Top-k Manhattan Spatial Skyline Queries

  • Wanbin Son
  • Fabian Stehn
  • Christian Knauer
  • Hee-Kap Ahn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8344)


Efficiently retrieving relevant data from a huge spatial database is and has been the subject of research in fields like database systems, geographic information systems and also computational geometry for many years. In this context, we study the retrieval of relevant points with respect to a query and a scoring function: let P and Q be point sets in the plane, the skyline of P with respect to Q consists of points P for which no other point of P is closer to all points of Q. A skyline of a point set P with respect to a query set Q can be seen as the most “relevant” or “desirable” subset of P with respect to Q. As the skyline of a set P can be as large as the set P itself, it is reasonable to filter the skyline using a scoring function f, only reporting the k best skyline points with respect to f.

In this paper, we consider the top-k Manhattan spatial skyline query problem for monotone scoring functions, where distances are measured in the L 1 metric. We present an algorithm that computes the top-k skyline points in near linear time in the size of P. The presented strategy improves over the direct approach of first using the state-of-the-art algorithm to compute the Manhattan spatial skyline [1] and then filtering it by the scoring function by a log(|P|) factor. The improvement has been validated in experiments that show a speedup of up to an order of magnitude.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Son, W., Hwang, S.-w., Ahn, H.-K.: MSSQ: Manhattan Spatial Skyline Queries. In: Pfoser, D., Tao, Y., Mouratidis, K., Nascimento, M.A., Mokbel, M., Shekhar, S., Huang, Y. (eds.) SSTD 2011. LNCS, vol. 6849, pp. 313–329. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  2. 2.
    Kung, H.T., Luccio, F., Preparata, F.: On finding the maxima of a set of vectors. Journal of the Association for Computing Machinery 22(4), 469–476 (1975)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Preparata, F., Shamos, M.: Computational Geometry: An Introduction. Springer-Verlag (1985)Google Scholar
  4. 4.
    Börzsönyi, S., Kossmann, D., Stocker, K.: The skyline operator. In: ICDE 2001: Proc. of the 17th International Conference on Data Engineering, pp. 421–430. IEEE Computer Society (2001)Google Scholar
  5. 5.
    Godfrey, P., Shipley, R., Gryz, J.: Maximal vector computation in large data sets. In: VLDB 2005: Proc. of the 31st International Conference on Very Large Data Bases, pp. 229–240. IEEE Computer Society (2005)Google Scholar
  6. 6.
    Chomicki, J., Godfery, P., Gryz, J., Liang, D.: Skyline with presorting. In: ICDE 2003: Proc. of the 19th International Conference on Data Engineering, pp. 717–816. IEEE Computer Society (2003)Google Scholar
  7. 7.
    Papadias, D., Tao, Y., Fu, G., Seeger, B.: An optimal and progressive algorithm for skyline queries. In: SIGMOD 2003: Proc. of the 2003 ACM SIGMOD International Conference on Management of Data, pp. 467–478. ACM (2003)Google Scholar
  8. 8.
    Sharifzadeh, M., Shahabi, C.: The spatial skyline queries. In: VLDB 2006: Proc. of the 32nd International Conference on Very Large Data Bases, pp. 751–762, VLDB Endowment (2006)Google Scholar
  9. 9.
    Lee, M.W., Son, W., Ahn, H.K., Hwang, S.W.: Spatial skyline queries: exact and approximation algorithms. GeoInformatica 15(4), 665–697 (2011)CrossRefGoogle Scholar
  10. 10.
    Goncalves, M., Vidal, M.-E.: Reaching the top of the skyline: An efficient indexed algorithm for top-k skyline queries. In: Bhowmick, S.S., Küng, J., Wagner, R. (eds.) DEXA 2009. LNCS, vol. 5690, pp. 471–485. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Xu, C., Gao, Y.: A novel approach for selecting the top skyline under users’ references. In: ICIME 2010: Proc. of the 2nd IEEE International Conference on Information Management and Engineering, pp. 708–712. IEEE (2010)Google Scholar
  12. 12.
    Vlachou, A., Vazirgiannis, M.: Ranking the sky: Discovering the importance of skyline points through subspace dominance relationships. Data & Knowledge Engineering 69(9), 943–964 (2010)CrossRefGoogle Scholar
  13. 13.
    Lee, J., You, G.W., Hwang, S.W.: Personalized top-k skyline queries in high-dimensional space. Information Systems 34(1), 45–61 (2009)CrossRefzbMATHGoogle Scholar
  14. 14.
    Brando, C., Goncalves, M., González, V.: Evaluating top-k skyline queries over relational databases. In: Wagner, R., Revell, N., Pernul, G. (eds.) DEXA 2007. LNCS, vol. 4653, pp. 254–263. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  15. 15.
    Goncalves, M., Vidal, M.-E.: Top-k skyline: A unified approach. In: Meersman, R., Tari, Z. (eds.) OTM-WS 2005. LNCS, vol. 3762, pp. 790–799. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  16. 16.
    Chan, T.M., Pǎtraşcu, M.: Counting inversions, offline orthogonal range counting, and related problems. In: SODA 2010: Proc. of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 161–173. Society for Industrial and Applied Mathematics (2010)Google Scholar
  17. 17.
    Rockafellar, R.T.: Convex Analysis. Princeton University Press (1996)Google Scholar
  18. 18.
    Blelloch, G.E.: Space-efficient dynamic orthogonal point location, segment intersection, and range reporting. In: SODA 2008: Proc. of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 894–903. Society for Industrial and Applied Mathematics (2008)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Wanbin Son
    • 1
  • Fabian Stehn
    • 2
  • Christian Knauer
    • 2
  • Hee-Kap Ahn
    • 1
  1. 1.Department of Computer Science and EngineeringPOSTECHPohangRepublic of Korea
  2. 2.Institute of Computer ScienceUniversität BayreuthBayreuthGermany

Personalised recommendations