Slideshow:
Intro: kd-tree
Brief review of Binary Search Tree
Binary Search Tree is unbalanced (different distance from root to leaf nodes)
Definition: kd-tree
Example:
Properties of a kd-tree
Top level: (using search key x1)
Properties of a kd-tree
Second level: (using search key x1, and y1 and y2)
I.e.: just like a Binary Search Tree - but with multiple sets of keys
- Order of presentation:
- The kd-tree
as a main memory
data structure
based on the
Binary Search Tree
- Adaptation of the kd-tree for disk storage
- The kd-tree
as a main memory
data structure
based on the
Binary Search Tree
- Binary Search Tree:
- Binary Search Tree (BST) =
a binary tree where:
- The values in the nodes
in the left subtree
of the node
x
in the tree has a
smaller value
than
x
- The values in the nodes in the right subtree of the node x in the tree has a greater value than x
- The values in the nodes
in the left subtree
of the node
x
in the tree has a
smaller value
than
x
- Binary Search Tree (BST) =
a binary tree where:
- Example of a
binary search tree:
Notice the above property holds for every node in the binary tree:
- Node 3:
- Node 1:
- Node 6:
- Node 9:
- Node 3:
- kd-tree:
- The kd-tree is a
generalization of
the classic
Binary Search Tree (BST)
- The search key used
at different levels
belongs to a
different dimension (domain)
- The dimensions at different levels will wrap around (i.e., circulate)
- The kd-tree is a
generalization of
the classic
Binary Search Tree (BST)
- Example: a 2-dimensional
kd-tree:
Properties:
- Subtrees of
x1 must
satisfy this
property:
- Subtrees of
y1
and y2 must
satisfy this
property:
- And so on (for every level of the kd-tree)
- Subtrees of
x1 must
satisfy this
property: