Slideshow:
Intro: Quad-tree
Intro: Quad-tree
Example: the initial search space
Intro: Quad-tree
Example: the search space after 1 division
Structure of a node of a Quad-tree
Example: a 2-way split quad-tree node
Dictical note on my presentation vs. the text book
While preparing my teaching notes, I assume
would partition the search space into:
Dictical note on my presentation vs. the text book
After making many figures, I discovered the quad node:
would partition the search space into:
Example of a quad-tree index
Input data:
Quad tree index (and data file (in squares):
- Quad-tree:
- Quad-tree = an index structure that divides a search space in half (exactly !) in every dimension
- Example:
- Original search space:
- The quad-tree will
divide the
search space as
follows:
- Original search space:
- Structure of
a quad-tree node:
- A quad-tree node contains
the following:
- 1 search key value for
each dimension
-
2n
child nodepointers
(n way split)
- One
parent node pointer
(except for the
root node)
- 1 search key value for
each dimension
- The child node pointers will
point to
every possible combination
of
< and
≥
relationships
with the
search key values
Example: a 2-dimensional quad-tree node
The node corresponds to the following division:
- A quad-tree node contains
the following:
- Warning:
- The book was
not clear on
where to put the
= bucket
- So I assumed they would
do it just like the
kd-tree
(Because the Quad-tree is similar to the kd-tree)
- After preparing the
teaching material, I
discovered that the
book's example in
Figure 14.43 (on page 682)
put the
= values in the
left/bottom half:
- I already made
my notes with this
assumption:
Anyway:
- This (little) detail is not important to understand the concept.
However:
- The difference does cause my examples to differ from the ones presented in the text book
- The book was
not clear on
where to put the
= bucket
- Data on people who buy jewelry:
(age, salary (in $1,000)) A(25,60) D(45,60) G(50,75) J(50,100) B(50,120) E(70,110) H(85,140) K(30,260) C(25,400) F(45,350) I(50,275) L(60,260)
- A Quad-tree for the
data: