Indexes%20on%20Sequential%20Files

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Indexes on Sequential Files
Source our textbook, slides by
Hector Garcia-Molina
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How to Represent a Relation

• Suppose we scatter its records arbitrarily among
  the blocks of the disk
• How to answer SELECT FROM R?
• Scan every block
• ridiculously slow
• would require lots of overhead info in each block
  and each record header

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How to Represent a Relation

• Reserve some blocks for the relation
• No need to scan entire disk
• How to answer SELECT FROM R WHERE cond ?
• Scan all the records in the reserved blocks
• Still ridiculously slow

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Indexes

• Use indexes -- special data structures -- that
  allow us to find all the records that satisfy a
  condition "efficiently"
• Possible data structures
• simple indexes on sorted files
• secondary indexes on unsorted files
• B-trees
• hash tables

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Sorted Files

• Sorted file records (tuples) of the file
  (relation) are in sorted order of the field
  (attribute) of interest.
• This field might or might not be a key of the
  relation.
• This field is called the search key.
• A sorted file is also called a sequential file.

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Index on Sequential File

• An index is another file containing key-pointer
  pairs of the form (K,a)
• K is a search key
• a is an address (pointer)
• The record at address a has search key K
• Particularly useful when the search key is the
  primary key of the relation

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Dense Indexes

• An index with one entry for every key in the data
  file
• What's the point?
• Index is much smaller than data file when record
  contains much more than just the search key
• If index is small enough to fit in main memory,
  record with a certain search key can be found
  quickly binary search in memory, followed by
  only one disk I/O

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Example of a Dense Index
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Some Numbers

• relation with 1,000,000 tuples
• block size is 4096 bytes
• 10 records per block
• thus 100,000 blocks, gt 400 Mbytes
• key field is 30 bytes
• pointer is 8 bytes
• thus at least 100 key-pointer pairs per block
• thus dense index size is 10,000 blocks, about 40
  Mbytes
• since log(10,000) 13, takes at most 14 disk
  I/O's for a search

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Sparse Index

• Uses less space than a dense index
• Requires more time to find a record with a given
  key
• In a sparse index, there is just one
  (key,pointer) pair per data block.
• The key is for the first record in the block.

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Sparse Index Example
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Using a Sparse Index

• To find the record with key K, search the index
  for the largest key K
• Use binary search to do this
• Retrieve the indicated data block
• Search the block for the record with key K

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Comparing Sparse and Dense Indexes

• Sparse index uses much less space
• In the previous numeric example, sparse index
  size is now only 1000 index blocks, about 4
  Mbytes
• Dense index, unlike sparse, lets us answer "is
  there a record with key K?" without having to
  retrieve a data block

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Multiple Levels of Index

• Make an index for the index
• Can continue this idea for more levels, but
  usually only two levels in practice
• Second and higher level indexes must be sparse,
  otherwise no savings

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Two-Level Index Example
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Numeric Example Again

• Suppose we put a second-level index on the
  first-level sparse index
• Since first-level index uses 1000 blocks and 100
  key-pointer pairs fit per block, we need 10
  blocks for second-level index
• Very likely to keep the second-level index in
  memory
• Thus search requires at most two disk I/O's (one
  for block of first-level index, one for data
  block)

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Duplicate Search Keys

• What if more than one record has a given search
  key value? (Then the search key is not a key of
  the relation.)
• Solution 1 Use a dense index and allow
  duplicate search keys in it.
• To find all data records with search key K,
  follow all the pointers in the index with search
  key K

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Solution 1 Example
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Duplicate Search Keys with Dense Index

• Solution 2 only keep record in index for first
  data record with each search key value (saves
  some space in the index)
• To find all data records with search key K,
  follow the one pointer in the index and then move
  forward in the data file

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Solution 2 Example
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Duplicate Search Keys with Sparse Index

• Recall that index has an entry for just the first
  data record in each block
• To find all data records with key K
• find last entry (E1) in index with key K
• move toward front of index until reaching entry
  (E2) with key lt K
• Check data blocks pointed to by entries from E2
  to E1 for records with search key K

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Dupl. Keys w/ Sparse Index
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Variation on Previous Scheme

• Index entry for a data block holds smallest
  search key that is new (did not appear in a
  previous block)
• If there is no new search key in that block, then
  index entry holds the lone search key in the
  block
• To find all data record with key K
• search index for first entry whose key is either
  K, or lt K but next key is gt K
• if a record with key K is in that block then scan
  forward from there

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Variation Example
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Inserting and Deleting Data

• Recall three main techniques
• create/delete overflow blocks
• overflow blocks do not have entries in a sparse
  index
• may be able to insert new blocks in sequential
  order
• new block needs an entry in a sparse index
• changing an index can create same problems
• make room in a full block by sliding some data to
  an adjacent block combine adjacent blocks if
  they get too empty

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General Strategy

• When data file changes, index must adapt
• Details depend on whether index is sparse or
  dense and how data file modifications are
  implemented
• Index file is itself sequential, so same
  strategies as for modifying data files can be
  applied to index files

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Effects of Actions on Index
Action Dense Index Sparse Index
Create empty overflow block none none
Delete empty overflow block none none
Create empty (main) block none insert
Delete empty (main) block none delete
Insert record insert maybe update
Delete record delete maybe update
Slide record update maybe update
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Explanations for Actions

• create/destroy empty overflow block has no effect
  on
• dense index since it refers to records
• sparse index since it refers to main records
• create/destroy empty main block
• no effect on dense index as above
• insert/delete entry in sparse index
• insert/delete/slide record
• insert/delete/update entry in dense index
• only change sparse index if affects first record
  in block

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Deletion from sparse index
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Deletion from sparse index

• delete record 40

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Deletion from sparse index

• delete record 30

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Deletion from sparse index

• delete records 30 40

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Deletion from dense index
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Deletion from dense index

• delete record 30

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Insertion, sparse index case

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Insertion, sparse index case

• insert record 34

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Insertion, sparse index case

• insert record 15

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• Illustrated Immediate reorganization
• Variation
• insert new block (chained file)
• update index

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Insertion, sparse index case

• insert record 25

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Insertion, dense index case

• Similar
• Often more expensive . . .