ISYS 300 Search Trees, BTrees and B Trees

1
ISYS 300 Search Trees, B-Trees and B Trees
2
How we got here?

• Created an inverted index from text
• Used the index for a text searching (vector
  model)
• There can be tens of thousands on items in an
  index How can we access them quickly?
• Note These are important techniques beyond text
  searching there are many places they can be
  used.

3
Finding Items in an Inverted Index

• Sorted List
• Binary search
• Linked List
• Hard to search without an index
• Easy to insert and delete items
• Binary Trees
• Always two choices (20 questions)
• Multi-way Trees (B-Trees and B Trees)
• Several choices at choice point
• High fan-out. Not as deep as binary trees
• Other techniques to remember but probably not a
  good choice here
• Hashing
• Content-based retrieval (neural networks)

4
Graphs

• A graph is a set of nodes and edges
• Some common graph problems include
• Layout of highways, telephone lines
• The structure of the Web
• Social networks

5
Trees and Hierarchies Some Terminology

• A Tree is a data structure in which one node
  links to other nodes in exactly one way.
• We often think of a tree as a hierarchy
• For a hierarchy, we often talk about parents
  (up the hierarchy) and children (lower in the
  hierarchy).
• We often pick one central node as the root of a
  tree and the nodes with no children as the
  leaves
• The depth of a tree is the (average) distance
  from the root to the children
• Lots of times we say tree when we mean
  hierarchies
• Trees can be used for searching with keys.
  That is, an element providing directions for
  moving around in the tree.

6
Balanced, Binary, Search Trees

• Binary Search tree (there are always 2 choices)
• Each node contains a key
• Left sub-trees stored all keys smaller than the
  parent key
• Right sub-trees stored all keys larger than the
  parent key
• Balanced trees
• Every parent has an approximately equal number of
  left-and right sub-trees

7
Using Trees for Storing Data and Then Searching
for it there

• Storing Data in a Balanced Binary Tree
• In a balanced tree, the number of steps to find
  an answer (the depth) is
• NumSteps Levels NumItems

8
Operations on Binary Search Trees

• Search
• Create a New Tree
• Insert New Items
• Delete Items

9
Inserting Data into a Search Tree

• Walk down the tree to the node closest in value
  to the one to be inserted
• Link the new node in if this results in an
  unbalanced tree go to the next page.

10
Balancing a Binary Search Tree

The left tree is slightly less efficient than the
right tree. On the left tree, there are more
items deep in the tree than at the higher level.
11
B Trees (Multi-Way Trees)

• Description
• Each node can have more than one key (multi-way
  tree)
• If a node has m keys, it will have m1 children
  branches.
• All keys in i-1 branch are smaller than key I
  This makes it useful for searching, it is the
  search tree property.
• All leaves are at the same depth.
• Advantages of B-Tree over Binary Tree
• Useful when reading long records off a disk

12
B tree
10
25
4
8
13
18
21
22
28
39
51
52
0
3
13
B Tree

• B Trees
• B-tree that stores all data in the leaves.
• That way, the B-Tree can be kept in a separate
  file from the data

14
B tree
(F, M)
(Ap, Bs, E)
(Gr, H, L)
(P, Ru, T)
1
2
3
4
5
6
7
8
9
10
11
12
15
Searching a Tree that is Not Well Structured

• The moves in some games can be organized as a
  tree (a game space)
• Tic-tac-toe, Chess
• Have to make estimates of the value of each
  choice
• A value can be calculated for the alternatives.
  Further, we can have a rule (such as MIN-MAX) for
  selecting alternatives.
• Can do learning (remember what were good choices)