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Indexing: Part III
CPS 216
Advanced Database Systems
2
Announcements (February 15)
Homework #1 graded
Verify your grades on Blackboard
Homework #2 assigned today
Due in 2½ weeks
Reading assignments for this and next week
“The” query processing survey by Graefe
Due next Wednesday
Midterm and course project proposal in 3½ weeks
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Static hashing
What if a bucket is full?
key bucket number
hash function h
bucket 0
bucket 1
bucket i
bucket N -
ki 1 ki 2 ki 3 …
bucket i
h ( k ) = i
With records or record pointers
bucket i overflow
bucket i overflow
Does it make sense to use a hash-based index as a sparse index on a sorted table?
Performance of static hashing
Depends on the quality of the hash function!
Best (hopefully average) case: one I/O!
Worst case: all keys hashed into one bucket!
See Knuth vol. 3 for good hash functions
Rule of thumb: keep utilization at 50%-80%
How do we cope with growth?
Extensible hashing
Linear hashing
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Extensible hashing ( TODS 1979)
Idea 1: use i bits of output by hash function and
dynamically increase i as needed
Problem: ++ i = double the number of buckets!
Idea 2: use a directory
Just double the directory size
Many directory entries can point to the same bucket
Only split overflowed buckets
“One more level of indirection solves everything!”
i
h ( k ) 0 1 1 0 1 0 1 1
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Extensible hashing example (slide 1)
Insert k with h ( k ) = 0101
Bucket too full?
++local depth, split bucket, and ++global
depth (double the directory size) if necessary
Allowing some overflow is fine too
Directory Buckets
Local depth
Global depth (always the max of local depths)
Summary of extensible hashing
Pros
Handles growing files
No full reorganization
Cons
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Linear hashing ( VLDB 1980)
Grow only when utilization exceeds a given
threshold
No extra indirection
Some extra math to figure out the right bucket
Insert 0101 Threshold exceeded; grow! 0000 1010
i = 1 Number of bits in use = d log 2 n e n = 2 Number of primary buckets
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Linear hashing example (slide 2)
Grows linearly (hence the name)
Always split the ( n – 2blog^2 n c)-th bucket (0-based index)
Intuitively, the first bucket with the lowest depth Not necessarily the bucket being inserted into!
Insert 0001
Insert 1100
Threshold exceeded; grow! 0000 1111 0101
i = 2 n = 3
Linear hashing example (slide 3)
i = 2 n = 4
Insert 1110 Threshold exceeded; grow!
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Linear hashing example (slide 4)
Look up 1110
Bucket 110 (6-th bucket) is not here
Then look in the (6 – 2blog^2 n c)-th bucket (= 2nd)
i = 3 n = 5
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Summary of linear hashing
Pros
Handles growing files No full reorganization
Cons
