1. INDEXING (CHAPTER 11)
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2. TOPICS
Basic concepts
Hashing
B+-tree
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3. INTRODUCTION Review E-R data model Conceptual Logical
Relational data model
SQL
Physical
relation = a file
Org. of records on a disk page
Organization of attributes within a record
Index Files
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4. Software Architecture of a DBMS
Query Parser
Query Optimizer
Query Interpretor
Relational Algebra operators: , , , , , , , , 
Index structures
Abstraction of records
Buffer Pool Manager
File System
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5. Implementation of б бSalary=30,000(Employee) Emp table:
SS#
Name
Age
Salary
dno 1
Joe 24
20000 2
Mary 20
25000 3
Bob 22
27000 4
Kathy 30
30000 5
Shideh
4000
Emp table:
бSalary=30,000(Employee)
Process the select operator using a file scan (linear scan)
F1 = Open the file corresponding to Employee
P = read first page of F1
While P is not null
For each record in P, if the record satisfies the selection predicate then produce as output
P = read next page of F1 /* P becomes null when EoF is reached */
SS#
Name
Age
Salary
dno 4
Kathy 30
30000 5
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6. Implementation of б бSalary=30,000(Employee) Emp table:
SS#
Name
Age
Salary
dno 1
Joe 24
20000 2
Mary 20
25000 3
Bob 22
27000 4
Kathy 30
30000 5
Shideh
4000
Emp table:
бSalary=30,000(Employee)
Process the select operator using a file scan (linear scan)
F1 = Open the file corresponding to Employee
P = read first page of F1
While P is not null
For each record in P, if the record satisfies the selection predicate then produce as output
P = read next page of F1
SS#
Name
Age
Salary
dno 4
Kathy 30
30000 5
Fetch the page from
disk if not in the
buffer pool
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7. Implementation of б бSalary=30,000(Employee) Emp table:
SS#
Name
Age
Salary
dno 1
Joe 24
20000 2
Mary 20
25000 3
Bob 22
27000 4
Kathy 30
30000 5
Shideh
4000
Emp table:
бSalary=30,000(Employee)
Process the select operator using a file scan (linear scan)
F1 = Open the file corresponding to Employee
P = read first page of F1
While P is not null
For each record in P, if the record satisfies the selection predicate then produce as output
P = read next page of F1
SS#
Name
Age
Salary
dno 4
Kathy 30
30000 5
Header
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8. TERMINOLOGY
An exact match selection predicate: бSalary=30,000(Employee) , бFirstName=“Shideh”(Employee)
A range selection predicate: бSalary>30,000(Employee) , бSalary<30,000(Employee), бSalary>30,000 and Salary < 32,000 (Employee)
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9. Analogy: Catalog cards in the library (more than one index).
INTRODUCTION (Cont…)
Motivation: Speed-up those queries that reference only a small portion of the records in a file.
Analogy: Catalog cards in the library (more than one index).
Evaluation:
1. Access time (find)
2. Insertion time (find + add)
3. Deletion time (find + delete)
4. Space overhead
Search-key: The attribute (or set of attributes) used to lookup records in a file
Primary index: The index whose search key specifies the sequential order of the records within a file.
Secondary index: The index whose search key does not specify the sequential order of the records within a file.
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10. Indexing
Mapping of records to a finite space using a function (computation)
E.g.,
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11. K
F(K) 10
10-1=9 11
11-2=9 12
12-3=9 13
13-4=9 14
14-5=9 15
15-6=9 16
16-7=9 17
17-8=9 18
18-9=9 19
19-10=9 20
20-2=18 21
21-3=18 22
22-4=18 … 29
29-11=18 30
30-3=27 31
31-4=27 39
39-12=27 K
F(K) 40
40-4=36 .. 49
49-13=36 50
50-5=45 … 59
59-14=45 69
69-15=54 79
79-16=64 89
89-17=72 99
99-18=81
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12. KEY OBSERVATIONS
A deterministic function (analytical) to map a large set of key values, potentially infinite in size, to a set that is small and finite.
The deterministic function might be a randomizing function making it appropriate for processing exact-match selection predicate.
To process range selection predicates, the deterministic function should be order-preserving.
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13. Assume, size of disk page = 2 data records = 5 index records.
INTRODUCTION (Cont…)
Example:
Assume, size of disk page = 2 data records = 5 index records.
Indexing or not indexing?
SELECT age SELECT age
FROM personnel FROM personnel
WHERE name = “Alice” WHERE name = “Don”
Alaska
Arizona
California
Florida
Indiana
Ohio
Alaska Bob
Alaska George
Arizona David
California Hellen
California Jack
Florida Frank
Florida Charles 4
Indiana Joe
Ohio Alice
Ohio David
Alice
Bob
Charles
David
Frank
George
Hellen
Jack
Joe
State Name Age Other!
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14. Assume, size of disk page = 2 data records = 5 index records.
INTRODUCTION (Cont…)
Example:
Assume, size of disk page = 2 data records = 5 index records.
Primary vs. Secondary”
SELECT name SELECT age
FROM personnel FROM personnel
WHERE state = “Ohio” WHERE name = “David”
Alaska
Boston
California
Florida
Indiana
Ohio
Alaska Bob
Alaska George
Boston David
California Hellen
California Jack
Florida Frank
Florida Charles 4
Indiana Joe
Ohio Alice
Ohio David
Alice
Bob
Charles
David
Frank
George
Hellen
Jack
Joe
State Name Age Else!
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15. Example: (page = 2 data = 5 index)
INTRODUCTION (Cont…)
Example: (page = 2 data = 5 index)
Exact match vs. Range
SELECT name SELECT name
FROM personnel FROM personnel
WHERE state = “California” WHERE state >= “Alaska” and
state <= “Florida”
Speedup by employing binary search (is it possible?)
Alaska
Mass
California
Florida
Indiana
Ohio
Alaska Bob
Alaska George
Mass David
California Hellen
California Jack
Florida Frank
Florida Charles 4
Indiana Joe
Ohio Alice
Ohio David
Alice
Bob
Charles
David
Frank
George
Hellen
Jack
Joe
State Name Age Else!
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16. Dense Index Files
Dense index — Index record appears for every search-key value in the file.
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17. Example of Sparse Index Files
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18. Multilevel Index
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19. HASHING Hash function: K: the set of all search key values
V: the set of all bucket address
h(K): K V
K is large (perhaps infinite) but set of search-key values actually stored in the database is much smaller than K.
Fast lookup: To find Ki, search the bucket with h(Ki) address.
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20. HASHING (Cont…) Example:
K = salary (set of all 6 digit integers)
V = 1000 buckets addressed from 0 to 999
h(k) = k mod 1000.
SELECT name
FROM personnel
WHERE salary = “120,100”
To find a 120,100 salary, we should search bucket number 100.
Hash is only appropriate for Exact match queries.
A bad hash function maps the value to a subset of (or a few) buckets (e.g., h(k) = k mod 10.
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21. HASHING (Cont…) Clustered Hash Index Non-clustered Hash Index:
The index structure and its buckets are represented as a file (say file.hash)
The relation is stored in file.hash (I.e., each entry in file.hash corresponds to a record in relation)
Assuming no duplicates: the record can be accessed in 1 IO.
Non-clustered Hash Index:
The relation remains intact
Each entry in file.hash has the following format: (search-key value, RID)
Assuming no duplicates: the record can be accessed in 2 IO.
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22. HEAP FILE ORGANIZATION
Assume a student table: Student(name, age, gpa, major)
t(Student) = 16
P(Student) = 4
Bob, 21, 3.7, CS
Kane, 19, 3.8, ME
Louis, 32, 4, LS
Chris, 22, 3.9, CS
Mary, 24, 3, ECE
Lam, 22, 2.8, ME
Martha, 29, 3.8, CS
Chad, 28, 2.3, LS
Tom, 20, 3.2, EE
Chang, 18, 2.5, CS
James, 24, 3.1, ME
Leila, 20, 3.5, LS
Kathy, 18, 3.8, LS
Vera, 17, 3.9, EE
Pat, 19, 2.8, EE
Shideh, 16, 4, CS
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23. Non-Clustered Hash Index
A non-clustered hash index on the age attribute with 4 buckets,
h(age) = age % B
(24, (1, 2))
(20, (4,3))
(32, (3,1))
(16, (4,4))
(21, (1, 1))
(20, (1,3))
(24, (3,3))
(17, (2,4))
(28, (4,2))
(29, (3,2)) 1 2
(18, (1, 4)) 3
(22, (2,2))
(19, (2, 1))
(22, (4,1))
(19, (3, 4))
(18, (2,3))
Bob, 21, 3.7, CS
Kane, 19, 3.8, ME
Louis, 32, 4, LS
Chris, 22, 3.9, CS
Mary, 24, 3, ECE
Lam, 22, 2.8, ME
Martha, 29, 3.8, CS
Chad, 28, 2.3, LS
Tom, 20, 3.2, EE
Chang, 18, 2.5, CS
James, 24, 3.1, ME
Leila, 20, 3.5, LS
Kathy, 18, 3.8, LS
Vera, 17, 3.9, EE
Pat, 19, 2.8, EE
Shideh, 16, 4, CS
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24. Clustered Hash Index
A clustered hash index on the age attribute with 4 buckets,
h(age) = age % B
Mary, 24, 3, ECE
Shideh, 16, 4, CS
Louis, 32, 4, LS
Leila, 20, 3.5, LS
Bob, 21, 3.7, CS
Tom, 20, 3.2, EE
James, 24, 3.1, ME
Vera, 17, 3.9, EE
Chad, 28, 2.3, LS
Martha, 29, 3.8, CS 1 2
Kathy, 18, 3.8, LS 3
Lam, 22, 2.8, ME
Kane, 19, 3.8, ME
Chris, 22, 3.9, CS
Pat, 19, 2.8, EE
Chang, 18, 2.5, CS
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25. Non-Clustered Hash Index
A non-clustered hash index on the age attribute with 4 buckets,
h(age) = age % B
Pointers are page-ids
500
(24, (1, 2))
(20, (4,3))
1001
(32, (3,1))
(16, (4,4))
(21, (1, 1))
(20, (1,3))
(24, (3,3))
(17, (2,4))
(28, (4,2))
(29, (3,2))
500
706 1
1001 2
706
(18, (1, 4))
101 3
101
(22, (2,2))
(19, (2, 1))
(22, (4,1))
(19, (3, 4))
(18, (2,3))
Bob, 21, 3.7, CS
Kane, 19, 3.8, ME
Louis, 32, 4, LS
Chris, 22, 3.9, CS
Mary, 24, 3, ECE
Lam, 22, 2.8, ME
Martha, 29, 3.8, CS
Chad, 28, 2.3, LS
Tom, 20, 3.2, EE
Chang, 18, 2.5, CS
James, 24, 3.1, ME
Leila, 20, 3.5, LS
Kathy, 18, 3.8, LS
Vera, 17, 3.9, EE
Pat, 19, 2.8, EE
Shideh, 16, 4, CS
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26. Clustered Hash Index (SEQUENTIAL LAYOUT)
A clustered hash index on the age attribute with 4 buckets,
h(age) = age % 4
When the number of buckets are known in advance, the system may assume a sequentially laid file to eliminate the need for the hash directory.
Shideh, 16, 4, CS
Leila, 20, 3.5, LS
James, 24, 3.1, ME
Mary, 24, 3, ECE
Bob, 21, 3.7, CS
Kathy, 18, 3.8, LS
Kane, 19, 3.8, ME
Louis, 32, 4, LS
Vera, 17, 3.9, EE
Lam, 22, 2.8, ME
Pat, 19, 2.8, EE
Tom, 20, 3.2, EE
Martha, 29, 3.8, CS
Chris, 22, 3.9, CS
Chad, 28, 2.3, LS
Chang, 18, 2.5, CS
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27. Clustered Hash Index (SEQUENTIAL LAYOUT)
A clustered hash index on the age attribute with 4 buckets,
h(age) = age % 4
When the number of buckets are known in advance, the system may assume a sequentially laid file to eliminate the need for the hash directory.
Offset (bucket-id –1) times page size is for bucket-id
Shideh, 16, 4, CS
Leila, 20, 3.5, LS
James, 24, 3.1, ME
Offset 0 is for bucket 0
Offset Page Size is for bucket 1
Mary, 24, 3, ECE
Bob, 21, 3.7, CS
Kathy, 18, 3.8, LS
Kane, 19, 3.8, ME
Louis, 32, 4, LS
Vera, 17, 3.9, EE
Lam, 22, 2.8, ME
Pat, 19, 2.8, EE
Tom, 20, 3.2, EE
Martha, 29, 3.8, CS
Chris, 22, 3.9, CS
Chad, 28, 2.3, LS
Chang, 18, 2.5, CS
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28. Block
address
on disk
Bucket
Number 1 2
M-2
M-1
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29. Example of Non-Clustered Hash Index
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30. Overflow buckets Main buckets 340 981 460 1 181 2 321 551 761 91 22 72
340
981
Record pointer
460 1
Record pointer
181
Record pointer 2
Record pointer
321
551
Record pointer
761 91
Record pointer
Record pointer
Record pointer 22 72 9
522
Record pointer
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31. HASHING (Cont…) Loading factor Why a bucket might overflow?
B = # of buckets, S = # of records per bucket, R = # of records in the relation
loading - factor = R / (B×S)
The loading factor should not exceed 80%, if that happens, double B and re-hash.
Why a bucket might overflow?
Heavy loading of the file
Poor hash functions
Statistical peculiarities
If a bucket overflows?
Chaining: chain an empty bucket to the bucket that overflows.
Open addressing: If bucket h(k) is full, store the record in h(k) + 1, if that is also full, try h(k) + 2, and so on.
Two hash functions: If bucket h(k) is full, store the record in h’(k).
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32. HASHING (Cont…)
Problem: The file grows and shrinks over time. Hence, how one should choose the hash function:
1. Based on current file size performance degradation as DB grows
2. Based on anticipated file size waste space initially (and reduced buffer hits)
3. Periodical reorganization time consuming
3.1. Choose new hash function
3.2. Recompute hash value on every record
3.3. Generate new bucket assignments
Solution:
Dynamic hash functions: dynamic modification of h to accommodate growth and shrinkage of the DB. (e.g., extendible hashing)
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33. HASHING (Cont…)
Extendible hashing
Choose a hash function (h) such that it results in a b (b = 32) bit binary number.
The directory has a header that contains its depth, d.
Each directory entry points to a hash bucket.
Buckets are created on demand, as records are inserted.
Each bucket contains a local depth used to find data.
Directory depth 1
bucket 2
directory 00 01 10
siblings 11
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34. HASHING (Cont…) Extendible hashing (continued):
Every time a bucket overflows, its local depth is increased. If the local depth is greater than the depth of the directory, the directory’s depth is increased, causing the directory to double in size.
Each directory entry has one sibling or buddy. Two entries are buddies if they have identical bit patterns except for the dth bit.
Every time a bucket overflows, its local depth is increased.
If the local depth is greater than the depth of the directory, then the directory’s depth is increased, causing the directory to double in size.
A bucket can overflow at any desired loading factor. That is, a split might happen every time a bucket is 80% full.
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35. HASHING (Cont…) Retrieval with Extendible hashing: Retrieve (K0)
Calculate h’ = h(K0)
Read depth d of the directory
Interpret the d initial bits of h’ as an integer base 2, term this r.
Retrieve the bucket pointed to by the rth entry
Find the record in this bucket
5.1. If a hashing technique is used to organize the records in a bucket, use the d bits defined on that bucket
5.2. If necessary, follow the collision resolution scheme within this bucket.
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36. HASHING (Cont…) Insertion with Extendible hashing: Insert (K0)
Apply the first four steps of Retrieve (K0) to find bucket b.
If the insertion of K0 into b result in no overflow then Insert K0 into b and return
Otherwise, obtain a new bucket b’
Set the local depth of b’ and b to equal (local depth of b + 1)
If the new depth is NOT greater than the depth of the directory
5.1. Distinguish between b and b’ using their new d and set the appropriate entry(ies) of the directory to point to each
5.2. Rehash the entries in bucket b and assign each individual entry to the appropriate bucket b or b’
5.3. Insert (K0)
If the new depth is greater than the depth of the directory
6.1 Increase the depth of the directory, doubling its size
6.2. Set each entry and its buddy to point to the old bucket that it was pointing to
6.3. Rehash the entries in bucket b and assign each individual entry to the appropriate bucket b or b’
6.4. Insert (K0)
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37. HASHING (Cont…) Deletion with Extendible hashing: Delete (K0)
Apply the first four steps of Retrieve (K0) to find bucket b.
If K0 is not b then return with value no found
Otherwise, delete the entry corresponding to K0
If the sum of the number of entries on this page and its sibling page are below the size of a bucket then:
4.1. Copy the entries in the two buckets into one bucket b’
4.2. Depth of b’ = (depth of b - 1)
4.3. Free bucket b
4.4. Locate the two hash directory entries pointing to b and its buddy. Set these two pointers to b’
4.5. If every pointer in the directory equals its sibling pointer then decrease the depth of the directory by one and set each entry in an obvious manner.
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38. Use of Extendable Hash Structure: Example
Initial Hash structure, bucket size = 2
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39. Example (Cont.)
Hash structure after insertion of one Brighton and two Downtown records 1
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40. Hash structure after insertion of Mianus record
Example (Cont.)
Hash structure after insertion of Mianus record 00 01 10 11
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41. Hash structure after insertion of three Perryridge records
Example (Cont.)
000
001
010
011
100
101
110
111
Hash structure after insertion of three Perryridge records
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42. Example (Cont.)
Hash structure after insertion of Redwood and Round Hill records
000
001
010
011
100
101
110
111
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43. Extendible Hashing
A hash-index structure might be represented as a file.
The directory might be represented in a disk page.
Each budget is represented as a disk page (including the overflow pages).
Assuming the disk page size is 128 Kilobytes, an index structure with 100 pages would consist of:
1 page for the index directory: assuming each entry in the directory is an RID (disk page number, slot number), it consists of two integers (4 bytes each) for a total of 8 bytes. Thus, the directory is 800 bytes long and fits in one disk page.
100 pages: one for each bucket.
Directory occupies less than 1% of the total file size.
Conclusion: The size of the hash-index file is dominated by the number of buckets.
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44. HASHING (Cont…) Extendible hashing:
The insertion algorithm of extendible hashing might crash when
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45. HASHING (Cont…)
Hashing vs. Indexing
Hashing is appropriate for exact match queries: (cannot support range queries)
SELECT A1, A2, …
FROM r
WHERE (Ai = c)
Indexing is appropriate for both range and exact match queries:
WHERE (Ai <= c1) and (Ai > c2)
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46. Example
Suppose that we are using extendable hashing on a file that contains records with the following search key values:
2, 3, 5, 7, 11, 17, 19, 23, 29, 31
Show the extendible hash structure for a 5 bit machine assuming hash function is h(x) = x mod 8 and buckets can hold three records
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47. B+-TREE B+-tree is a multi-level tree structured directory
Clustered: Leaf nodes contain the records, themselves. ….
...
Root
Internal Nodes
Leaf Nodes
Data File
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48. B+-TREE (Cont…)
Non-clustered: Leaf nodes contain the pairs (P, K), where P is a pointer to the record in the file and K is a search-key.
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49. B+-TREE (Cont…) Leaf nodes Maintain between to n-1 values per leaf.
If i < j then Ki < Kj
Every search-key value in the file appears in some leaf node.
Suppose Li and Lj are two leaves and i < j, then every search value in Li is less than every search value in Lj. P1 K1 P2
. . .
Pn-1
Kn-1 Pn
(n-1) 2 5 7 10
(n = 4) 5 7 10 15 17 18
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50. B+-TREE (Cont…) 5 7 10 Internal nodes
Maintain between to n pointers per internal node
root is an exception: It must have more than one pointer.
Suppose a node with m pointers and 2<= i < m:
Pi points to subtree containing search-key values < Ki and >= Ki-1.
Pm points to subtree containing search-key values >= Km-1.
P1 points to subtree containing search-key values < K1. n 2 2 3 5 7 10 6 11
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51. B+-TREE (Cont…) Lookup Find 7: 4 Ios
Find 4-20: 5 IOs (assuming primary index), 9 IOs (assuming secondary index)
More than 10% selection: it is more efficient to do sequential scan (do not use the secondary index).
Example: 10,000 records, select 1000 of them, 1000 records per disk page: (Sequential search: 10 IOs, Secondary index: potentially IOs) 30 8 41 50 4 7 10 20 40 47 52
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52. B+-TREE (Cont…) Analysis References:
“B” in B+-tree stands for Balanced. i.e., the length of every path from the root to a leaf node is the same.
Hence, good performance for lookup, insertion, and deletion
K: number of search key values in a file, then the path is < log (K).
#K = 1,000,000, and 10 <= n <= 100 then at most 3 to 9 nodes be accessed.
Insertion and Deletion should not destroy the balance of the tree.
References:
J. Jannink, Inplementing Deletion in B+-Trees, SIGMOD RECORD, Volume 24, Number 1 (March 1995), pages
D. Comer, The Ubiquitous B-tree, ACM Computing Surveys, Volume 11, Number 2 (June 1979), pages n 2
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53. B+-TREE (Cont…) n = 4; Internal nodes: 2 to 4 pointers
Leaf nodes: 2 to 3 values 8 25 10 20 4 7 30 40
Insert 41 8 25 4 7 10 20 30 40 41
Insert 47 30 40 41 47 8 25 41 4 7 10 20 30 40 41 47
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54. B+-TREE (Cont…) Insert 50 Insert 52 9/16/2018 8 25 10 20 4 7 30 40 4147 50
Insert 50
Insert 52 41 47 50 52 8 25 41 50 41 8 25 50 4 7 10 20 30 40 41 47 50 52
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55. B+-TREE (Cont…) Delete 20 underflow 9/16/2018 30 10 20 4 7 40 41 47 5052 8
Delete 20 30
underflow 8 41 50 4 7 10 30 40 41 47 50 52 30 41 50 4 7 10 30 40 41 47 50 52
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56. HEAP FILE ORGANIZATION
Assume a student table: Student(name, age, gpa, major)
t(Student) = 16
P(Student) = 4
Bob, 21, 3.7, CS
Kane, 19, 3.8, ME
Louis, 32, 4, LS
Chris, 22, 3.9, CS
Mary, 24, 3, ECE
Lam, 22, 2.8, ME
Martha, 29, 3.8, CS
Chad, 28, 2.3, LS
Tom, 20, 3.2, EE
Chang, 18, 2.5, CS
James, 24, 3.1, ME
Leila, 20, 3.5, LS
Kathy, 18, 3.8, LS
Vera, 17, 3.9, EE
Pat, 19, 2.8, EE
Shideh, 16, 4, CS
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57. Non-Clustered Secondary B+-Tree
A non-clustered secondary B+-tree on the gpa attribute
3.6
(2.3, (4, 2))
(3, (1,2))
(3.7, (1, 1))
(3.9, (4,1))
(2.5, (2,3))
(3.1, (3,3))
(3.8, (3,2))
(3.9, (2,4))
(2.8, (2,2))
(3.2, (1,3)
(3.8, (2,1))
(4, (3,1))
(2.8, (3,4))
(3.8, (1,4))
(3.5, (4,3))
(4, (4,4))
Bob, 21, 3.7, CS
Kane, 19, 3.8, ME
Louis, 32, 4, LS
Chris, 22, 3.9, CS
Mary, 24, 3, ECE
Lam, 22, 2.8, ME
Martha, 29, 3.8, CS
Chad, 28, 2.3, LS
Tom, 20, 3.2, EE
Chang, 18, 2.5, CS
James, 24, 3.1, ME
Leila, 20, 3.5, LS
Kathy, 18, 3.8, LS
Vera, 17, 3.9, EE
Pat, 19, 2.8, EE
Shideh, 16, 4, CS
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58. Non-Clustered Primary B+-Tree
A non-clustered primary B+-tree on the gpa attribute
3.6
(2.3, (1, 1))
(3, (2,1))
(3.7, (3, 1))
(3.9, (4,1))
(2.5, (1,2))
(3.1, (2,2))
(3.8, (3,2))
(3.9, (4,2))
(2.8, (1,3))
(3.2, (2,3)
(3.8, (3,3))
(4, (4,3))
(2.8, (1,4))
(3.8, (3,4))
(3.5, (2,4))
(4, (4,4))
Chad, 28, 2.3, LS
Mary, 24, 3, ECE
Bob, 21, 3.7, CS
Chris, 22, 3.9, CS
Kathy, 18, 3.8, LS
Vera, 17, 3.9, EE
Chang, 18, 2.5, CS
James, 24, 3.1, ME
Lam, 22, 2.8, ME
Kane, 19, 3.8, ME
Louis, 32, 4, LS
Tom, 20, 3.2, EE
Pat, 19, 2.8, EE
Leila, 20, 3.5, LS
Martha, 29, 3.8, CS
9/16/2018
Shideh, 16, 4, CS

59. Clustered B+-Tree 2.9 3.6 3.8 Chad, 28, 2.3, LS Mary, 24, 3, ECE
A clustered B+-tree on the gpa attribute
It is impossible to have a clustered secondary B+-tree on an attribute.
2.9
3.6
3.8
Chad, 28, 2.3, LS
Mary, 24, 3, ECE
Bob, 21, 3.7, CS
Chris, 22, 3.9, CS
Kathy, 18, 3.8, LS
Vera, 17, 3.9, EE
Chang, 18, 2.5, CS
James, 24, 3.1, ME
Lam, 22, 2.8, ME
Kane, 19, 3.8, ME
Louis, 32, 4, LS
Tom, 20, 3.2, EE
Pat, 19, 2.8, EE
Leila, 20, 3.5, LS
Martha, 29, 3.8, CS
Shideh, 16, 4, CS
9/16/2018