research-article

Nearest-neighbor searching under uncertainty

Authors:

Pankaj K. Agarwal,

Swaminathan Sankararaman,

Wuzhou ZhangAuthors Info & Claims

PODS '12: Proceedings of the 31st ACM SIGMOD-SIGACT-SIGAI symposium on Principles of Database Systems

Pages 225 - 236

https://doi.org/10.1145/2213556.2213588

Published: 21 May 2012 Publication History

Abstract

Nearest-neighbor queries, which ask for returning the nearest neighbor of a query point in a set of points, are important and widely studied in many fields because of a wide range of applications. In many of these applications, such as sensor databases, location based services, face recognition, and mobile data, the location of data is imprecise. We therefore study nearest neighbor queries in a probabilistic framework in which the location of each input point and/or query point is specified as a probability density function and the goal is to return the point that minimizes the expected distance, which we refer to as the expected nearest neighbor (ENN). We present methods for computing an exact ENN or an ε-approximate ENN, for a given error parameter 0 < ε 0 < 1, under different distance functions. These methods build an index of near-linear size and answer ENN queries in polylogarithmic or sublinear time, depending on the underlying function. As far as we know, these are the first nontrivial methods for answering exact or ε-approximate ENN queries with provable performance guarantees.

References

[1]

P. K. Agarwal, S.-W. Cheng, Y. Tao, and K. Yi, Indexing uncertain data, Proc. ACM Symposium on Principles of Database Systems, 2009, pp. 137--146.

Digital Library

[2]

P. K. Agarwal, S. Har-Peled, M. Sharir, and Y. Wang, Hausdorff distance under translation for points and balls, ACM Transactions on Algorithms, 6 (2010), 71:1--71:26.

Digital Library

[3]

P. K. Agarwal and J. Matousek, Ray shooting and parametric search, SIAM Journal on Computing, 22 (1993), 794--806.

Digital Library

[4]

C. C. Aggarwal, Managing and Mining Uncertain Data, Springer, 2009.

Digital Library

[5]

A. Andoni and P. Indyk, Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions, Communications of the ACM, 51 (2008), 117--122.

Digital Library

[6]

S. Arya, T. Malamatos, and D. M. Mount, Space-time tradeoffs for approximate nearest neighbor searching, Journal of the ACM, 57 (2009), 1:1--1:54.

Digital Library

[7]

F. Aurenhammer and R. Klein, Voronoi diagrams, in: Handbook of Computational Geometry (J. E. Goodman and J. O'Rourke, eds.), Elsevier Science Publishers, Amsterdam, 2000, pp. 201--290.

[8]

G. Beskales, M. A. Soliman, and I. F. IIyas, Efficient search for the top-k probable nearest neighbors in uncertain databases, Proc. International Conference on Very Large Databases, 1 (2008), 326--339.

Digital Library

[9]

S. Cabello, Approximation algorithms for spreading points, Journal of Algorithmss, 62 (2007), 49--73.

Digital Library

[10]

S. Cabello and M. J. van Kreveld, Approximation algorithms for aligning points, Proc. 19th ACM Symposium on Computational Geometry, 2003, pp. 20--28.

Digital Library

[11]

R. Cheng, J. Chen, M. Mokbel, and C.-Y. Chow, Probabilistic verifiers: Evaluating constrained nearest-neighbor queries over uncertain data, Proc. IEEE International Conference on Data Engineering, 2008, pp. 973--982.

Digital Library

[12]

R. Cheng, L. Chen, J. Chen, and X. Xie, Evaluating probability threshold k-nearest-neighbor queries over uncertain data, Proc. 12th International Conference on Extending Database Technology: Advances in Database Technology, 2009, pp. 672--683.

Digital Library

[13]

R. Cheng, X. Xie, M. L. Yiu, J. Chen, and L. Sun, Uv-diagram: A voronoi diagram for uncertain data, Proc. IEEE International Conference on Data Engineering, 2010, pp. 796--807.

[14]

K. L. Clarkson, Nearest-neighbor searching and metric space dimensions, Nearest-Neighbor Methods for Learning and Vision: Theory and Practice, (2006), 15--59.

[15]

N. N. Dalvi, C. Ré, and D. Suciu, Probabilistic databases: diamonds in the dirt, Communications of the ACM, 52 (2009), 86--94.

Digital Library

[16]

M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf, Computational Geometry: Algorithms and Applications, Springer-Verlag, 2000.

Digital Library

[17]

A. Guttman, R-trees: a dynamic index structure for spatial searching, Proc. ACM SIGMOD International Conference on Management of Data, 1984, pp. 47--57.

Digital Library

[18]

S. Har-Peled, Geometric Approximation Algorithms, American Mathematical Society, 2011.

Digital Library

[19]

M. Hua, J. Pei, W. Zhang, and X. Lin, Ranking queries on uncertain data: a probabilistic threshold approach, Proc. ACM SIGMOD International Conference on Management of Data, 2008, pp. 673--686.

Digital Library

[20]

P. Indyk, Nearest neighbors in high-dimensional spaces, in: Handbook of Discrete and Computational Geometry (J. E. Goodman and J. O'Rourke, eds.), CRC Press LLC, 2004.

[21]

M. Jooyandeh, A. Mohades, and M. Mirzakhah, Uncertain voronoi diagram, Information Processing Letters, 109 (2009), 709--712.

Digital Library

[22]

P. Kamousi, T. M. Chan, and S. Suri, Closest pair and the post office problem for stochastic points, Proc. 12th International Conference on Algorithms and Data Structures, 2011, pp. 548--559.

Digital Library

[23]

H.-P. Kriegel, P. Kunath, and M. Renz, Probabilistic nearest-neighbor query on uncertain objects, Proc. 12th International Conference on Database Systems for Advanced Applications, 2007, pp. 337--348.

Digital Library

[24]

F. Li, B. Yao, and P. Kumar, Group enclosing queries, IEEE Transactions on Knowledge and Data Engineering, 23 (2011), 1526 --1540.

Digital Library

[25]

H. Li, H. Lu, B. Huang, and Z. Huang, Two ellipse-based pruning methods for group nearest neighbor queries, Proc. 13th Annual ACM International Workshop on Geographic Information Systems, 2005, pp. 192--199.

Digital Library

[26]

Y. Li, F. Li, K. Yi, B. Yao, and M. Wang, Flexible aggregate similarity search, Proc. ACM SIGMOD International Conference on Management of Data, 2011, pp. 1009--1020.

Digital Library

[27]

X. Lian and L. Chen, Probabilistic group nearest neighbor queries in uncertain databases, IEEE Transactions on Knowledge and Data Engineering, 20 (2008), 809--824.

Digital Library

[28]

V. Ljosa and A. Singh, Apla: Indexing arbitrary probability distributions, Proc. IEEE International Conference on Data Engineering, 2007, pp. 946--955.

[29]

M. Löffler and M. J. van Kreveld, Largest bounding box, smallest diameter, and related problems on imprecise points, Computational Geometry, 43 (2010), 419--433.

Digital Library

[30]

Y. Luo, H. Chen, K. Furuse, and N. Ohbo, Efficient methods in finding aggregate nearest neighbor by projection-based filtering, Proc. 12th International Conference on Computational Science and Its Applications, 2007, pp. 821--833.

Digital Library

[31]

D. Papadias, Q. Shen, Y. Tao, and K. Mouratidis, Group nearest neighbor queries, Proc. IEEE International Conference on Data Engineering, 2004, pp. 301--312.

Digital Library

[32]

N. Sarnak and R. E. Tarjan, Planar point location using persistent search trees, Communications of the ACM, 29 (1986), 669--679.

Digital Library

[33]

J. Sember and W. Evans, Guaranteed voronoi diagrams of uncertain sites, Proc. 20th Canadian Conference on Computational Geometry, 2008.

[34]

M. Sharifzadeh and C. Shahabi, Vor-tree: R-trees with voronoi diagrams for efficient processing of spatial nearest neighbor queries, Proc. International Conference on Very Large Databases, 3 (2010), 1231--1242.

Digital Library

[35]

M. Sharir and P. K. Agarwal, Davenport-Schinzel Sequences and Their Geometric Applications, Cambridge University Press, New York, 1995.

Digital Library

[36]

G. Trajcevski, R. Tamassia, H. Ding, P. Scheuermann, and I. F. Cruz, Continuous probabilistic nearest-neighbor queries for uncertain trajectories, Proc. 12th International Conference on Extending Database Technology: Advances in Database Technology, 2009, pp. 874--885.

Digital Library

[37]

M. J. van Kreveld, M. Löffler, and J. S. B. Mitchell, Preprocessing imprecise points and splitting triangulations, SIAM Journal on Computing, 39 (2010), 2990--3000.

Digital Library

[38]

M. Yiu, N. Mamoulis, and D. Papadias, Aggregate nearest neighbor queries in road networks, IEEE Transactions on, Knowledge and Data Engineering, 17 (2005), 820--833.

Digital Library

[39]

S. M. Yuen, Y. Tao, X. Xiao, J. Pei, and D. Zhang, Superseding nearest neighbor search on uncertain spatial databases, IEEE Transactions on Knowledge and Data Engineering, 22 (2010), 1041--1055.

Digital Library

Cited By

Karlaš BLi PWu RGürel NChu XWu WZhang C(2020)Nearest neighbor classifiers over incomplete informationProceedings of the VLDB Endowment10.14778/3430915.343091714:3(255-267)Online publication date: 1-Nov-2020
https://dl.acm.org/doi/10.14778/3430915.3430917
Wang HZhang J(2019)Covering Uncertain Points in a TreeAlgorithmica10.1007/s00453-018-00537-681:6(2346-2376)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1007/s00453-018-00537-6
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

Nearest-neighbor searching under uncertainty
1. Information systems
  1. Information retrieval
    1. Document representation
    2. Search engine architectures and scalability
      1. Search engine indexing
2. Theory of computation
  1. Design and analysis of algorithms

Recommendations

Nearest-Neighbor Searching Under Uncertainty II

Nearest-neighbor search, which returns the nearest neighbor of a query point in a set of points, is an important and widely studied problem in many fields, and it has a wide range of applications. In many of them, such as sensor databases, location-...
Nearest neighbor searching under uncertainty II
PODS '13: Proceedings of the 32nd ACM SIGMOD-SIGACT-SIGAI symposium on Principles of database systems

Nearest-neighbor (NN) search, which returns the nearest neighbor of a query point in a set of points, is an important and widely studied problem in many fields, and it has wide range of applications. In many of them, such as sensor databases, location-...
Nearest-Neighbor Searching Under Uncertainty I

Nearest-neighbor queries, which ask for returning the nearest neighbor of a query point in a set of points, are important and widely studied in many fields because of a wide range of applications. In many of these applications, such as sensor databases, ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

PODS '12: Proceedings of the 31st ACM SIGMOD-SIGACT-SIGAI symposium on Principles of Database Systems

May 2012

332 pages

ISBN:9781450312486

DOI:10.1145/2213556

Editor:
Markus Krötzsch
University of Oxford, UK
,
General Chair:
Maurizio Lenzerini
University of Rome La Sapienza, Italy
,
Program Chair:
Michael Benedikt
University of Oxford, UK

Copyright © 2012 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]

Sponsors

SIGMOD: ACM Special Interest Group on Management of Data

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 21 May 2012

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Conference

SIGMOD/PODS '12

Sponsor:

SIGMOD

SIGMOD/PODS '12: International Conference on Management of Data

May 21 - 23, 2012

Arizona, Scottsdale, USA

Acceptance Rates

PODS '12 Paper Acceptance Rate 26 of 101 submissions, 26%;

Overall Acceptance Rate 642 of 2,707 submissions, 24%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

29
Total Citations
View Citations
421
Total Downloads

Downloads (Last 12 months)4
Downloads (Last 6 weeks)0

Reflects downloads up to 08 Mar 2025

Other Metrics

View Author Metrics

Citations

Cited By

Karlaš BLi PWu RGürel NChu XWu WZhang C(2020)Nearest neighbor classifiers over incomplete informationProceedings of the VLDB Endowment10.14778/3430915.343091714:3(255-267)Online publication date: 1-Nov-2020
https://dl.acm.org/doi/10.14778/3430915.3430917
Wang HZhang J(2019)Covering Uncertain Points in a TreeAlgorithmica10.1007/s00453-018-00537-681:6(2346-2376)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1007/s00453-018-00537-6
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
Patroumpas KKoutras CChoudhary AWu KDong B(2017)Probabilistic k-Nearest Neighbor Monitoring of Moving GaussiansProceedings of the 29th International Conference on Scientific and Statistical Database Management10.1145/3085504.3085525(1-12)Online publication date: 27-Jun-2017
https://dl.acm.org/doi/10.1145/3085504.3085525
Agarwal PHar-Peled SSuri SYıldız HZhang W(2017)Convex Hulls Under UncertaintyAlgorithmica10.1007/s00453-016-0195-y79:2(340-367)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1007/s00453-016-0195-y
Wang HZhang J(2017)Computing the Center of Uncertain Points on Tree NetworksAlgorithmica10.1007/s00453-016-0158-378:1(232-254)Online publication date: 1-May-2017
https://dl.acm.org/doi/10.1007/s00453-016-0158-3
Wang HZhang J(2017)Covering Uncertain Points in a TreeAlgorithms and Data Structures10.1007/978-3-319-62127-2_47(557-568)Online publication date: 5-Jul-2017
https://doi.org/10.1007/978-3-319-62127-2_47
Agarwal PAronov BHar-Peled SPhillips JYi KZhang W(2016)Nearest-Neighbor Searching Under Uncertainty IIACM Transactions on Algorithms10.1145/295509813:1(1-25)Online publication date: 10-Oct-2016
https://dl.acm.org/doi/10.1145/2955098
Agarwal PKumar NSintos SSuri SMilo TTan W(2016)Range-Max Queries on Uncertain DataProceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/2902251.2902281(465-476)Online publication date: 15-Jun-2016
https://dl.acm.org/doi/10.1145/2902251.2902281
Li JWang H(2016)Range queries on uncertain dataTheoretical Computer Science10.1016/j.tcs.2015.09.005609:P1(32-48)Online publication date: 4-Jan-2016
https://dl.acm.org/doi/10.1016/j.tcs.2015.09.005
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Table of Conten