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# R-trees (data structure)

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### R-trees (data structure)

1. 1. By: Mahe Samrin Firdous M.E Software Engineering(1st Sem)
2. 2. “A Dynamic Index Structure For Spatial Searching”. The B-Tree provided a foundation for R-Trees Region-Trees (R-Trees)
3. 3. R1 R2 R1 R2 R3 R4 R5 R3 R4 R5 R6 R7 R6 R7 R8 R9 R10 R8 R9 R10 R13 R14 R13 R14 R15 R16 R15 R16
4. 4. B-Trees cannot store new types of data Specifically people wanted to store geometrical data and multi-dimensional data The R-Tree provided a way to do that (thanks to Antonin Guttman ‘84) Allows Overlapping.
5. 5. R-Trees can organize any-dimensional data by representing the data by a minimum bounding region(MBR). Each node bounds it’s children. The leaves point to the actual objects (stored on disk pages) The height is always log n. It is height balanced. Root has at least two children
6. 6. a b c d m a b c d e f g h i j k l m n o p
7. 7. a b c d m e fn a b c d e f g h i j k l m n o p
8. 8. a b c d m e fn h g i o p a b c d e f g h i j k l m n o p j k l
9. 9. • Similar to insertion into B+-tree but may insert into any leaf; leaf splits in case capacity exceeded. –Which leaf to insert into? (Choose Leaf) –How to split a node? (Node Split)
10. 10. m n o p
11. 11. m n o
12. 12. 17 a b c d a b c d Bad split Good split
13. 13. • Search for the rectangle • If the rectangle is found, remove it. • Adjust the rectangles making them smaller. • If the node is too empty (deficient): • delete the node recursively at its parent • insert all entries of the deleted node into the R-tree Re-use of INSERT routine Incrementally refines spatial structure
14. 14. Similar to B-tree search Quite easy & straight forward (Traverse the whole tree starting at the root node) No guarantee on good worst-case performance! (Possible overlapping of rectangles of entries within a single node!). Again, dependent on geometries. Average case-O(logMn)
15. 15. • R+ trees differ from R trees in that: – No overlapping – An object ID may be stored in more than one leaf node. • Advantages – Search is easier. – A fewer nodes are visited than with the R-tree. • Disadvantages – Since rectangles are duplicated, it is larger than R tree. – Construction & maintenance is more complex. R-Tree MBRs R+-Tree MBRs
16. 16. • Data objects in the map are represented by the Minimum Bounding Rectangles (MBRs)
17. 17. The initial application that motivated Guttman to his pioneering research was VLSI design (i.e., how to efficiently answer whether a space is already covered by a chip or not). A VLSI integrated-circuit
18. 18. The system extracts robust features from images. These features are used for indexing the images in a database using an R-tree. When a query is made about whether a test image is a replica of an image in the database, then the R-tree is traversed. Original Fingerprint image (left side) and a fake finger (right side), almost indistinguishable.
19. 19. Template of the pores and search along ridges. Fingerprint image (a) where pores can be easily noticed as small “holes” along ridges flow (as evident in the zoom (b)). (a) (b)
20. 20. In astronomical data collections, there are many data that can be thought of as points in a multi-dimensional space and are then suitable to be indexed using R- trees .Coordinates on the sky can be (and often are) represented in a database as ordered couples of longitude and latitude.
21. 21. A common example of spatial data can be seen in a road map. Spatial data lets you use R-tree indexing .A road map is a two-dimensional object that contains points, lines, and polygons that can represent cities, roads, and political boundaries such as states or provinces.
22. 22. Supplier: Divya, Affinis Technosoft, Excellex, JB Systems, Sterling Securities, Dotway Technologies, Sofgen India ,etc
23. 23. Virtual Sky Astronomy for iPad, iPhones on the App Store.
24. 24. In many scientific applications such as Earth Observation System (EOSDIS) it is a daunting task to index ever increasing volume of complex data that are continuously added to databases. To efficiently manage multidimensional data in scientific and data warehousing environments, R- tree based index structures have been widely used