The VLDB Journal

, Volume 23, Issue 1, pp 129–145 | Cite as

Toward efficient multidimensional subspace skyline computation

  • Jongwuk Lee
  • Seung-won Hwang
Regular Paper


Skyline queries have attracted considerable attention to assist multicriteria analysis of large-scale datasets. In this paper, we focus on multidimensional subspace skyline computation that has been actively studied for two approaches. First, to narrow down a full-space skyline, users may consider multiple subspace skylines reflecting their interest. For this purpose, we tackle the concept of a skycube, which consists of all possible non-empty subspace skylines in a given full space. Second, to understand diverse semantics of subspace skylines, we address skyline groups in which a skyline point (or a set of skyline points) is annotated with decisive subspaces. Our primary contributions are to identify common building blocks of the two approaches and to develop orthogonal optimization principles that benefit both approaches. Our experimental results show the efficiency of proposed algorithms by comparing them with state-of-the-art algorithms in both synthetic and real-life datasets.


Skyline queries Subspace skyline  Skycube Skyline group Point-based space partitioning 



This research was supported by the MKE (The Ministry of Knowledge Economy), Korea, and Microsoft Research, under IT/SW Creative research program supervised by the NIPA (National IT Industry Promotion Agency) (NIPA-2012-H0503- 12-1036).


  1. 1.
    Bartolini, I., Ciaccia, P., Patella, M.: Efficient sort-based skyline evaluation. ACM Trans. Database Syst. 33(4), 31–79 (2008)CrossRefGoogle Scholar
  2. 2.
    Bentley, J.L., Clarkson, K.L., Levine, D.B.: Fast linear expected-time algorithms for computing maxima and convex hulls. In: SODA, pp. 179–187 (1990)Google Scholar
  3. 3.
    Bentley, J.L., Kung, H.T., Schkolnick, M., Thompson, C.D.: On the average number of maxima in a set of vectors and applications. J. ACM 25(4), 536–543 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Börzsönyi, S., Kossmann, D., Stocker, K.: The skyline operator. In: ICDE, pp. 421–430 (2001)Google Scholar
  5. 5.
    Chomicki, J., Godfery, P., Gryz, J., Liang, D.: Skyline with presorting. In: ICDE, pp. 717–719 (2003)Google Scholar
  6. 6.
    Godfrey, P., Shipley, R., Gryz, J.: Maximal vector computation in large data sets. In: VLDB, pp. 229–240 (2005)Google Scholar
  7. 7.
    Godfrey, P., Shipley, R., Gryz, J.: Algorithms and analysis for maximal vector computation. VLDB J. 16(1), 5–28 (2007)CrossRefGoogle Scholar
  8. 8.
    Kailasam, G.T., Lee, J., Rhee, J.-W., Kang, J.: Efficient skycube computation using point and domain-based filtering. Inf. Sci. 180(7), 1090–1103 (2010)CrossRefGoogle Scholar
  9. 9.
    Kossmann, D., Ramsak, F., Rost, S.: Shooting stars in the sky: an online algorithm for skyline queries. In: VLDB, pp. 275–286 (2002)Google Scholar
  10. 10.
    Kung, H.T., Luccio, F., Preparata, F.P.: On finding the maxima of a set of vectors. J. ACM 22(4), 469–476 (1975)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Lee, J., Hwang, S.: BSkyTree: Scalable skyline computation using a balanced pivot selection. In: EDBT, pp. 195–206 (2010) Google Scholar
  12. 12.
    Lee, J., Hwang, S.: QSkycube: efficient skycube computation using point-based space partitioning. Proc. VLDB Endow. 4(3), 185–196 (2010)Google Scholar
  13. 13.
    Lee, K.C., Zheng, B., Li, H., Lee, W.-C.: Approaching the skyline in Z order. In: VLDB, pp. 279–290 (2007)Google Scholar
  14. 14.
    Lee, K.C.K., Lee, W.-C., Zheng, B., Li, H., Tian, Y.: Z-SKY: an efficient skyline query processing framework based on Z-order. VLDB J. 19(3), 333–362 (2010)CrossRefGoogle Scholar
  15. 15.
    Papadias, D., Tao, Y., Fu, G., Seeger, B.: An optimal and progressive algorithm for skyline queries. In: SIGMOD, pp. 467–478 (2003)Google Scholar
  16. 16.
    Pei, J., Fu, A.W., Lin, X., Wang. H.: Computing compressed multidimensional skyline cubes efficiently. In: ICDE, pp. 96–105 (2007)Google Scholar
  17. 17.
    Pei, J., Jin, W., Ester, M., Tao, Y.: Catching the best views of skyline: a semantic approach based on decisive subspaces. In: VLDB, pp. 253–264 (2005)Google Scholar
  18. 18.
    Pei, J., Yuan, Y., Lin, X., Jin, W., Ester, M., Liu, Q., Wang, W., Tao, Y., Yu, J.X., Zhang, Q.: Towards multidimensional subspace skyline analysis. ACM Trans. Database Syst. 31(4), 1335–1381 (2006)CrossRefGoogle Scholar
  19. 19.
    Raïssi, C., Pei, J., Kister, T.: Computing closed skycubes. Proc. VLDB Endow. 3(1), 838–847 (2010)Google Scholar
  20. 20.
    Tan K., Eng P., Ooi, B.C.: Efficient progressive skyline computation. In: VLDB, pp. 301–310 (2001)Google Scholar
  21. 21.
    Tao, Y., Xiao, X., Pei, J.: SUBSKY: efficient computation of skylines in subspaces. In: ICDE, pp. 65–74 (2006)Google Scholar
  22. 22.
    Tao, Y., Xiao, X., Pei, J.: Efficient skyline and top-k retrieval in subspaces. IEEE Trans. Knowl. Data Eng. 19(8), 1072–1088 (2007)CrossRefGoogle Scholar
  23. 23.
    Vlachou, A., Doulkeridis, C., Kotidis, Y., Vazirgiannis, M.: SKYPEER: efficient subspace skyline computation over distributed data. In: ICDE, pp. 416–425 (2007)Google Scholar
  24. 24.
    Xia, T., Zhang, D.: Refreshing the sky: the compressing skycube with efficient support for frequent updates. In: SIGMOD, pp. 491–502 (2006)Google Scholar
  25. 25.
    Yiu, M.L., Lo, E., Yung, D.: Measuring the sky: on computing data cubes via skylining the measures. IEEE Trans. Knowl. Data Eng. 24(3), 492–505 (2012)CrossRefGoogle Scholar
  26. 26.
    Yuan, Y., Lin, X., Liu, Q., Wang, W., Yu, J.X., Zhang, Q.: Efficient computation of the skyline cube. In: VLDB, pp. 241–252 (2005)Google Scholar
  27. 27.
    Zhang, S., Mamoulis, N., Cheung, D.W.: Scalable skyline computation using object-based space partitioning. In: SIGMOD, pp. 483–494 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringPohang University of Science and Technology (POSTECH)PohangRepublic of Korea

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