research-article

(Approximate) uncertain skylines

Authors:

Peyman Afshani,

Pankaj K. Agarwal,

Kasper Green Larsen,

Jeff M. PhillipsAuthors Info & Claims

ICDT '11: Proceedings of the 14th International Conference on Database Theory

Pages 186 - 196

https://doi.org/10.1145/1938551.1938576

Published: 21 March 2011 Publication History

Abstract

Given a set of points with uncertain locations, we consider the problem of computing the probability of each point lying on the skyline, that is, the probability that it is not dominated by any other input point. If each point's uncertainty is described as a probability distribution over a discrete set of locations, we improve the best known exact solution. We also suggest why we believe our solution might be optimal. Next, we describe simple, near-linear time approximation algorithms for computing the probability of each point lying on the skyline. In addition, some of our methods can be adapted to construct data structures that can efficiently determine the probability of a query point lying on the skyline.

References

[1]

P. K. Agarwal and M. Sharir. Arrangements of surfaces in higher dimensions. In J. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 49--119. North-Holland, 2000.

[2]

P. Agrawal, O. Benjelloun, A. D. Sarma, C. Hayworth, S. Nabar, T. Sugihara, and J. Widom. Trio: A system for data, uncertainty, and lineage. In ACM Symposium on Principles of Database Systems, 2006.

[3]

M. J. Atallah and Y. Qi. Computing all skyline probabilities for uncertain data. In ACM Symposium on Principles of Database Systems, pages 279--287, 2009.

Digital Library

[4]

J. L. Bentley. Multidimensional binary search trees used for associative searching. Communications of the ACM, 18(9):509--517, 1975.

Digital Library

[5]

S. Börzsönyi, D. Kossman, and K. Stocker. The skyline operator. In IEEE International Conference on Data Engineering, 2001.

Digital Library

[6]

C.-Y. Chan, H. V. Jagadish, K.-L. Tan, A. K. H. Tung, and Z. Zhang. Finding κ-dominant skylines in high dimensional space. In ACM-SIGMOD International Conference on Management of Data, 2006.

Digital Library

[7]

R. Cheng, D. V. Kalashnikov, and S. Prabhakar. Evaluating probabilitic queries over imprecise data. In ACM-SIGMOD International Conference on Management of Data, 2003.

Digital Library

[8]

G. Cormode, A. Deligiannakis, M. Garafalakis, and A. McGregor. Probabilistic histograms for probabilistic data. In International Conference on Very Large Data Bases, 2009.

Digital Library

[9]

G. Cormode and M. Garafalakis. Histograms and wavelets of probabilitic data. In IEEE International Conference on Data Engineering, 2009.

Digital Library

[10]

G. Cormode, F. Li, and K. Yi. Semantics of ranking queries for probabilistic data and expected ranks. In IEEE International Conference on Data Engineering, 2009.

Digital Library

[11]

N. Dalvi and D. Suciu. Efficient query evaluation on probabilitic databases. The VLDB Journal, 16:523--544, 2007.

Digital Library

[12]

A. Das Sarma, A. Lall, D. Nanongkai, R. J. Lipton, and J. Xu. Representative skylines using threshold-based preference distributions. In IEEE International Conference on Data Engineering, 2011.

Digital Library

[13]

A. Das Sarma, A. Lall, D. Nanongkai, and J. Xu. Randomized mutli-pass streaming skyline algorithms. In International Conference on Very Large Data Bases, 2009.

Digital Library

[14]

M. de Berg, O. Cheong, M. van Kreveld, and M. Overmars. Computational Geometry Algorithms and Applications. Springer, 2008.

Digital Library

[15]

H. Edelsbunner, L. J. Guibas, and J. Stolfi. Optimal point location on a monotone subdivision. SIAM Journal of Computing, 15:317--340, 1986.

Digital Library

[16]

V. Koltun and C. H. Papadimitriou. Approximately dominating representatives. Theoretical Computer Science, 371:148--154, 2007.

Digital Library

[17]

D. Kossman, F. Ramsak, and S. Rost. Shooting stars in the sky: an optimal algorithm for skyline queries. In International Conference on Very Large Data Bases, 2002.

Digital Library

[18]

H. T. Kung, F. Luccio, and F. P. Preparata. On finding the maxima of a set of vectors. Journal of ACM, 22(4):469--476, 1975.

Digital Library

[19]

J. Li, B. Saha, and A. Deshpande. A unified approach to ranking in probabilistic databases. In International Conference on Very Large Data Bases, 2009.

Digital Library

[20]

X. Lian and L. Chen. Monochromatic and bichromatic reverse skyline search over uncertain databases. In ACM-SIGMOD International Conference on Management of Data, 2008.

Digital Library

[21]

M. Löffler and J. M. Phillips. Shape fitting of point sets with probability distributions. In European Symposium on Algorithms, 2009.

[22]

M. Löffler and J. Snoeyink. Delaunay triangulations of imprecise points in linear time after preprocessing. In Symposium on Computational Geometry, pages 298--304, 2008.

Digital Library

[23]

R. Motwani and P. Raghavan. Randomized Algorithms. Cambridge University Press, 1995.

Digital Library

[24]

D. Nanongkai, A. Das Sarma, A. Lall, R. J. Lipton, and J. Xu. Regret-minimizing representative databases. In International Conference on Very Large Data Bases, 2010.

Digital Library

[25]

D. Papadias, Y. Tao, G. Fu, and B. Seeger. An optimal and progressive algorithm for skyline queries. In ACM-SIGMOD International Conference on Management of Data, 2003.

Digital Library

[26]

J. Pei, B. Jiang, X. Lin, and Y. Yuan. Probabilistic skylines on uncertain data. In International Conference on Very Large Data Bases, 2007.

Digital Library

[27]

F. P. Preparata and M. I. Shamos. Computational Geometry An Introduction. Springer, 1985.

Digital Library

[28]

K.-L. Tan, P.-K. Eng, and B. C. Ooi. Efficient progressive skyline computation. In International Conference on Very Large Data Bases, 2001.

Digital Library

[29]

Y. Tao, R. Cheng, X. Xiao, W. K. Ngai, B. Kao, and S. Prabhakar. Indexing multi-dimensional uncertain data with arbitrary probability density functions. In International Conference on Very Large Data Bases, 2005.

Digital Library

[30]

D. E. Willard. New data structures for orthogonal range queries. SIAM Journal of Computing, 14(1):232--253, 1985.

Digital Library

[31]

W. Zhang, X. Lin, Y. Zhang, W. Wang, and J. X. Yu. Probabilistic skyline operator over sliding windows. In IEEE International Conference on Data Engineering, 2009.

Digital Library

Cited By

Agrawal ALi YXue JJanardan R(2020)The most-likely skyline problem for stochastic pointsComputational Geometry10.1016/j.comgeo.2020.101609(101609)Online publication date: Jan-2020
https://doi.org/10.1016/j.comgeo.2020.101609
Groz BMallmann-Trenn FMathieu CVerdugo V(2020)Skyline Computation with Noisy ComparisonsCombinatorial Algorithms10.1007/978-3-030-48966-3_22(289-303)Online publication date: 8-Jun-2020
https://dl.acm.org/doi/10.1007/978-3-030-48966-3_22
Huang LLi JKlein P(2017)Stochastic k-center and j-flat-center problemsProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3039686.3039694(110-129)Online publication date: 16-Jan-2017
https://dl.acm.org/doi/10.5555/3039686.3039694
Show More Cited By

Index Terms

(Approximate) uncertain skylines
1. Information systems
  1. Data management systems
  2. Information storage systems
    1. Record storage systems
      1. Record storage alternatives

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cover image ACM Other conferences

ICDT '11: Proceedings of the 14th International Conference on Database Theory

March 2011

285 pages

ISBN:9781450305297

DOI:10.1145/1938551

Program Chair:
Tova Milo
Tel Aviv University, Israel

Copyright © 2011 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 21 March 2011

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EDBT/ICDT '11

EDBT/ICDT '11: EDBT/ICDT '11 joint conference

March 21 - 24, 2011

Uppsala, Sweden

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Cited By

Agrawal ALi YXue JJanardan R(2020)The most-likely skyline problem for stochastic pointsComputational Geometry10.1016/j.comgeo.2020.101609(101609)Online publication date: Jan-2020
https://doi.org/10.1016/j.comgeo.2020.101609
Groz BMallmann-Trenn FMathieu CVerdugo V(2020)Skyline Computation with Noisy ComparisonsCombinatorial Algorithms10.1007/978-3-030-48966-3_22(289-303)Online publication date: 8-Jun-2020
https://dl.acm.org/doi/10.1007/978-3-030-48966-3_22
Huang LLi JKlein P(2017)Stochastic k-center and j-flat-center problemsProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3039686.3039694(110-129)Online publication date: 16-Jan-2017
https://dl.acm.org/doi/10.5555/3039686.3039694
Liu JZhang HXiong LLi HLuo JBailey JMoffat AAggarwal Cde Rijke MKumar RMurdock VSellis TYu J(2015)Finding Probabilistic k-Skyline Sets on Uncertain DataProceedings of the 24th ACM International on Conference on Information and Knowledge Management10.1145/2806416.2806452(1511-1520)Online publication date: 17-Oct-2015
https://dl.acm.org/doi/10.1145/2806416.2806452
Bhattacharya AAwate S(2015)Probabilistic aggregate skyline join queriesProceedings of the 27th International Conference on Scientific and Statistical Database Management10.1145/2791347.2791350(1-12)Online publication date: 29-Jun-2015
https://dl.acm.org/doi/10.1145/2791347.2791350
Li CFan CLuo JZhong FZhu B(2015)Expected computations on color spanning setsJournal of Combinatorial Optimization10.1007/s10878-014-9764-729:3(589-604)Online publication date: 1-Apr-2015
https://dl.acm.org/doi/10.1007/s10878-014-9764-7
Huang LLi J(2015)Approximating the Expected Values for Combinatorial Optimization Problems over Stochastic PointsAutomata, Languages, and Programming10.1007/978-3-662-47672-7_74(910-921)Online publication date: 20-Jun-2015
https://doi.org/10.1007/978-3-662-47672-7_74
Kamousi PChan TSuri S(2014)Closest pair and the post office problem for stochastic pointsComputational Geometry: Theory and Applications10.1016/j.comgeo.2012.10.01047:2(214-223)Online publication date: 1-Feb-2014
https://dl.acm.org/doi/10.1016/j.comgeo.2012.10.010
Fan CLuo JZhong FZhu B(2013)Expected Computations on Color Spanning SetsFrontiers in Algorithmics and Algorithmic Aspects in Information and Management10.1007/978-3-642-38756-2_15(130-141)Online publication date: 2013
https://doi.org/10.1007/978-3-642-38756-2_15
Kamousi PChan TSuri S(2011)Closest pair and the post office problem for stochastic pointsProceedings of the 12th international conference on Algorithms and data structures10.5555/2033190.2033236(548-559)Online publication date: 15-Aug-2011
https://dl.acm.org/doi/10.5555/2033190.2033236
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