Slideshow:
Lookup records using a Quad-tree index
The lookup algorithm for Quad-tree is a generalization of the BST lookup procedure:
Lookup records using a Quad-tree index
- Example
Find the record using search key (age=50, salary=100) the this Quad-tree:
Lookup records using a Quad-tree index
- Example
Find the record using search key (age=50, salary=100) the this Quad-tree:
Lookup records using a Quad-tree index
- Example
Find the record using search key (age=50, salary=100) the this Quad-tree:
Lookup records using a Quad-tree index
- Example
Find the record using search key (age=50, salary=100) the this Quad-tree:
Inserting a new search key (+ pointer) into a Quad-tree index
Inserting a new search key (+ pointer) into a Quad-tree index
- Example
Insert the (new) search key (age=35, salary=300)
Inserting a new search key (+ pointer) into a Quad-tree index
- Example
Find the disk block that hold the (new) search key (age=35, salary=300):
Inserting a new search key (+ pointer) into a Quad-tree index
- Example
Split the full disk block using the middle value of each dimension (each dimension is split in half):
Inserting a new search key (+ pointer) into a Quad-tree index
- Example
Hang the 4 (= 22) buckets under the new internal node (age=37, salary=350):
Deleting a search key (+ pointer) from a Quad-tree index
Note: a Quad-tree index is just a
simplified
kd-tree index !
- Lookup 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( x1, x2, ..., xn ) { Find the leaf node L (block) that is used to store (x1, x2, ..., xn); if ( leaf node L (block) has enough space ) { insert (x1, x2, ..., xn) in L; return; } else { /* ====================================================== 1. Split leaf node L into 2n parts !!! Each dimension exactly in HALF 2. Add an internal node with search key for these 2n leaf nodes ====================================================== */ Let m1 = the middle of the x1 range of values in L; Let m2 = the middle of the x2 range of values in L; ... Let mn = the middle of the xn range of values in L; Split the records in L into 2n blocks according m1, m2, ..., mn Replace L by an internal node I with seacrh key (m1, m2, ..., mn); Make the 2n blocks as child nodes of I; } }Example:
- Insert the
record (age=35,
salary= 300) in the
following quad-tree:
- Find the
leaf node L:
- Split the
overflow node at the
mid values
(age=(25+50)/2 = 37 and
salary=(300+400)2 = 350):
- Add an
internal search node containing the
mid search key values:
(age=37,
salary=350)
- Insert the
record (age=35,
salary= 300) in the
following quad-tree:
- Delete operation:
- Same comment on
delete as in
the kd-tree:
- The delete operation is very complex and require many block accesses
- Work-around::
- Instead of actually deleting
the record:
- the system marks the record as deleted
- From time to time, the system rebuild the kd-tree from scratch to remove the deleted records.
- Instead of actually deleting
the record:
- Same comment on
delete as in
the kd-tree:
- We can always represent
a Quad-tree using a
kd-tree by:
- Replacing
a quad-tree node by
3 (three) kd-tree nodes as
follows:
- Replacing
a quad-tree node by
3 (three) kd-tree nodes as
follows: