1. Danzhou Liu Ee-Peng Lim Wee-Keong Ng
Efficient k Nearest Neighbor Queries on Remote Spatial Databases Using Range Estimation
Danzhou Liu Ee-Peng Lim Wee-Keong Ng
Center for Advanced Information Systems, School of Computer Engineering
Nanyang Technological University, Nanyang Ave, Singapore , Singapore

2. Outline Introduction Related work
k-NN query algorithm based on range estimation
Range estimation methods
Experiments
Conclusions
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3. Introduction
Spatial database provides persistent storage for spatial objects (e.g., points, polylines, polygons)
Spatial database supports
Representation of spatial attributes
Storage/indexing of spatial data values using some spatial indices (e.g., R-tree and Quadtree)
Queries involving spatial attributes
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4. k-Nearest Neighbor Queries
Definition
k-Nearest Neighbor (k-NN) query: locating k spatial objects nearest to a given query point
Wide range of applications:
Geographic Information Systems (GIS), e.g., finding the nearest two hospitals
Computer Aided Design (CAD), e.g, finding the nearest three resistors in a circuit board
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5. Motivation Large volume of spatial data on WWW
Geospatial Data Clearinghouse (a collection of over 250 spatial database servers)
Yahoo, Tiger and other map services
Limited Web-based query interfaces
Support simple spatial queries (e.g., window queries)
No support for remote index access
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6. The Geospatial Data Clearinghouse
Large amount of useful geospatial information on WWW
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7. The Geospatial Data Clearinghouse
Limited Web-based query interface; supports only window queries
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8. Objective
Develop efficient algorithms to evaluate k-NN queries on remote spatial databases using window queries:
Propose a generic k-NN query processing algorithm that accommodates different range estimation methods
Develop efficient range estimation methods
Conduct experiments to evaluate performance of proposed range estimation methods
Develop sampling methods to obtain statistical knowledge of remote databases needed for range estimation methods
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9. Related Work
Algorithms for simple k-NN queries may be divided into three major groups:
Partition-based algorithms
Graph-based algorithms
Range-based algorithms
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10. Partition-based Algorithms
Retrieve k nearest neighbors from spatial indices by pruning away nodes that cannot lead to k nearest neighbors
Examples
Branch-and-bound R-tree traversal algorithm
Pipelined fashion algorithm
Not applicable to Web environment
Spatial indices are usually not available to non-local applications
Creating local indices is infeasible due to large amount of data
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11. Graph-based Algorithms
Pre-compute nearest neighbors of spatial objects; create new index structures for pre-computed nearest neighbor information to support search
Example
Voronoi-based algorithm
Not applicable to Web environment
Retrieving all spatial objects on remote database servers is sometimes impractical
Creating local indices is infeasible due to large amount of data
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12. Range-based Algorithms
Use range queries to retrieve k nearest neighbors
Examples
Use sampling for range estimation
Use distance distributions for range estimation
Use reference points for range estimation
Not applicable to Web environment
Determining sample size and selecting samples of spatial objects properly are still a challenge
Creating local indices is infeasible due to large amount of data
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13. Proposed k-NN Algorithm
Based on range estimation
New strategies for k-NN query evaluation in Web environment are required
Use window queries for probing spatial database
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14. Density-based Range Estimation Method
Based on uniform spatial object distribution assumption
Range estimated by EstiRange1 function is
Ranges estimated by EstiRange2 function are
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15. Bucket-based Range Estimation Method
Use summary information about partitions or buckets of spatial objects for range estimation
Summary information
Bucket MBB, number of spatial objects in bucket
Buckets are created using different strategies [1]
Sort the set of max distance between buckets and query point
Range estimated is the minimal bucket-query point max distance that contains at least k nearest neighbor objects
Use one window query
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16. Example: k = 5
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17. Experiments
New Jersey road dataset from TIGER [30]
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18. Performance measures:
Number of iterations h A
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19. Experimental Results
Minimum, maximum and upper bounds on the number of iterations of the density-based range estimation method
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20. Iteration and accuracy of the density-based range estimation method
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21. Experimental Results
Efficiency of density-based and bucket-based range estimation methods
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22. Conclusions
A window query approach to evaluate k-NN queries on remote spatial databases motivated by
Large amount of spatial information on the Web
Limited query interface
Proposed range estimation methods
Performances increase with k.
No a clear winner
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23. SSDBM2002

24. Types of Range Estimation Methods
Tight estimation methods
Estimated range is not large enough; i.e., both EstiRange1 and EstiRange2 functions may be invoked
e.g., density-based method
Loose estimation methods
Estimated range is large enough; i.e., only the EstiRange1 function is invoked
e.g., bucket-based method
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25. Future Work
Extending range estimation methods with sampling techniques to determine data distribution
Current range estimation methods depend on statistical knowledge provided by database owners
Investigate how the statistical knowledge can be approximated through sampling
Developing strategies to select the appropriate range estimation methods for evaluating k-NN queries.
Developing Web applications of k-NN queries.
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26. Four Strategies to Create Buckets
Equi-Count, Equi-Area, Min-Skew, and Min-Overlap partitioning strategies [1]
Charminar Dataset
Spatial Densities in Charminar
Equi-Area Partitioning
Equi-Count Partitioning
Min-Skew Partitioning
Min-Overlap Partitioning
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