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hash introduction
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CS143: Hash Index
2
What is a Hash Table?
• Hash Table– Hash function
• h(k): key ‡ integer [0…n]• e.g., h(‘Susan’) = 7
– Array for keys: T[0…n]– Given a key k, store it in
T[h(k)]
5
Susan4
James3
2
Neil1
0
h(Susan) = 4h(James) = 3h(Neil) = 1
3
Why Hash Table?
• Direct access• Saved space
– Do not reserve a space forevery possible key
• How can we use this idea fora record search in a DBMS?
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Hashing for DBMS(Static Hashing)
(key, record)
.
..
Disk blocks (buckets)
search key Æ h(key)
0
1
2
3
4
5
Issues?
• What hash function?• Overflow?• How to store records?
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Record storage
1. Whole record
2. Key and pointer
.
..
record
.
.
.
recordkey 1
h(key)
h(key)
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Overflow and Chaining
• Inserth(a) = 1h(b) = 2h(c) = 1h(d) = 0h(e) = 1
• Deleteh(b) = 2h(c) = 1
0
1
2
3
Do we keep keys sorted inside a block?
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Questions
• Q: Do we keep keys sortedinside a block?
• Q: How much space shouldwe use for “good”performance?
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What Hash Function?
• Example– Key = ‘x1 x2 … xn’ n byte
character string– Have b buckets– h: (x1 + x2 + ….. xn) mod b
• Desired property– Uniformity: same # of keys for
every bucket• Reference
– “The Art of ComputerProgramming Vol. 3” by Knuth
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Major Problem ofStatic Hashing
• How to cope with growth?– Data tends to grow in size– Overflow blocks unavoidable
102030
405060
708090
39313536
323834
33
overflow blockshash buckets
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Idea 1
• Periodic reorganization
– New hash function– Complete reassignment of records– Very expensive
102030
4050…
33
102030
405060
708090
33
405060
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Idea 2
• Why don’t we split a bucketwhen it overflows?
0 a
3 b
2 d
1 c
e
Insert: h(g) = 1
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(a) Use i of b bits output byhash function
Extendible Hashing(two ideas)
00110101h(K) Æ
b
use i Æ grows over time
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(b) Use directory thatmaintains pointers to hashbuckets (indirection)
Extendible Hashing(two ideas)
..
.
.
..
c
e
hash bucketdirectory
h(c)
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Example• h(k) is 4 bits; 2 keys/bucket
Insert 0111, 1010
1
1
1
0001
1001
1100
0
1
i =
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Example continued
Insert 0000
1
0001
2
1001
1010
2
1100
00
01
10
11
2i =
0111
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Example continued
Insert 1011
00
01
10
11
2i =
21001
1010
21100
20111
20000
0001
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Questions onExtendible Hashing
• Q: What will happen if wehave a lot of duplicate searchkeys?
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Duplicate keys
• Insert 0001
1
1
1
0001
0
1
i =0001
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Questions onExtendible Hashing
• Can we provide minimumspace guarantee?
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Space Waste
2
1
40001
40000
0000
4i =
3
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Extendible Hashing:Deletion
• Two optionsa) No merging of bucketsb) Merge buckets and shrink
directory if possible
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Bucket Merge Example
Can we merge a and b? b and c?
Can we shrink the directory?
1
0001
2
1001
2
1100
00
01
10
11
2i =a
b
c
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Bucket MergeCondition
• Bucket merge condition– Bucket i’s are the same– First (i-1) bits of the hash key
are the same
• Directory shrink condition– All bucket i’s are smaller than
the directory i
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Summary ofExtendible Hashing
• Can handle growing files– No periodic reorganizations
• Indirection– Up to 2 disk accesses to
access a key
• Directory doubles in size– Not too bad if the data is not
too large
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Hashing vs. Tree
• Can an extendible-hash indexsupport?
SELECTFROM RWHERE R.A > 5
• Which one is better, B+treeor Extendible hashing?
SELECTFROM RWHERE R.A = 5
