Implementing the Topological Model Succinctly

  • José Fuentes-SepúlvedaEmail author
  • Gonzalo Navarro
  • Diego Seco
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11811)


We show that the topological model, a semantically rich standard to represent GIS data, can be encoded succinctly while efficiently answering a number of topology-related queries. We build on recent succinct planar graph representations so as to encode a model with m edges within \(4m+o(m)\) bits and answer various queries relating nodes, edges, and faces in \(o(\log \log m)\) time, or any time in \(\omega (\log m)\) for a few complex ones.


  1. 1.
    ISO/IEC 13249–3:2016. Information technology - Database languages - SQL multimedia and application packages - Part 3: Spatial. Technical report (2016)Google Scholar
  2. 2.
    Biggs, N.: Spanning trees of dual graphs. J. Comb. Theor. B 11(2), 127–131 (1971)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Clark, D.R.: Compact PAT Trees. Ph.D. thesis, University of Waterloo, Canada (1996)Google Scholar
  4. 4.
    Cohen, H., Porat, E.: Fast set intersection and two-patterns matching. Theor. Comp. Sci. 411(40–42), 3795–3800 (2010)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Ferragina, P., Manzini, G., Mäkinen, V., Navarro, G.: Compressed representations of sequences and full-text indexes. ACM Trans. Alg. 3(2), 20 (2007)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Ferres, L., Fuentes-Sepúlveda, J., Gagie, T., He, M., Navarro, G.: Fast and compact planar embeddings. Comput. Geom. Theor. App. (2018), to appear. Available at Preliminary version in Proceedings WADS 2017
  7. 7.
    Munro, J.I., Raman, V.: Succinct representation of balanced parentheses and static trees. SIAM J. Comput. 31(3), 762–776 (2001)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Navarro, G.: Compact Data Structures: A Practical Approach. CUP, Cambridge (2016)CrossRefGoogle Scholar
  9. 9.
    Patrascu, M., Roditty, L.: Distance oracles beyond the Thorup-Zwick bound. SIAM J. Comput. 43(1), 300–311 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Raman, R., Raman, V., Satti, S.: Succinct indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets. ACM Trans. Alg. 3(4), 43 (2007)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Scholl, M.O.: Spatial Databases with Application to GIS. MK, Uganda (2002)Google Scholar
  12. 12.
    Turán, G.: On the succinct representation of graphs. Discr. Appl. Math. 8(3), 289–294 (1984)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Worboys, M., Duckham, M.: GIS: A Computing Perspective, 2nd edn. CRC, Boca Raton (2004)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • José Fuentes-Sepúlveda
    • 1
    Email author
  • Gonzalo Navarro
    • 1
    • 3
  • Diego Seco
    • 2
    • 3
  1. 1.Department of Computer ScienceUniversity of ChileSantiagoChile
  2. 2.Department of Computer ScienceUniversidad de ConcepciónConcepciónChile
  3. 3.IMFD — Millennium Institute for Foundational Research on DataSantiagoChile

Personalised recommendations