CPSC-608 Database Systems Fall 2008 Instructor: Jianer Chen Office: HRBB 309B Phone: Notes #9

Linear hashing Another dynamic hashing scheme Two ideas: (a) Use i low order bits of hash grows b i (b) File grows linearly 2

Example b=4 bits, i =2, 2 keys/bucket m = 01 (max used block) Future growth buckets 3

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

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 ] Rule 5

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 6

Example b=4 bits, i =2, 2 keys/bucket m = 01 (max used block) Future growth buckets 0101 can have overflow chains! insert 0101 If h(k)[i ]  m, then look at bucket h(k)[i ] else, look at bucket h(k)[i ] - 2 i -1 Rule 7

Note In textbook, n is used instead of m n=m m = 01 (max used block) Future growth buckets n=10 8

Example b=4 bits, i =2, 2 keys/bucket m = 01 (max used block) Future growth buckets 10 9

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

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

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

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

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

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

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

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

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

If U > threshold then increase m (and maybe i )  When do we expand file? Keep track of: # used slots total # of slots = U 19

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 - 20

Example: BAD CASE Very full Very emptyNeed to move m here… Would waste space… 21

Hashing - How it works - Dynamic hashing - Extensible - Linear Summary 22

Next: Indexing vs. hashing Index definition in SQL Multiple key access 23

Hashing good for probes given key e.g., SELECT … FROM R WHERE R.A = 5 Indexing vs. Hashing 24

INDEXING (including B-trees) good for range searches : e.g., SELECT FROM R WHERE R.A > 5 Indexing vs. Hashing 25

Index definition in SQL Create index name on rel (attr) Create unique index name on rel (attr) defines candidate key Drop INDEX name 26

CANNOT SPECIFY TYPE OF INDEX (e.g. B-tree, hashing, …) OR PARAMETERS (e.g. load factor, size of hash, …) … at least not in SQL … Note 27

ATTRIBUTE LIST  MULTIKEY INDEX (next) e.g., CREATE INDEX foo ON R(A,B,C) Note 28

Motivation: Find records where DEPT = “Toy” AND SAL > 50k Multi-key Index 29

Strategy I: Use one index, say Dept. Get all Dept = “Toy” records and check their salary I1I1 30

Use 2 indexes; manipulate pointers ToySal > 50k Strategy II: 31

Multiple key index One idea: Strategy III: I1I1 I 21 I 22 32

Example Record Dept Index Salary Index Name=Joe DEPT=Sales SAL=15k Art Sales Toy 10k 15k 17k 21k 12k 15k 19k 33

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 34

Interesting application: Geographic data DATA: x y... 35

Queries: What city is at ? What is within 5 miles from ? Which is closest point to ? 36

h n b i a c o d Example e g f m l k j 37

h n b i a c o d Example e g f m l k j

h n b i a c o d Example e g f m l k j

h n b i a c o d Example e g f m l k j

h n b i a c o d Example e g f m l k j h i a b c d e f g n o m l j k 41

h n b i a c o d Example e g f m l k j h i a b c d e f g n o m l j k Search points near f Search points near b 42

Queries Find points with Y i > 20 Find points with X i < 5 Find points “close” to i = Find points “close” to b = 43

Many types of geographic index structures have been suggested –Quad trees –R trees 44

Two more types of multi key indexes Grid Partitioned hash 45

Grid Index Key 2 X 1 X 2 …… X n V 1 V 2 Key 1 V n To records with key 1 =V 3, key 2 =X 2 46

CLAIM Can quickly find records with –key 1 = V i  Key 2 = X j –key 1 = V i –key 2 = X j And also ranges… –E.g., key 1  V i  key 2 < X j 47

 But there is a catch with grid indexes! 48

 But there is a catch with grid indexes! How is grid index stored on disk? Like Arra y... X1X2X3X4X1X2X3X4X1X2X3X4 V1V2V3V1V2V3 49

 But there is a catch with grid indexes! How is grid index stored on disk? Like Arra y... X1X2X3X4 X1X2X3X4X1X2X3X4 V1V2V3V1V2V3 Problem: Need regularity so we can compute position of entry 50

Solution: Use Indirection Buckets V 1 V 2 V 3 * Grid only V 4 contains pointers to buckets Buckets -- X1 X2 X3 51

With indirection: Grid can be regular without wasting space We do have price of indirection 52

Can also index grid on value ranges SalaryGrid Linear Scale 123 ToySalesPersonnel 0-20K1 20K-50K2 50K

Grid files Good for multiple-key search Space, management overhead (nothing is free) Need partitioning ranges that evenly split keys

Idea: Key 1 Key 2 Partitioned hash function h1h

h1(toy)=0000 h1(sales)=1001 h1(art)= h2(10k)=01100 h2(20k)=11101 h2(30k)=01110 h2(40k)=00111., EX: Insert 56

h1(toy)=0000 h1(sales)=1001 h1(art)= h2(10k)=01100 h2(20k)=11101 h2(30k)=01110 h2(40k)=00111., EX: Insert 57

h1(toy)=0000 h1(sales)=1001 h1(art)= h2(10k)=01100 h2(20k)=11101 h2(30k)=01110 h2(40k)= Find Emp. with Dept. = Sales  Sal=40k 58

h1(toy)=0000 h1(sales)=1001 h1(art)= h2(10k)=01100 h2(20k)=11101 h2(30k)=01110 h2(40k)= Find Emp. with Sal=30k look here! 59

h1(toy)=0000 h1(sales)=1001 h1(art)= h2(10k)=01100 h2(20k)=11101 h2(30k)=01110 h2(40k)= Find Emp. with Dept. = Sales look here! 60

Hashing discussion: - Indexing vs. hashing - SQL index definition - Multiple key access - Multi-key index Variations: grid, geo data - Partitioned hash Summary 61