1. Efficient Cost Models for Spatial Queries Using R-Trees
Reference: Y Theodoridis, E Stefanakis, T Sellis, Efficient cost models for spatial queries using R-trees, IEEE Transactions on Knowledge and Data Engineering , 2000
Speaker: Kai-Yun Ho
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2. Outline Introduction Background
Analytical Cost Models for Spatial Queries
Selection Oueries
Join Oueries
Introducing a Path Buffer
Evaluation of the Cost Models
Conclusions
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3. Introduction
Spatial queries addressed by users of SDBMS usually involve selection (point or range) and join operations.
We present analytical models that estimate the cost of selection and join queries using R-tree-based structures.
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4. Background (1/2)
The processing of any type of spatial query can be accelerated when a spatial index exists.
Selection queries
Search all data rectangles that overlap the query window q.
Join queries
Search all pairs of rectangles that overlap each other.
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5. Background (2/2)
For both operations, the total cost is measured by the total amount of page accesses in the R-tree index.
By definition, the number of node accesses is always greater than or equal to the number of actual disk accesses.
The equality only holds for the case where no buffering scheme exists.
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6. Background : R-tree r A C B r A D D G E B C E F G F
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7. Analytical Cost Models for Spatial Queries
What is sought?
A formula that estimates the average number NA of node accesses using only knowledge about data properties.
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8. For Selection Oueries (1/2)
The number of nodes at level l intersected by the query window q
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9. For Selection Oueries (2/2)
A function of the data properties NR1 and DR1
…..…. … f0 f1
fh-1 +
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10. For Join Oueries 1 - £ + h l and where
For the upper levels of two R-tree : ( ) 1 2 - + R h l
and
where
因為對於兩顆tree來說，access的node個數是一樣的，所以NA(R1,R2,l1)=NA(R2,R1,i2)
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11. Introducing a Path Buffer (1/2)
The existence of such a buffer mainly affects the performance of the tree index that plays the role of the query set.
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12. Disk Access (DA)
data set
query set
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13. Introducing a Path Buffer (2/2)
“query” tree R2 and “data” tree R1
: the propagation of R1 down to leaf adds no extra cost (disk
accesses) to R2 that has already reached its leaf level.
: each propagation of R2 down to its lower levels adds equal
cost to R1
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14. Evaluation of the Cost Models
synthetic and real data sets
LBeach data set : consisting of 53,143 line segments (stored as rectangles) indicating roads of Long Beach, California.
MGcounty data set : consisting of 39,221 line segments (stored as rectangles)indicating roads of Montgomery County, Maryland.
synthetic random
synthetic skewed
LBeach real data
MGcounty real data
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15. Evaluation of the Cost Models
For selection queries on synthetic random data set
Density D=0.1
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16. Evaluation of the Cost Models
For join queries on synthetic random data set
node and disk
accesses
Density D=2
Density D=1
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17. Evaluation of the Cost Models
Performance comparison for selection queries on
(a) skewed and (b) real data.
(a)
(b)
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18. Evaluation of the Cost Models
For join queries on (a) skewed and (b) real data.
(a)
(b)
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19. Conclusions
For query optimization purposes, efficient cost models should be also available in order to make accurate cost estimations under various data distributions.
The proposed cost formulae are functions of data properties only, and, therefore, can be used without any knowledge of the R-tree index properties.
Experimental results on both synthetic and real data sets showed that the proposed analytical model is very accurate.
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20. Q & A
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