Slideshow:
Lookup algorithm for a kd-tree index
Example lookup operation using a kd-tree index
Find the record with search key age=35 and salary=500K
Insert algorithm for a kd-tree index
Example insert operation in a kd-tree index
Insert the record with search key age=35 and salary=500K
Example insert operation in a kd-tree index
Find for the leaf node that contains age = 35 and salary = 500K:
Leaf node is full, so we split it into two halves using the median (35) of the age values.
Example insert operation in a kd-tree index
Result kd-tree after inserting the record:
Deleting records from a kd-tree index
- Lookup Algorithm:
Record lookup( x ) { n = root node; // Start at the root /* ======================================== Traverse internal nodes to reach a leaf ======================================== */ while ( n ≠ leaf node ) { n is indexed using component i; if ( x.compi < n.key ) n = n.left; else n = n.right; } /* ============================ We have reached a leaf node ============================ */ if ( x ∈ n (leaf node) ) { return Record for x } else { return No Found; } }Example: lookup age = 35 and salary = 500K
- Insert Algorithm for the
kd-tree:
insert ( Record x ) { Use the search key in x to find: the leaf node L that will hold x if ( L has space store store x ) { insert record x in (block) L; } else { Let i = search dimension in parent node of L Let j = the next dimension after i /* ========================================= Split the leaf node L in dimension j ========================================= */ K = the median of search key values in dimension j; Move all records with key < K into block L1; Move all records with key >= K into block L2; Replace L by an internal node with key K; Set: K.left = L1; K.right = L2; } }
- Example:
- Insert the record
for a person with
age = 35 and
salary = 500K into the
following
kd-tree:
- Search for the leaf node
that holds age = 35,
salary = 500K:
- This level must use
age to
make a branch decision.
Therefore:
- Find the median
of the age value in
the data records:
25 400 35 500 <---- Median 45 350
- Use the median value = 35 to split the records
Result:
- Find the median
of the age value in
the data records:
- Insert the record
for a person with
age = 35 and
salary = 500K into the
following
kd-tree:
- Delete
- The delete operation is
very complex
and require
many block accesses
(If you remember the delete algorithm in Binary Search Tree you will understand --- you may need to replace the deleted record by its successor)
- Work-around::
- Instead of actually deleting
the record:
- We mark the record as deleted (tomb stone record)
- From time to time, the system rebuild the kd-tree from scratch to remove the deleted records.
- Instead of actually deleting
the record:
- The delete operation is
very complex
and require
many block accesses