou, M., Kollios, G., Tsotras, V.J., Gunopulos, D.: Efficient indexing of spatiotemporal objects. In: Jensen, C.S., Jeffery, K., Pokorný, J., Šaltenis, S., Bertino, E., Böhm, K., Jarke, M. (eds.) EDBT 2002. LNCS, vol. 2287, pp. 251–268. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Jacobson, G.: Space-efficient static trees and graphs. In: IEEE Symposium on Foundations of Computer Science (FOCS), pp. 549–554 (1989)Google Scholar
  8. 8.
    Knuth, E.: Efficient representation of perm groups. Combinatorica 11, 33–43 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Larsson, N.J., Moffat, A.: Off-line dictionary-based compression. Proc. IEEE 88(11), 1722–1732 (2000)CrossRefGoogle Scholar
  10. 10.
    Munro, J.I., Raman, R., Raman, V., Rao, S.: Succinct representations of permutations and functions. Theor. Comput. Sci. 438, 74–88 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Nascimento, M.A., Silva, J.R.O.: Towards historical R-trees. In: George, K.M., Lamont, G.B. (eds.) Proceedings of the 1998 ACM Symposium on Applied Computing, SAC 1998, pp. 235–240. ACM (1998).
  12. 12.
    Rasetic, S., Sander, J., Elding, J., Nascimento, M.A.: A trajectory splitting model for efficient spatio-temporal indexing. In: Proceedings of the 31st International Conference on Very Large Data Bases, pp. 934–945. VLDB Endowment (2005)Google Scholar
  13. 13.
    Tao, Y., Papadias, D.: MV3R-tree: a spatio-temporal access method for timestamp and interval queries. In: Apers, P.M.G., Atzeni, P., Ceri, S., Paraboschi, S., Ramamohanarao, K., Snodgrass, R.T. (eds.) Proceedings of 27th International Conference on Very Large Data Bases, VLDB 2001, pp. 431–440. Morgan Kaufmann (2001)Google Scholar
  14. 14.
    Vazirgiannis, M., Theodoridis, Y., Sellis, T.K.: Spatio-temporal composition and indexing for large multimedia applications. ACM Multimedia Syst. J. 6(4), 284–298 (1998)CrossRefGoogle Scholar
  15. 15.
    Wang, L., Zheng, Y., Xie, X., Ma, W.Y.: A flexible spatio-temporal indexing scheme for large-scale GPS track retrieval. In: Mobile Data Management, pp. 1–8. IEEE (2008)Google Scholar
  16. 16.
    Worboys, M.F.: Event-oriented approaches to geographic phenomena. Int. J. Geogr. Inf. Sci. 19(1), 1–28 (2005)CrossRefGoogle Scholar
  17. 17.
    Xu, X., Han, J., Lu, W.: RT-tree: an improved R-tree index structure for spatiotemporal databases. In: Proceedings of the 4th International Symposium on Spatial Data Handling, vol. 2, pp. 1040–1049 (1990)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Nieves R. Brisaboa
    • 1
  • Adrián Gómez-Brandón
    • 1
  • Gonzalo Navarro
    • 2
  • José R. Paramá
    • 1
    Email author
  1. 1.Depto. de ComputaciónUniversidade da CoruñaCoruñaSpain
  2. 2.Department of Computer ScienceUniversity of ChileSantiagoChile

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