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CS 245Notes 51 CS 245: Database System Principles Hector Garcia-Molina Notes 5: Hashing and More

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CS 245Notes 52 key h(key) Hashing Buckets (typically 1 disk block)

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CS 245Notes Two alternatives records (1) key h(key)

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CS 245Notes 54 (2) key h(key) Index record key 1 Two alternatives Alt (2) for “secondary” search key

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CS 245Notes 55 Example hash function Key = ‘x 1 x 2 … x n ’ n byte character string Have b buckets h: add x 1 + x 2 + ….. x n – compute sum modulo b

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CS 245Notes 56 This may not be best function … Read Knuth Vol. 3 if you really need to select a good function. Good hash Expected number of function:keys/bucket is the same for all buckets

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CS 245Notes 57 Within a bucket: Do we keep keys sorted? Yes, if CPU time critical & Inserts/Deletes not too frequent

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CS 245Notes 58 Next: example to illustrate inserts, overflows, deletes h(K)

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CS 245Notes 59 EXAMPLE 2 records/bucket INSERT: h(a) = 1 h(b) = 2 h(c) = 1 h(d) =

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CS 245Notes 510 EXAMPLE 2 records/bucket INSERT: h(a) = 1 h(b) = 2 h(c) = 1 h(d) = d a c b h(e) = 1

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CS 245Notes 511 EXAMPLE 2 records/bucket INSERT: h(a) = 1 h(b) = 2 h(c) = 1 h(d) = d a c b h(e) = 1 e

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CS 245Notes a b c e d EXAMPLE: deletion Delete: e f f g

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CS 245Notes a b c e d EXAMPLE: deletion Delete: e f f g maybe move “g” up c

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CS 245Notes a b c e d EXAMPLE: deletion Delete: e f f g maybe move “g” up c d

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CS 245Notes 515 Rule of thumb: Try to keep space utilization between 50% and 80% Utilization = # keys used total # keys that fit

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CS 245Notes 516 Rule of thumb: Try to keep space utilization between 50% and 80% Utilization = # keys used total # keys that fit If < 50%, wasting space If > 80%, overflows significant depends on how good hash function is & on # keys/bucket

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CS 245Notes 517 How do we cope with growth? Overflows and reorganizations Dynamic hashing

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CS 245Notes 518 How do we cope with growth? Overflows and reorganizations Dynamic hashing Extensible Linear

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CS 245Notes 519 Extensible hashing: two ideas (a) Use i of b bits output by hash function b h(K) use i grows over time…

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CS 245Notes 520 (b) Use directory h(K)[i ] to bucket

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CS 245Notes 521 Example: h(k) is 4 bits; 2 keys/bucket i = Insert 1010

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CS 245Notes 522 Example: h(k) is 4 bits; 2 keys/bucket i = Insert

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CS 245Notes 523 Example: h(k) is 4 bits; 2 keys/bucket i = Insert New directory i = 2 2

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CS 245Notes Insert: i = Example continued

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CS 245Notes Insert: i = Example continued

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CS 245Notes Insert: i = Example continued

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CS 245Notes i = Insert: 1001 Example continued

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CS 245Notes i = Insert: 1001 Example continued

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CS 245Notes i = Insert: 1001 Example continued i = 3 3

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CS 245Notes 530 Extensible hashing: deletion No merging of blocks Merge blocks and cut directory if possible (Reverse insert procedure)

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CS 245Notes 531 Deletion example: Run thru insert example in reverse!

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CS 245Notes 532 Note: Still need overflow chains Example: many records with duplicate keys insert if we split:

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CS 245Notes 533 Solution: overflow chains insert 1100 add overflow block: 1101

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CS 245Notes 534 Extensible hashing Can handle growing files - with less wasted space - with no full reorganizations Summary + Indirection (Not bad if directory in memory) Directory doubles in size (Now it fits, now it does not) - -

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CS 245Notes 535 Linear hashing Another dynamic hashing scheme Two ideas: (a) Use i low order bits of hash grows b i (b) File grows linearly

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CS 245Notes 536 Example b=4 bits, i =2, 2 keys/bucket m = 01 (max used block) Future growth buckets

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CS 245Notes 537 Example b=4 bits, i =2, 2 keys/bucket m = 01 (max used block) Future growth buckets If h(k)[i ] m, then look at bucket h(k)[i ] else, look at bucket h(k)[i ] - 2 i -1 Rule

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CS 245Notes 538 Example b=4 bits, i =2, 2 keys/bucket m = 01 (max used block) Future growth buckets If h(k)[i ] m, then look at bucket h(k)[i ] else, look at bucket h(k)[i ] - 2 i -1 Rule insert 0101

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CS 245Notes 539 Example b=4 bits, i =2, 2 keys/bucket m = 01 (max used block) Future growth buckets If h(k)[i ] m, then look at bucket h(k)[i ] else, look at bucket h(k)[i ] - 2 i -1 Rule 0101 can have overflow chains! insert 0101

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CS 245Notes 540 Note In textbook, n is used instead of m n=m m = 01 (max used block) Future growth buckets n=10

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CS 245Notes 541 Example b=4 bits, i =2, 2 keys/bucket m = 01 (max used block) Future growth buckets insert 0101

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CS 245Notes 542 Example b=4 bits, i =2, 2 keys/bucket m = 01 (max used block) Future growth buckets insert

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CS 245Notes 543 Example b=4 bits, i =2, 2 keys/bucket m = 01 (max used block) Future growth buckets insert

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CS 245Notes 544 Example Continued: How to grow beyond this? m = 11 (max used block) i = 2...

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CS 245Notes 545 Example Continued: How to grow beyond this? m = 11 (max used block) i =

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CS 245Notes 546 Example Continued: How to grow beyond this? m = 11 (max used block) i =

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CS 245Notes 547 Example Continued: How to grow beyond this? m = 11 (max used block) i =

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CS 245Notes 548 If U > threshold then increase m (and maybe i ) When do we expand file? Keep track of: # used slots total # of slots = U

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CS 245Notes 549 Linear Hashing Can handle growing files - with less wasted space - with no full reorganizations No indirection like extensible hashing Summary + + Can still have overflow chains -

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CS 245Notes 550 Example: BAD CASE Very full Very emptyNeed to move m here… Would waste space...

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CS 245Notes 551 Hashing - How it works - Dynamic hashing - Extensible - Linear Summary

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CS 245Notes 552 Next: Indexing vs Hashing Index definition in SQL Multiple key access

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CS 245Notes 553 Hashing good for probes given key e.g., SELECT … FROM R WHERE R.A = 5 Indexing vs Hashing

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CS 245Notes 554 INDEXING (Including B Trees) good for Range Searches: e.g., SELECT FROM R WHERE R.A > 5 Indexing vs Hashing

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CS 245Notes 555 Index definition in SQL Create index name on rel (attr) Create unique index name on rel (attr) defines candidate key Drop INDEX name

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CS 245Notes 556 CANNOT SPECIFY TYPE OF INDEX (e.g. B-tree, Hashing, …) OR PARAMETERS (e.g. Load Factor, Size of Hash,...)... at least in SQL... Note

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CS 245Notes 557 ATTRIBUTE LIST MULTIKEY INDEX (next) e.g., CREATE INDEX foo ON R(A,B,C) Note

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CS 245Notes 558 Motivation: Find records where DEPT = “Toy” AND SAL > 50k Multi-key Index

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CS 245Notes 559 Strategy I: Use one index, say Dept. Get all Dept = “Toy” records and check their salary I1I1

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CS 245Notes 560 Use 2 Indexes; Manipulate Pointers ToySal > 50k Strategy II:

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CS 245Notes 561 Multiple Key Index One idea: Strategy III: I1I1 I2I2 I3I3

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CS 245Notes 562 Example Record Dept Index Salary Index Name=Joe DEPT=Sales SAL=15k Art Sales Toy 10k 15k 17k 21k 12k 15k 19k

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CS 245Notes 563 For which queries is this index good? Find RECs Dept = “Sales” SAL=20k Find RECs Dept = “Sales” SAL > 20k Find RECs Dept = “Sales” Find RECs SAL = 20k

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