- 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
- One parent node pointer
- 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:
- Note:
- 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 their
example in
Figure 14.43 (on page 682)
put the
= values in the
left/bottom half:
Anyway, this little detail is not important to understand the concept.
But it does cause than my example to differ from the one 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:
- Search Algorithm:
- At each internal node,
select
the subtree based
on the relationship of
the search key and
the key value
stored in the internal node:
- At each internal node,
select
the subtree based
on the relationship of
the search key and
the key value
stored in the internal node:
- Example: find the person with
age = 50 and
salary = 100
- Insert Algorithm for Quad-Tree:
Insert( x, y ) { Find the leaf node L (block) that is used to store (x, y); if ( leaf node L (block) has enough space ) { insert (x,y) in L return; } else { Let mx and my be the mid point values of L; Split the records in L into 22 blocks according the mx and my Replace L by an internal node I with key (mx, my); Make the 22 blocks as child nodes of I; } }
- We can always represent
a Quad-tree using a
kd-tree by
replacing
a quad-tre node by
3 kd-tree nodes as
follows:
- Fact:
- A quad-tree is
similar to
a kd-tree
- The techniques discussed in the kd-tree applies to the Quad-tree.
- A quad-tree is
similar to
a kd-tree