Download B Tree Index Files by Huy Nguyen

Indexing and Hashing
(emphasis on B+ trees)
By Huy Nguyen
Cs157b
0900-1015 TR
Lee, Sin-Min
Storage
• We have been studying database languages
and queries and have yet to study how data is
stored.
• We will look at how data is accessed and the
different Index methods used.
• Different types index methods have good and
bad qualities which I will try to address.
Indices
• Indices is used to look up, input and delete
data in a ordered manner.
• Speed and efficiency is a main goal in the
different types of Indexing.
• Speed and efficiency includes access
type, access time, insertion time, deletion
time, and space overhead.
Definitions
• Pointer- identifies the disk block and offset
in the disk block.
• Index record- holds search key value and
pointers to the records with the value.
• Clustering index- an index whose search
key also defines the sequential order of
the file.
Index-Sequential File Organization
• Index-Sequential files are files (which holds
information for data) ordered sequentially on a
search key.
• Main disadvantage is that performance
degrades as file size grows for lookups and
sequential scans.
• Degradation can be fixed with reorganization of
the file. Reorganization require lot of overhead
space so frequent reorganization is undesirable.
B+ Tree Index Files
• Index-Sequential file organization is used
but not as much as B+ index structure.
• B+ Tree indexing maintain efficiency
despite insertion and deletion of data.
• They use idea of a balance tree in which
every path from the root of the tree to a
leaf is of the same length.
B+ Tree Index Files(cont’d)
• In a B+ Tree data structures, each node
corresponds to a disk block.
• Each node is kept between half-full and
completely full.
• A node in a B+- tree has n-1 search key
values K1, K2….Kn-1 and n pointers P1,
P2…Pn.
B+ Tree Index Files(cont’d)
• Search-key values are kept in sorted
order.
• Leaf nodes store the records instead of
pointers to records.
• Search-key values are kept in sorted order
B+ Tree Index Files(cont’d)
• Pointer P points to a file record with a
search key value of a K.
• Each leaf holds up to n-1 values .
• A non-leaf node can hold up to n pointers
and must hold n/2 ceiling pointers.
B+ Tree Index Files(cont’d)
• Number of pointers in a node is called fan
out of a node.
• The root must hold at least 2 pointers but
can have less than n/2.
Example of B+-Tree of Order 4
(with L = 5)
41
22
12
15
20
22
24
27
28
29
30
35
45
49
30 35 41 45
32 37 43 46
34 38 44 48
39
49
51
53
54
55
75
60
55
57
58
59
67
60 67
62 72
64 74
65
66
87
91 100
75 87 91 100
77 88 94 110
80 90 97 112
83
99 114
85
120
Search in a B+ Tree
• Search: Start at root; use key comparisons
to go to leaf.
Inserting a Data Entry into a B+
Tree
1) Find correct leaf node
2) Add index entry to the node
3) If enough space, done!
4) Else, split the node
Redistribute entries evenly between the current
node and the new node
5) Insert <middle key, ptr to new node> to the
parent
6) Go to Step 3
After
After
Deleting a Data Entry from a B+
Tree
1) Find correct leaf node
2) Remove the entry from the node
3) If the node is at least half full, done!
4) Else, possibly borrow some entries from a
sibling
5) If not possible, merge the node with the sibling
6) Delete the separator between the node and the
sibling from the parent node
7) Go to Step 3
After
Binary Trees VS. BTrees
• Binary tree only have 2 children max.
• For large files binary tree will be too high
because of the limit of children and not enough
keys per records.
• Btrees disk size can have many children
depending on the disk block.
• Btrees are more realistic for indexing files
because they easily maintain balance and can
store many keys in only a few records.
B+ VS. B- Trees
• B+ trees store redundant search key values
because index is smaller.
• In a B+ tree, all pointers to data records exists at
the leaf-level nodes.
• B-tree eliminates redundancy but require
additional pointers to do so.
• In a B-tree, pointers to data records exist at all
levels of the tree.
References
• http://www.cs.sjsu.edu/~lee/cs157b/cs157
b.html
• http://www.cs.ualberta.ca/~drafiei/291/note
s/6-tree-indexes.pdf
• A. Silberschatz, H.F. Korth, S. Sudershan:
Database System Concepts, 5th ed.,
McGraw-Hill, 2006