1. Physical Design: Types of Indexes & Files
University of Manitoba Asper School of Business 3500 DBMS Bob Travica
Physical Design:
Types of Indexes
& Files
Based on G. Post, DBMS: Designing & Building Business Applications
Updated 2020

2. Physical Data Storage Topics of interest: File types for storing data
Index types - Data structures for retrieving data (Index to sequential file, Linked List, B+-Tree, Hash Table)
Additional Physical Design Methods (file partitioning, clustering)

3. Terminology
Data entry or data element - a special short record containing usually the key attribute, address to the rest of data (pointer), and sometimes other addresses; used for creating indexes
Pointer = address of data, designation of data location
DBMS task = any of CRUD operations

4. DBMS Tasks (CRUD) Store (write, create) data Retrieve (read) data
Insert a row.
Retrieve (read) data
Read entire table (scan all rows).
Read arbitrary/random row.
Modify (update) data
(Change “Crag” into “Craig”;
random read first)
Delete data.
(2 steps: mark + ”pack”;
LastName FirstName Phone
Adams Kimberly (406)
Allbright Searoba (619)
Anderson Charlotte (701)
Baez Bessie (606)
Baez Lou Ann (502)
Bailey Gayle (360)
Bell Luther (717)
Carter Phillip (219)
Carver Bernice (804)
Crag Melinda (502)
x Duvall Pierre (502)
Adkins Inga (706)

5. File Types & Access Methods (Indexes)
Indexed Sequential Access Method (ISAM) &
Sequential File
Linked List index
B+-Tree index
Hash index

6. Sequential File
Two formats: Sorted file and unsorted file (record insertion by
appending at the end). .
Uses:
When data don’t change much
Data retrieved in same order
When table is huge and space is expensive.
When transporting / converting data to a different system.
File Employee (sorted on employee ID)

7. Operations on Sequential Files
Read entire file sequentially:
Easy and fast
Read next record:
Fast
Random Read/Sequential (pattern matching):
Slow
Probability of any row lookup = 1/N
(N=number of records)
Delete, Insert, Modify:
First find, then do… So, slow.
Row Prob. # Reads
A 1/N 1
B 1/N 2
C 1/N 3
D 1/N 4
E 1/N 5
… 1/N i

8. Sequential Access to Sorted Sequential File
Sequential search
Find: Brown; 2 lookups, Find: Jones; 10 lookups
Go one by one from top
Min lookups = 1, Max = 10
On the average = (N+1)/2 = (10+1)/2= 11/2 = 5.5, i.e. 6 lookups
Key Attribute LastName
Adams
 Brown
Cadiz
Dorfmann
Eaton
Farris
Goetz
Hanson
Inez
 Jones
N =10 records

9. Insertion into Sorted Sequential File
Insert record Inez:
Find insert location, mark top & bottom parts of the old file.
Copy the top to new file.
Add new row.
Copy the bottom to new file.
Delete old file ID
LastName
FirstName
DateHired 8 6 7 2
Carpenter
Eaton
Farris
Gibson
Carlos
Anissa
Dustin
Bill
12/29/2001
8/23/2001
3/28/2001
3/31/2001 5 9 3 1 10
James
O’Connor
Reasoner
Reeves
Shields
Leisha
Jessica
Katy
Keith
Howard
1/6/2001
/23/2001
2/17/2001
1/29/2001
7/13/2001
Old File
Top
Bottom
1. copy
New File
2. insert
3. copy

10. Indexed Sequential Access Method (ISAM)
Record
address
Records (Table), sorted or unsorted
ISAM index is a small file with columns key and pointer.
Index can be put on multiple attributes.
A11
A22
A32
A42
A47
A58
A63
A67
A78
A83
ID LastName FirstName DateHired
1 Reeves Keith 1/29/2001
2 Gibson Bill 3/31/2001
3 Reasoner Cathy 2/17/2001
4 Hopkins Alan 2/8/ 2001
5 James Leisha 1/6/ 2001
6 Eaton Anissa 8/23/ 2001
7 Farris Dustin 3/28/ 2001
8 Carpenter Carlos 12/29/ 2001
9 O'Connor Jessica 7/23/ 2001
10 Shields Howard 7/13/ 2001
index on ID
index on LastName
ID Pointer
1 A11
2 A22
3 A32
4 A42
5 A47
6 A58
7 A63
8 A67
9 A78
10 A83
Index on ID
LastName Pointer
Carpenter A67
Eaton A58
Farris A63
Gibson A22
Hopkins A42
James A47
O'Connor A78
Reasoner A32
Reeves A11
Shields A83
Index on LastName
An index is sorted, search run
on it, and the pointer (address location)
used to fetch the record sought.
Re-indexing (index refreshing) when
new record is inserted.

11. Search of ISAM Index Binary search method: Task: Find Jones
Index on LastName
Binary search method:
Task: Find Jones
Binary search
1) Split & test middle value Goetz vs. Jones.
Result: Jones comes after Goetz (Jones > Goetz), so look down + discard upper half
2) Split & test: Jones < Kalida, so look up
3) Split & test: Jones > Inez, so look down
4) Split & test: Jones = Jones, so match!
Adams
Brown
Cadiz
Dorfmann
Eaton
Farris
Goetz
Hanson
Inez
Jones
Kalida
Lomax
Miranda
Norman
(N=14) 1
Match in 4th lookup 3 4 2

12. Binary Search (Cont.)
4 lookups in total; manual calculation of lookups:
1) 14/2=7
2) 7/2=3.5, round to 4;
3) 4:2=2
4) 2:2=1
Or by formula log2 N:
log214= …, round
up to 4.
Check: 2x2=4; 4x2=8; 8x2=16
that is, appx Number of lookups is the exponential to which 2 should be raised to get the score ~ N.

13. Linked List Index
Linked List Index consists of data entries with 3 pieces:
key value, pointer to next element, and pointer to a stored record.
Complete records
- randomly stored
location
record
8 Carpenter Carlos 12/29/2001
A67
2 Gibson Bill 3/31/2001
A22
Linked List Index
- sorted via pointers
pointer
to stored
record
6 Eaton Anissa 8/23/2001
A58
pointer
to next
index
item
index
element
location
7 Farris Dustin 3/28/2001
A63
Carpenter
B87
B29
A67
Gibson
B38 00
A22
Eaton
B29
B71
A58
Indicates last record
Farris
B71
B38
A63

14. Linked List: Insert Task
Task: Insert the Eccles row
Procedure:
1. Identify place of Eccles index element
in sorting order (Eccles is after Eaton
and before Farris).
2. Store Eccles element at an available
location (B14)
3. Move pointer from Eaton element to Eccles element – B71 (referencing Farris element)
4. Insert pointer in Eaton to point to the Eccles record – new location B14 4.
RECORDS 1.
B14
Eaton
B29
B71
A58 X 3. 2.
B14
Eccles
B71
A97
Farris
B71
B38
A63

15. Tree (hierarhical) Indexes
Three = a hierarchical structure with a root element on top, branches,
nodes, and leaves.
Root = start point
Node (data entry)
Leaf (bottom node with
no children)
Depth (n) = number of levels
Degree (m) = max. no. of children per node:
If m=2 then it is a binary (B) tree
If>2 then it is a B+ tree.
Root
value
<
<=
Comparison symbol for locating
smaller values
Comparison symbols for locating bigger values and an equal value

16. B+-Tree
Increased retrieval power and performs optimally on other tasks.
Typical index method in modern DBMSes
Characteristics:
Root, non-leaf nodes (some values of key attribute, used for
navigating through Tree), leaf-nodes (all key values, point to records)
Degree, m >= 3
Every non-leaf node (except Root) has between m/2 and m children
Leaf-nodes (Leaves) are at the same level/depth & in the
sequential order.

17. B+-Tree Example Degree = 3
<
315
<=
<
231
<=..<
287
<=
<
458
<=..<
792
<=
<
156
<=
<
231
<=
<
287
<=
<
315
<=
347
<=
<
458
<= 692
<=
<
792
<=
records
Degree = 3
At minimum m/2=1.5  2 children
Maximum 3 children
Search procedure (e.g., find 692) using comparisons:
Less than
Equal or Greater than
Between
Note sequential order at leaf level (156…792), as ISAM index.

18. B+-Tree: Insert Task Insert 257 Find location, starting from Root.
Easy with extra space.
Just insert 257 in appropriate sequence.
Test 1: 257 vs 315
315
<
<=
231
<= <
287
458
792
347
692
156
Test 2
257
Test 3

19. Tree Creation
Either a B or B+ tree index is easiest to build (conceptually, manually) from the leaf level.
Properties of the tree index must be respected.
4. Work out the node values. A node value is one of the leaf values satisfying comparisons (<, =, >).
Example: the value on the left side node must be bigger than 156 and 231, but smaller than 287 and 315.
3. Pick the comparison symbols; these must be used consistently across the tree. The root value must comply with
comparison symbols and the edge values in the leaf dataset (315 and 347). Example: 347 must be bigger than any value
on the left side of the tree, and it must be equal or smaller than any value on the right side of the tree.
347
<
<=
287
231
156
315
692
458
792
2. Pick a root value to be appx. in the middle of leaf dataset
Edge values
1. Line up the values to be stored from min to max

20. B+-Tree Strengths
Designed to give good performance for any type of data and usage.
Lookup speed is based on degree/depth.
Random and sequential retrieval fast.
Insert, delete, modify fast.
Many changes are easy.
Occasionally large sections must be reorganized to balance the tree.

21. Direct Access / Hashed Example
Convert a PK value directly to location address.
Prime modulus hash algorithm:
Choose prime number*.
Divide key value by prime no. and use modulus (remainder) as address to storage:
124 / 101 =
Take left digit as row no. and
right digit as column no.
Very fast random retrieval (e.g., POS retrieving price on product no. (key).
Slower sequential access.
Collision/overflow space for duplicates
Must reorganize if hash table full.
Example
Prime = 101
Key value = 124
Modulus = 2 | 3
112
101
133
Overflow for values in collision,
sequential order (ex: 202) 1 2 3
102
123
122
111
124
Location
in hash table
row 2
column 3
The prime should be such that the result of division >0; modulus is increasing by 1; reducing possibility of colliding values. For example, prime of 101 works well with
numbers in the range A value of 202 is the first collision, and other values in the range up to 301 will collide.
1. where would the value 104 be stored?
2. where would the value 200 be stored?
3. which value can be stored in 65?
cell 23
pointers to
records

22. Comparison of Index Types
Choice depends on data usage.
How often do data change?
What percent of the data is used at one time?
How big are the tables?
How many transactions are processed per second?
B+-Tree is best overall
Hashing is good for high-speed random access
Sequential/ISAM is good if entire larger tables often used

23. Storing Data Columns
Different methods of storing data within each row.
Fixed (Positional)
Simple, common
Fixed with overflow
(Memo/highly variable text;
VARCHAR data type)
A101: -Extra Large
Overflow text
A321: an-Premium
A532: r-Cat

24. Data Clustering Grouping related data together to improve retrieval.
Data should be close to each other on one disk.
Preferably within the same disk page or cylinder.
Minimize disk reads and seeks.
Example: cluster each invoice with the matching order.

25. Data Clustering Keeping data on the same drive
Keeping data close together
Same cylinder
Same I/O page
Consecutive sectors
Order
Order# Customer# OrderDate
OrderItem
Order# Item# 078 Quantity 3
Order# Item
Order# Item# 987 Quantity 1
Order# Item
Order# Item# 240 Quantity 2
Order# 1124

26. Data Partitioning Split table: Horizontally or Vertically
Infrequent access to some rows
Large tables
Move less used rows to
slower / cheaper storage
Horizontal Partition
High speed
hard disk
Low cost
optical disk
Active
customers
Customer# Name Address Phone
2234 Inouye 9978 Kahlea Dr
5532 Jones 887 Elm St
0087 Hardaway 112 West
0109 Pippen 873 Lake Shore
Current
Customers
Customers w/ no
purchase in last 3 years

27. Data Partitioning Vertical Partition
Some columns less used and large (long)
Store often used data on hi speed disk.
Store less used data on optical disk.
DBMS retrieves both automatically as needed.
Vertical Partition
High speed
hard disk
Low cost
optical disk
Item# Name QOH Description TechnicalSpecifications
875 Bolt 268 1/4” x 10 Hardened, meets standards ...
937 Injector 104 Fuel injector Designed 1995, specs . . .

28. RAID and Disk Striping Redundant Array of Independent Drives - RAID
Instead of one massive drive, use many smaller drives.
Split table to store parts on different drives - Striping
Drives can simultaneously retrieve portions of data -
parallel processing).
CustID Name Phone
115 Jones
225 Inez
333 Shigeta
938 Smith
Solutions to questions on the hash table.
1. 01 (102:101=1 & 1)
2. 10 (919:101=9 & 10)
3. 101x1+31=101+31=132 4.
101x2+31=202+31= 233
101x3+31=303+31= 334