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Towards estimating expected sizes of probabilistic skylines

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Abstract

We consider the maximal vector problem on uncertain data, which has been recently posed by the study on processing skyline queries over a probabilistic data stream in the database context. Let D n be a set of n points in a d-dimensional space and q (0 < q ⩽1) be a probability threshold; each point in D n has a probability to occur. Our problem is concerned with how to estimate the expected size of the probabilistic skyline, which consists of all the points that are not dominated by any other point in D n with a probability not less than q. We prove that the upper bound of the expected size is O(min{n, (−ln q)(ln n)d−1}) under the assumptions that the value distribution on each dimension is independent and the values of the points along each dimension are distinct. The main idea of our proof is to find a recurrence about the expected size and solve it. Our results reveal the relationship between the probability threshold q and the expected size of the probabilistic skyline, and show that the upper bound is poly-logarithmic when q is not extremely small.

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References

  1. Kung H T, Luccio F, Preparata F P. On finding the maxima of a set of vectors. J ACM, 1975, 22: 469–476

    Article  MATH  MathSciNet  Google Scholar 

  2. Barndorff-Nielsen O, Sobel M. On the distribution of the number of admissible points in a vector random sample. Theor Probab Appl, 1966, 11: 249–269

    Article  MathSciNet  Google Scholar 

  3. Bentley J L, Kung H T, Schkolnick M, et al. On the average number of maxima in a set of vectors and applications. J ACM, 1978, 25: 536–543

    Article  MATH  MathSciNet  Google Scholar 

  4. Buchta C. On the average number of maxima in a set of vectors. Inf Process Lett, 1989, 33: 63–65

    Article  MATH  MathSciNet  Google Scholar 

  5. Golin M J. Maxima in convex regions. In: Proceedings of the 4th Annual ACM-SIAMSymposium on Discrete Algorithms, Philadelphia, PA, USA, 1993. 352–360

  6. Börzsönyi S, Kossmann D, Stocker K. The skyline operator. In: Proceedings of the 17th International Conference on Data Engineering, Washington DC, USA, 2001. 421–430

  7. Zhang WJ, Lin XM, Zhang Y, et al. Probabilistic skyline operator over sliding windows. In: Proceedings of International Conference on Data Engineering, Los Alamitos, CA, USA, 2009. 1060–1071

  8. Pei J, Jiang B, Lin X M, et al. Probabilistic skylines on uncertain data. In: Proceedings of the 33rd International Conference on Very Large Data Bases, Vienna, Austria, 2007. 15–26

  9. Godfrey P. Skyline cardinality for relational processing. In: Foundations of Information and Knowledge Systems, Wilhelminenburg Castle, Austria, 2004. 78–97

  10. Godfrey P, Shipley R, Gryz J. Algorithms and analyses for maximal vector computation. VLDB J, 2007, 16: 5–28

    Google Scholar 

  11. Lin X M, Yuan Y D, Wang W, et al. Stabbing the sky: Efficient skyline computation over sliding windows. In: Proceedings of the 21st International Conference on Data Engineering, Washington DC, USA, 2005. 502–513

  12. Knuth D E. The Art of Computer Programming, Volume 1 (3rd ed): Fundamental Algorithms. Redwood City: Addison Wesley Longman Publishing Co, Inc, 1997

    Google Scholar 

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Authors and Affiliations

  1. National Key Laboratory for Parallel and Distributed Processing, School of Computer, National University of Defense Technology, Changsha, 410073, China

    YongTao Yang & YiJie Wang

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  1. YongTao Yang
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  2. YiJie Wang
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Correspondence to YongTao Yang.

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Yang, Y., Wang, Y. Towards estimating expected sizes of probabilistic skylines. Sci. China Inf. Sci. 54, 2554–2564 (2011). https://doi.org/10.1007/s11432-011-4387-4

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  • DOI: https://doi.org/10.1007/s11432-011-4387-4

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