1. Indexing
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2. Index Concept
Main idea: A separate data structure used to locate records
Many, many, many, many flavors of index organization have been proposed and tried
including structures which combine hashing and indexing
Various buffering schemes are somewhat orthogonal
We’ll focus on
General concepts [chapter ]
ISAM (indexed sequential) [ch. 5.1]
B-trees and B+ trees [ch ]
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3. Index Terminology
Most generally, index is a list of value/address pairs
Each pair is an index “entry”
Value is the index “key”
Address will point to a data record, or to a data page
There might be many records on a page
The assumption is that the value/address pair will be much smaller in size than the full record
If index is small, a copy can be maintained in memory!
Permanent disk copy is still needed
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4. Key Terminology Index key field Primary index Secondary index
Not necessarily the same as the primary DB key of the table!
But called a “key” anyway
Primary index
Key is the primary (DB) key
Only one index per file
Secondary index
Key is not the primary DB key
Could be many indices per file (or none)
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5. More Indexing Terminology
Dense index
One index entry for each record (or page)
Non-dense or sparse index
Less than one index entry for each record
Inverted file:
File which has a dense secondary index
Clustering index
Preserves locality: close index entries refer to close data records
Multilevel indexing
each level is an index to the next level down
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6. Indexing Pitfalls Index itself is a file
Occupies disk space
Must worry about maintenance, consistency, recovery, etc.
Large indices won't fit in memory
May require multiple seeks to locate record entry
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7. Desiderata for Multilevel Indexes
Should support efficient random access
Should also support efficient sequential access, if possible
Should have low height
Should be efficiently updatable
Should be storage-efficient
Top level(s) should fit in memory
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8. ISAM = Indexed Sequential Access Method
IBM terminology
“Indexed Sequential” more general term (non-IBM)
ISAM as described in textbook (5.1) is very close to B+ tree
simpler versions exist
Main idea: maintain sequential file but give it an index
Sequentiality for efficient “batch” processing
Index for random record access
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9. ISAM Technique Build a dense index of the pages (1st level index)
Sparse from a record viewpoint
Then build an index of the 1st level index (2nd level index)
Continue recursively until top level index fits on 1 page
Some implementations may stop after a fixed # of levels
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10. Updating an ISAM File Data set must be kept sequential
So that it can be processed without the index
May have to rewrite entire file to add records
Could use overflow pages
chained together or in fixed locations (overflow area)
Index is usually NOT updated as records are added!
Once in a while the whole thing is “reorganized”
Data pages recopied to eliminate overflows
Index recreated
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11. ISAM Pros, Cons Pro Cons Relatively simple
Great for true sequential access
Cons
Not very dynamic
Inefficient if lots of overflow pages
Can only be one ISAM index per file
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12. B-Tree B-Tree is a type of multilevel index
from another standpoint: it's a type of balanced tree
Invented in 1972 by Boeing engineers R. Bayer and E. McCreight
By 1979: "the standard organization for indexes in a database system" (Comer)
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13. B-Tree Overview Assume for now that keys are fixed-length and unique
A B-tree can be thought of as a generalized binary search tree
multiple branches rather than just L or R
Trees are always perfectly balanced
Some wasted space in the nodes is tolerated
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14. B-Tree Concepts Each node contains
tree (index node) pointers, and
key values (with record or page pointers)
Given a key K and the two node pointers L and R around it
All key values pointed to by L are < K
All key values pointed to by R are > K
“Order p” means (up to) p tree pointers, (up to) p-1 keys
Terminology differs between authors
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15. B+ Tree vs. B-tree Textbook only discusses B+ trees
So do we from now on
Two big differences:
Original B-trees had record pointers in all of the index nodes; B+ trees only in leaf nodes
Given a key K and the two node pointers L and R around it
All key values pointed to by L are < K
All key values pointed to by R are >= K
B+ tree data pages are linked together to form a sequential file
Gives the advantages of ISAM
In our book, it’s a doubly-linked list
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16. Alternate Views of the Leaf Nodes
[cf. Chapter 4.3.1]
Leaf nodes might be actual data pages
Leaf nodes might contain pointers to the actual data records or pages
For B+ trees, this implies the leaf node format is different from the non-leaf node format
may hold different number of entries
The leaf nodes can be chained together, regardless of whether the actual data pages are!
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17. B+Tree Growth and Change
The big idea: When a node is full, it splits.
middle value is propagated upward
If we’re lucky, there’s room for it in the level above
two new nodes are at same level as original node
Height of tree increases only when the root splits
A very nice property
This is what keeps the tree perfectly balanced
Recommended: split only “on the way down”
On deletion: two adjacent nodes recombine if both are < half full
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18. Variations Could redistribute records between adjacent blocks
esp. on deletion (B* tree)
Variable order: accommodate varying key lengths Could store the whole record in the index block
especially if records are few and small
in a B+ tree, this would make sequential access especially efficient
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19. B+ Trees with Other Indices
Suppose you have a B+ tree for the file
Leaf nodes of the index are the actual pages of the file, doubly linked together for sequential access
Suppose you have some secondary indices
What happens when a B+ tree node splits or merges???
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20. Other Forms of Indexing
Bitmap indexes
One index per value (property) of interest
One bit per record
TRUE if record has a particular property
Indexed hash: hash function takes you to an entry in an index
allows physical record locations to change
Clever indexing schemes are useful in optimizing complex queries
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