Approximately Dominating Representatives

  • Vladlen Koltun
  • Christos H. Papadimitriou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3363)


We propose and investigate from the algorithmic standpoint a novel form of fuzzy query called approximately dominating representatives or ADRs. The ADRs of a multidimensional point set consist of a few points guaranteed to contain an approximate optimum of any monotone Lipschitz continuous combining function of the dimensions. ADRs can be computed by appropriately post-processing Pareto, or “skyline,” queries [14,1]. We show that the problem of minimizing the number of points returned, for a user-specified desired approximation, can be solved in polynomial time in two dimensions; for three and more it is NP-hard but has a polynomial-time logarithmic approximation. Finally, we present a polynomial-time, constant factor approximation algorithm for three dimensions.


Greedy Algorithm Skyline Query Approximate Optimum Multimedia Database Constant Factor Approximation Algorithm 
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.


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  1. 1.
    Balke, W.-T., Güntzer, U., Zheng, J.X.: Efficient Distributed Skylining for Web Information Systems. In: Bertino, E., Christodoulakis, S., Plexousakis, D., Christophides, V., Koubarakis, M., Böhm, K., Ferrari, E. (eds.) EDBT 2004. LNCS, vol. 2992, pp. 256–273. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Bentley, J.L., Kung, H.T., Schkolnick, M., Thompson, C.D.: On the average number of maxima in a set of vectors and applications. JACM 25, 536–543 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Brönnimann, H., Goodrich, M.T.: Almost Optimal Set Covers in Finite VC-Dimension. DCG 14(4), 463–479 (1995)zbMATHGoogle Scholar
  4. 4.
    Chakrabarti, K., Porkaew, K., Mehrotra, S.: Refining Top-k Selection Queries based on User Feedback. In: VLDB 2000 (2000)Google Scholar
  5. 5.
    Fagin, R.: Fuzzy Queries in Multimedia Database Systems. In: PODS 1998, pp. 1–10 (invited)Google Scholar
  6. 6.
    Fagin, R., Lotem, A., Naor, M.: Optimal Aggregation Algorithms for Middleware. In: PODS 2001 (2001)Google Scholar
  7. 7.
    Fagin, R.: Combining Fuzzy Information from Multiple Systems. JCSS 58(1), 83–99 (1999)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Fagin, R., Wimmers, E.L.: A formula for incorporating weights into scoring rules. TCS  239(2), 309–338 (2000)Google Scholar
  9. 9.
    Haussler, D., Welzl, E.: Epsilon-nets and simplex range queries. DCG 2, 127–151 (1987)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Lund, C., Yannakakis, M.: On the Hardness of Approximating Minimization Problems. JACM 41(5), 960–981 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Matoušek, J., Seidel, R., Welzl, E.: How to net a lot with little: small ε-nets for disks and halfspaces. In: SoCG 1990, pp. 16–22 (1990)Google Scholar
  12. 12.
    Papadimitriou, C.H., Yannakakis, M.: On the Approximability of Trade-offs and Optimal Access of Web Sources. In: FOCS 2000, pp. 86–92 (2000)Google Scholar
  13. 13.
    Papadimitriou, C.H., Yannakakis, M.: Multiobjective Query Optimization. In: PODS 2001 (2001)Google Scholar
  14. 14.
    Tan, K.-L., Eng, P.-K., Ooi, B.C.: Efficient Progressive Skyline Computation. In: VLDB 2001, pp. 301–310 (2001)Google Scholar
  15. 15.
    Vassilvitskii, S., Yannakakis, M.: Efficiently Computing Succinct Trade-Off Curves. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 1201–1213. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Vladlen Koltun
    • 1
  • Christos H. Papadimitriou
    • 1
  1. 1.Computer Science DivisionUniversity of CaliforniaBerkeleyUSA

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