6. 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.
7. 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
14. • 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)
21. • 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
22. 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)
23. • 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
24.
25. • Data objects in the map
are represented by the
Minimum Bounding
Rectangles (MBRs)
26. 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
27. 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.
28. 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)
29. 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.
30. 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.
34. 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
