r* tree by rohan sadale akshay kulkarni. motivation optimization criteria for r* tree high level...
DESCRIPTION
Motivation R Tree Every parent completely covers its children A child MBR may be covered by more than one parent. It is stored under only one of them. Minimizes only area. Multiple nodes should be visited because of overlap (MBRs).TRANSCRIPT
![Page 1: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/1.jpg)
R* Tree
By Rohan Sadale
Akshay Kulkarni
![Page 2: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/2.jpg)
Motivation
Optimization criteria for R* Tree
High level Algorithm
Example
Performance
Agenda
![Page 3: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/3.jpg)
Motivation R Tree
Every parent completely covers its children A child MBR may be covered by more than one
parent. It is stored under only one of them. Minimizes only area. Multiple nodes should be visited because of overlap
(MBRs).
![Page 4: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/4.jpg)
Motivation R+ Tree
Disjoint MBRs Prevents overlapping by duplicating objects
across leaf nodes
![Page 5: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/5.jpg)
Motivation R* Tree
Improved query performance over R-Tree But, higher construction cost Incorporates a combined optimization of:
-area -margin -overlap
![Page 6: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/6.jpg)
Follows an engineering approach to find best possible combinations of the criteria mentioned below:
Minimization of area covered by each MBR Minimization of overlap between MBRs Minimization of MBR margins Maximization of storage utilization
But, can’t do all at once. Need a heuristic approach.
Optimization criteria for R* Tree
![Page 7: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/7.jpg)
High Level Algorithm Same algorithm as the R-tree for query and delete
operations.
When inserting, the R*-tree uses a combined strategy. For inner nodes (non-leaf), enlargement and area
are minimized. For leaf nodes, overlap is minimized.
Deletion and reinsertion of entries allows them to "find" a place in the tree that may be more appropriate than their original location.
When a node overflows, a portion of its entries are removed from the node and reinserted into the tree.
This has the effect of producing more well-clustered groups of entries in nodes, reducing node coverage.
![Page 8: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/8.jpg)
R*-Tree example
a
b
c
e
d
f
g
i
h
j
N3
N4
N2
N1
N6N
5
N5
N6
N1
N2
N3
N4
jihgfedcba
![Page 9: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/9.jpg)
R*-Tree example
a
b
c
e
d
k
f
g
i
h
j
N3
N4
N2
N1
N6N
5
N5
N6
N1
N2
N3
N4
jihgfedcba
Insert k
![Page 10: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/10.jpg)
R*-Tree example
a
b
c
e
d
k
f
g
i
h
j
N3
N4
N2
N1
N6N
5
N5
N6
N1
N2
N3
N4
jihgfedcba
Insert kCheck for minimum area enlargement at root node.N5 or N6 ? - choose N5
k ?
![Page 11: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/11.jpg)
R*-Tree example
a
b
c
e
d
k
f
g
i
h
j
N3
N4
N2
N1
N6N
5
N5
N6
N1
N2
N3
N4
jihgfedcba
Insert kCheck for minimum area enlargement at next non leaf node. N1 or N2 ? - choose N1
k ?
![Page 12: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/12.jpg)
R*-Tree example
a
b
c
e
d
k
f
g
i
h
j
N3
N4
N2
N1
N6N
5
N5
N6
N1
N2
N3
N4
jihgfedcba
Insert kIf node capacity is 3., then where will ‘k’ go?Reinsertion of nodes from nearest MBRs (strategy - overlap minimization)
k ?
![Page 13: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/13.jpg)
R*-Tree example
a
b
c
e
d
k
f
g
i
h
j
N3
N4
N2
N1
N6N
5
N5
N6
N1
N2
N3
N4
jihgfedcba
Insert kIf node capacity is 3., then where will ‘k’ go?
kRe
inse
rt n
odes
from
N1
and
N2
![Page 14: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/14.jpg)
R*-Tree example
a
b
c
e
d
k
f
g
i
h
j
N3
N4
N2
N1
N6N
5
N5
N6
N1
N2
N3
N4
jihgfedkba
Insert kIf node capacity is 3., then where will ‘k’ go?- Reinsertion !!!
c
![Page 15: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/15.jpg)
R-Tree vs R+ Tree vs R* Tree
j
a b
c
e
f g
h i
12 3
1st level index
leafs
1 2 3
a b c e f g h i
d
d
new data
x new data: x
Initial data:{a,b,…,h,i}
Legend
Initial R-tree
![Page 16: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/16.jpg)
R-Tree
j
a b
c
e
f g
h i
1
23
1st level index
leafs
dnew data
x new data: x
Initial data:{a,b,…,h,i}
Legend
![Page 17: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/17.jpg)
R+ Tree
j
a b
c
e
f g
h i
1
23
1st level index
leafs
dnew data
x new data: x
Initial data:{a,b,…,h,i}
Legend
![Page 18: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/18.jpg)
R* Tree
j
a b
c
e
f g
h i
1
2
31st level index
leafs
dnew data
x new data: x
Initial data:{a,b,…,h,i}
Legend
![Page 19: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/19.jpg)
Performance Improved split heuristic produces pages that are more
rectangular and thus better for many applications.
Reinsertion method optimizes the existing tree, but increases complexity.
Efficiently supports point and spatial data at the same time.
![Page 20: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/20.jpg)
References
Encyclopedia of GIS: R*-tree, H. Kriegel, P. Kunath, page 987-992.
R-Trees: Theory and Applications, Yannis Manolopoulos, Alexandros Nanopoulos, Apostolos N. Papadopoulos and Yannis Theodoridis
Wikipedia - https://en.wikipedia.org/wiki/R*_tree
![Page 21: R* Tree By Rohan Sadale Akshay Kulkarni. Motivation Optimization criteria for R* Tree High level Algorithm Example Performance Agenda](https://reader036.vdocuments.us/reader036/viewer/2022062306/5a4d1b7e7f8b9ab0599ba430/html5/thumbnails/21.jpg)
Thank you :)