Combination Skyline Queries

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7600)


Given a collection of data objects, the skyline problem is to select the objects which are not dominated by any others. In this paper, we propose a new variation of the skyline problem, called the combination skyline problem. The goal is to find the fixed-size combinations of objects which are skyline among all possible combinations. Our problem is technically challenging as traditional skyline approaches are inapplicable to handle a huge number of possible combinations. By indexing objects with an R-tree, our solution is based on object-selecting patterns that indicate the number of objects to be selected for each MBR. We develop two major pruning conditions to avoid unnecessary expansions and enumerations, as well as a technique to reduce space consumption on storing the skyline for each rule in the object-selecting pattern. The efficiency of the proposed algorithm is demonstrated by extensive experiments on both real and synthetic datasets.


Skyline queries combinations dominance relationships R-trees 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Apt, K.: Principles of Constraint Programming. Cambridge University Press (2003)Google Scholar
  2. 2.
    Börzsönyi, S., Kossmann, D., Stocker, K.: The skyline operator. In: ICDE, pp. 421–430 (2001)Google Scholar
  3. 3.
    Chan, C.-Y., Jagadish, H.V., Tan, K.-L., Tung, A.K.H., Zhang, Z.: On High Dimensional Skylines. In: Ioannidis, Y., Scholl, M.H., Schmidt, J.W., Matthes, F., Hatzopoulos, M., Böhm, K., Kemper, A., Grust, T., Böhm, C. (eds.) EDBT 2006. LNCS, vol. 3896, pp. 478–495. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Chomicki, J., Godfrey, P., Gryz, J., Liang, D.: Skyline with presorting. In: ICDE, pp. 717–719 (2003)Google Scholar
  5. 5.
    Deb, K., Kalyanmoy, D.: Multi-Objective Optimization Using Evolutionary Algorithms. Wiley (2001)Google Scholar
  6. 6.
    Ehrgott, M., Gandibleux, X.: A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spectrum 22(4), 425–460 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Godfrey, P., Shipley, R., Gryz, J.: Maximal vector computation in large data sets. In: VLDB, pp. 229–240 (2005)Google Scholar
  8. 8.
    Guo, X., Ishikawa, Y.: Multi-objective Optimal Combination Queries. In: Hameurlain, A., Liddle, S.W., Schewe, K.-D., Zhou, X. (eds.) DEXA 2011, Part I. LNCS, vol. 6860, pp. 47–61. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    Guttman, A.: R-trees: A dynamic index structure for spatial searching. In: Yormark, B. (ed.) SIGMOD, pp. 47–57. ACM Press (1984)Google Scholar
  10. 10.
    Hadjieleftheriou, M., Hoel, E.G., Tsotras, V.J.: SaIL: A spatial index library for efficient application integration. GeoInformatica 9(4), 367–389 (2005)CrossRefGoogle Scholar
  11. 11.
    Lehman, T.J., Carey, M.J.: A study of index structures for main memory database management systems. In: VLDB, pp. 294–303 (1986)Google Scholar
  12. 12.
    Lin, X., Yuan, Y., Zhang, Q., Zhang, Y.: Selecting stars: The k most representative skyline operator. In: ICDE, pp. 86–95 (2007)Google Scholar
  13. 13.
    Papadias, D., Mamoulis, N., Delis, V.: Algorithms for querying by spatial structure. In: VLDB, pp. 546–557 (1998)Google Scholar
  14. 14.
    Papadias, D., Tao, Y., Fu, G., Seeger, B.: Progressive skyline computation in database systems. ACM Trans. Database Syst. 30(1), 41–82 (2005)CrossRefGoogle Scholar
  15. 15.
    Roy, S.B., Amer-Yahia, S., Chawla, A., Das, G., Yu, C.: Constructing and exploring composite items. In: SIGMOD, pp. 843–854 (2010)Google Scholar
  16. 16.
    Sarma, A.D., Lall, A., Nanongkai, D., Lipton, R.J., Xu, J.J.: Representative skylines using threshold-based preference distributions. In: ICDE, pp. 387–398 (2011)Google Scholar
  17. 17.
    Siddique, M.A., Morimoto, Y.: Algorithm for computing convex skyline objectsets on numerical databases. IEICE 93-D(10), 2709–2716 (2010)Google Scholar
  18. 18.
    Su, I.-F., Chung, Y.-C., Lee, C.: Top-k Combinatorial Skyline Queries. In: Kitagawa, H., Ishikawa, Y., Li, Q., Watanabe, C. (eds.) DASFAA 2010, Part II. LNCS, vol. 5982, pp. 79–93. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  19. 19.
    Tao, Y., Ding, L., Lin, X., Pei, J.: Distance-based representative skyline. In: ICDE, pp. 892–903 (2009)Google Scholar
  20. 20.
    Wan, Q., Wong, R.C.-W., Peng, Y.: Finding top-k profitable products. In: ICDE, pp. 1055–1066 (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Graduate School of Information ScienceNagoya UniversityJapan
  2. 2.Information Technology CenterNagoya UniversityJapan
  3. 3.National Institute of InformaticsJapan

Personalised recommendations