The R -tree: An Efficient and Robust Access Method for Points and - - PowerPoint PPT Presentation

The R∗-tree: An Efficient and Robust Access Method for Points and Rectangles

• N. Beckmann
• H. P. Kriegel
• R. Schneider
• B. Seeger

Praktische Informatik, Universitaet Bremen

February 23, 2013

Presented by Zhitao Gong

Beckmann et al. (Universitaet Bremen) R∗-tree February 23, 2013 1 / 19

Outline

1

Introduction

2

Reasonale for R∗-tree Principles of R-tree Possible Optimizations Criteria Problem and solution

3

Detailed Optimization

4

Performance Comparison Intuitive Example of Optimization Dataset Experiment Results

5

conclusion

Beckmann et al. (Universitaet Bremen) R∗-tree February 23, 2013 2 / 19

Reasonale for R∗-tree Principles of R-tree

Principles of R-tree I

General contraints Non-leaf node (cp, Rectangle) Leaf node (Oid, Rectangle) Capacity number of rectangles contained in one node

2 ≤ N ≤ M for root and m ≤ N ≤ M for non-root

where 2 ≤ m ≤ M/2 Height all leaves on the same level

Beckmann et al. (Universitaet Bremen) R∗-tree February 23, 2013 3 / 19

Reasonale for R∗-tree Principles of R-tree

Principles of R-tree II

Dynamic Features Insertions and deletions mixed with queries No periodic global re-organization Different sequences of insertion build up different trees

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Reasonale for R∗-tree Principles of R-tree

R-tree Example

R1 R3 R4 R9 R11 R13 R10 R12 R16 R15 R14 R8 R2 R6 R7 R17 R18 R19 R5 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R16 R17 R18 R19

Figure : R-tree example

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Reasonale for R∗-tree Possible Optimizations Criteria

Optimizations Criteria I

1 Minimizing dead space

R1 R3 R4 R9 R11 R13 R10 R12 R14 R8 R5

Figure : Dead Space for R1

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Reasonale for R∗-tree Possible Optimizations Criteria

Optimizations Criteria II

2 Minimizing overlap R1 R2

Figure : Overlap between R1 and R2

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Reasonale for R∗-tree Possible Optimizations Criteria

Optimizations Criteria III

3 Minimizing margin 4 Optimize storage utilization Beckmann et al. (Universitaet Bremen) R∗-tree February 23, 2013 8 / 19

Reasonale for R∗-tree Problem and solution

Problem and solution I

Senario Goal Efficient retrieval Criteria 4 possible optimizations

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Reasonale for R∗-tree Problem and solution

Problem and solution II

Problem The known parameters of good retrieval performance affect each other in a very complex way. What we want: deadspace↓, overlap↓, margin↓, storage utilization↑ ⇒ performance↑ deadspace↓ and overlap↓ ⇒ storage utilization↓ deadspace↓ or overlap↓ ⇒ margin↑

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Reasonale for R∗-tree Problem and solution

Problem and solution III

Solution Use an enginneering approach to find the best possible combination

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Detailed Optimization

InsertData Algorithm

Figure : InsertData Algorithm

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Detailed Optimization

Optimization of ChooseSubtree

R-tree least area enlargement smallest area

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Detailed Optimization

Optimization of ChooseSubtree

R-tree least area enlargement smallest area R∗-tree N points to leaves, determine the minimum overlap cost

least overlap enlargement least area enlargement smallest area

Otherwise, determine the minimum area cost

area enlargement smallest area

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Performance Comparison Intuitive Example of Optimization

Intuitive Example of Optimization

Figure : Overfilled

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Performance Comparison Intuitive Example of Optimization

Intuitive Example of Optimization

Figure : Overfilled Figure : Quad-R-tree

Beckmann et al. (Universitaet Bremen) R∗-tree February 23, 2013 14 / 19

Performance Comparison Intuitive Example of Optimization

Intuitive Example of Optimization

Figure : Overfilled Figure : Quad-R-tree Figure : R∗-tree

Beckmann et al. (Universitaet Bremen) R∗-tree February 23, 2013 14 / 19

Performance Comparison Dataset

Data file and Query file

Data file Uniform Cluster Parcel Real-data Gaussian Mixed-Uniform Query file rectangle intersection query point query rectangle encosure query

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Performance Comparison Experiment Results

Results for Uniform I

Disk Accesses

point inter 0.001 inter 0.01 inter 0.1 inter 1 encl 0.001 encl 0.001 50 100 150 200 250 300 disk accesses

Uniform Dataset lin_gut quad_gut greene R ∗ -tree

Figure : Normalized disk accesses data

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Performance Comparison Experiment Results

Results for Uniform II

Storage Utilization

lin_gut quad_gut greene R ∗ -tree 10 20 30 40 50 60 70 80 storage utilization

Uniform Dataset

Figure : Storage Utilization comparison

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Performance Comparison Experiment Results

Results for Uniform III

Disk Accesses Per insertion

lin_gut quad_gut greene R ∗ -tree 1 2 3 4 5 6 7 8 storage utilization

Uniform Dataset

Figure : Disk accesses per insertion

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conclusion

Conclusion

Efficient SAM and PAM Outstanding performance Generalizing to polygons

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