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.
- 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. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- P. K. Agarwal and J. Matousek, Ray shooting and parametric search, SIAM Journal on Computing, 22 (1993), 794--806. Google Scholar
Digital Library
- C. C. Aggarwal, Managing and Mining Uncertain Data, Springer, 2009. Google Scholar
Digital Library
- A. Andoni and P. Indyk, Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions, Communications of the ACM, 51 (2008), 117--122. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- 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.Google Scholar
- 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. Google Scholar
Digital Library
- S. Cabello, Approximation algorithms for spreading points, Journal of Algorithmss, 62 (2007), 49--73. Google Scholar
Digital Library
- S. Cabello and M. J. van Kreveld, Approximation algorithms for aligning points, Proc. 19th ACM Symposium on Computational Geometry, 2003, pp. 20--28. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- 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.Google Scholar
Cross Ref
- K. L. Clarkson, Nearest-neighbor searching and metric space dimensions, Nearest-Neighbor Methods for Learning and Vision: Theory and Practice, (2006), 15--59.Google Scholar
- N. N. Dalvi, C. Ré, and D. Suciu, Probabilistic databases: diamonds in the dirt, Communications of the ACM, 52 (2009), 86--94. Google Scholar
Digital Library
- M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf, Computational Geometry: Algorithms and Applications, Springer-Verlag, 2000. Google Scholar
Digital Library
- A. Guttman, R-trees: a dynamic index structure for spatial searching, Proc. ACM SIGMOD International Conference on Management of Data, 1984, pp. 47--57. Google Scholar
Digital Library
- S. Har-Peled, Geometric Approximation Algorithms, American Mathematical Society, 2011. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- 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.Google Scholar
- M. Jooyandeh, A. Mohades, and M. Mirzakhah, Uncertain voronoi diagram, Information Processing Letters, 109 (2009), 709--712. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- F. Li, B. Yao, and P. Kumar, Group enclosing queries, IEEE Transactions on Knowledge and Data Engineering, 23 (2011), 1526 --1540. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- X. Lian and L. Chen, Probabilistic group nearest neighbor queries in uncertain databases, IEEE Transactions on Knowledge and Data Engineering, 20 (2008), 809--824. Google Scholar
Digital Library
- V. Ljosa and A. Singh, Apla: Indexing arbitrary probability distributions, Proc. IEEE International Conference on Data Engineering, 2007, pp. 946--955.Google Scholar
Cross Ref
- M. Löffler and M. J. van Kreveld, Largest bounding box, smallest diameter, and related problems on imprecise points, Computational Geometry, 43 (2010), 419--433. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- D. Papadias, Q. Shen, Y. Tao, and K. Mouratidis, Group nearest neighbor queries, Proc. IEEE International Conference on Data Engineering, 2004, pp. 301--312. Google Scholar
Digital Library
- N. Sarnak and R. E. Tarjan, Planar point location using persistent search trees, Communications of the ACM, 29 (1986), 669--679. Google Scholar
Digital Library
- J. Sember and W. Evans, Guaranteed voronoi diagrams of uncertain sites, Proc. 20th Canadian Conference on Computational Geometry, 2008.Google Scholar
- 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. Google Scholar
Digital Library
- M. Sharir and P. K. Agarwal, Davenport-Schinzel Sequences and Their Geometric Applications, Cambridge University Press, New York, 1995. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
Index Terms
Nearest-neighbor searching under uncertainty
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 systemsNearest-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