Multidimensional Databases Prof. Navneet Goyal Computer Science Department BITS, Pilani.

Multidimensional Databases

Prof. Navneet Goyal

Computer Science Department

BITS, Pilani

April 18, 2023 Dr. Navneet Goyal, BITS, Pilani 2

Database Evolution

• Flat files• Hierarchical and Network• Relational• Distributed Relational• Multidimensional


Why Multi-Dimensional Databases?

• No single "best" data structure for all applications within an enterprise

• Organizations have abandoned the search for the HOLY GRAIL of globally accepted database

• Select the most appropriate data structure on a case-by-case basis from a palette of standard database structures

• Multidimensional Databases for OLAP?


Why Multi-Dimensional Databases?• From econometric research conducted at MIT in

the 1960s, the multidimensional database has matured into the database engine of choice for data analysis applications

• Inherent ability to integrate and analyze large volumes of enterprise data

• Offers a good conceptual fit with the way end-users visualize business data– Most business people already think about their

businesses in multidimensional terms– Managers tend to ask questions about product sales in

different markets over specific time periods


Multidimensional Database

Spreadsheets – A 2D database? Functionalities What about a stack of similar

spreadsheets for different times? Limitations?

We can not relate data in different sheets easily


Multidimensional Database

An MDDB is a computer software system designed to allow for the efficient and convenient storage and retrieval system of large volumes of data that is

1. Intimately related &

2. Stored, viewed and analyzed form different perspectives

These perspectives are called Dimensions


A Motivating Example

An automobile manufacturer wants to increase sale volumes by examining sales data collected throughout the organization. The evaluation would require viewing historical sales volume figures from multiple dimensions such as Sales volume by model Sales volume by color Sales volume by dealer Sales volume over time


Relational Structure


COLOR

MODEL

Mini Van

Sedan

Coupe

Red WhiteBlue

6 5 4

3 5 5

4 3 2

Sales Volumes

Multidimensional Array Structure


RDBMS vs. MDD

• Multidimensional array structure represents a higher level of organization than the relational table

• Perspectives are embedded directly into the structure in the multidimensional model

• All possible combinations of perspectives containing a specific attribute (the color BLUE, for example) line up along the dimension position for that attribute.

• Perspectives are placed in fields in the relational model - tells us nothing about field contents.


• MDD makes data browsing and manipulation intuitive to the end-user

• Any data manipulation action possible with a MDD is also possible using relational technology

• Substantial cognitive advantages in query formulation

• Substantial computational performance advantages in query processing when using MDD

RDBMS vs. MDD


RDBMS vs. MDD


Mutlidimensional Representation

Sales Volumes

DEALERSHIP

Mini Van

Coupe

Sedan

Blue Red White

MODEL

ClydeGleason

Carr

COLOR


Viewing Data - An Example

DEALERSHIP

Sales Volumes

MODEL

COLOR

Assume that each dimension has 10 positions, as shown in the cube above


Viewing Data - An Example

•How many records would be there in a relational table? •Implications for viewing data from an end-user standpoint?

MODEL COLOR DEALERSHIP VOLUMEMINI VAN BLUE CLYDE 2MINI VAN BLUE GLEASON 2MINI VAN BLUE CARR 2MINI VAN RED CLYDE 1MINI VAN WHITE GLEASON 3

•••RECORD NUMBER.... 998RECORD NUMBER.... 999RECORD NUMBER.... 1000

SALES VOLUMES FOR ALL DEALERSHIPS


• Volume figure when car type = SEDAN, color=BLUE, & dealer=GLEASON?

• RDBMS – all 1000 records might need to be searched to find the right record

• MDB has more ‘knowledge’ about where the data lies

• Max. of 30 position searches!!

• Average case15 vs. 500

Performance Advantages


• Total Sales across all colors and dealers when model = SEDAN?

• RDBMS – all 1000 records must be searched to get the answer

• MDB – Sum the contents of one 10x10 ‘slice’



• Data manipulation that requires a minute in RDBMS may require only a few seconds in MDB

• MDBs are an order of magnitude faster than RDBMSs

• Performance benefits are more for queries that generate cross-tab views of data

• The performance advantages offered by multidimensional technology facilitates the development of interactive decision support applications like OLAP that can be impractical in a relational environment.



• Any data manipulation action possible with a multidimensional database is also possible using relational technology

• MDBs however offer several advantages like:–Ease of data presentation and navigation

–Ease of maintenance

–Performance

RDBMS vs. MDB


• Intuitive spreadsheet like data views are natural output of MDBs

• Obtaining the same views in a relational environment, requires either a complex SQL or a SQL generator against a RDB to convert the table outputs into a more intuitive format

• Top N queries are not possible with SQL at all

Ease of Data Presentation & Navigation


• Ease of maintenance because data is stored as it is viewed

• No additional overhead is required to translate user queries into requests for data

• To provide same intuitiveness, RDBs use indexes and sophisticated joins which require significant maintenance and storage

Ease of Maintenance


• Performance of MDBs can be matched by RDBs through database tuning

• Not possible to tune the database for all possible adhoc queries

• Tuning requires resources of an expensive DB specialist

• Aggregate navigators are helping RDBs to catch up with MDBs as far as aggregation queries are concerned

Performance


Adding Dimension - An Example

MODEL

Mini Van

Coupe

Sedan

Blue Red White

ClydeGleason

Carr

COLOR

Sales Volumes

Coupe

Sedan

Blue Red White

ClydeGleason

Carr

COLOR

DEALERSHIP

Mini Van

Coupe

Sedan

Blue Red White

ClydeGleason

Carr

COLOR

JANUARY FEBRUARY MARCH

Mini Van


When is MDD (In)appropriate?

PERSONNEL

LAST NAMEEMPLOYEE# EMPLOYEE AGESMITH 01 21REGAN 12 19FOX 31 63WELD 14 31KELLY 54 27LINK 03 56KRANZ 41 45LUCUS 33 41WEISS 23 19

First, consider situation 1


Now consider situation 2

SALES VOLUMES FOR GLEASON DEALERSHIP

MODEL COLOR VOLUME

MINI VAN BLUE 6MINI VAN RED 5MINI VAN WHITE 4SPORTS COUPE BLUE 3SPORTS COUPE RED 5SPORTS COUPE WHITE 5SEDAN BLUE 4SEDAN RED 3SEDAN WHITE 2

1. Set up a MDD structure for situation 1, with LAST NAMEand Employee# as dimensions, and AGE as the measurement.2. Set up a MDD structure for situation 2, with MODEL andCOLOR as dimensions, and SALES VOLUME as the measurement.




COLOR

MODEL

Mini Van

Sedan

Coupe

Red WhiteBlue

6 5 4

3 5 5

4 3 2

Sales Volumes

EMPLOYEE #

LAST

NAME

Kranz

Weiss

Lucas

41 3331

45

19

Employee Age

41

31

56

63

21

19

Smith

Regan

Fox

Weld

Kelly

Link

01 14 54 03 1223

27

Note the sparse between the two MDD representations

MDD Structures for the Situations



Our sales volume dataset has a great number of meaningful interrelationships

Interrelationships more meaningful than individual data elements themselves.

The greater the number of inherent interrelationships between the elements of a dataset, the more likely it is that a study of those interrelationships will yield business information of value to the company.

Highly interrelated dataset types be placed in a multidimensional data structure for greatest ease of access and analysis



• No last name is matching with more than one emp # and no emp # is matching with more than one last name

• In contrast, there is a sales figure associated with every combination of model and color resulting in a completed filled up 3x3 matrix

• Performance suffers (RDB 9 vs. MDB 18)



• The relative performance advantages of storing multidimensional data in a multidimensional array increase as the size of the dataset increases

• The relative performance disadvantages of storing non-multidimensional data in a multidimensional array increase as the size of the dataset increases.

• NO inherent value of storing Non-multidimensional data (employee data) in multidimensional arrays


When is MDD Appropriate?

The greater the number of inherent interrelationships between the elements of a dataset, the more likely it is that a study of those interrelationships will yield business information of value to the company.

• Most companies have limited time and resources to devote to analyzing data

• It therefore becomes critical that these highly interrelated dataset types be placed in a multidimensional data structure for greatest ease of access and analysis.


When is MDD Appropriate?

Examples of applications that are suited formultidimensional technology:

1. Financial Analysis and Reporting2. Budgeting3. Promotion Tracking4. Quality Assurance and Quality Control5. Product Profitability


MDD Features - Rotation

Sales Volumes

COLOR

MODEL

Mini Van

Sedan

Coupe

Red WhiteBlue

6 5 4

3 5 5

4 3 2

MODEL

COLOR

SedanCoupe

Red

White

Blue 6 3 4

5 5 3

4 5 2( ROTATE 90

o )

View #1: ModelxColor View #2: ColorxModel

Mini Van

•Also referred to as “data slicing.”•Each rotation yields a different slice or two dimensional tableof data.



COLORCOLORMODEL

MODELDEALERSHIPDEALERSHIP

MODEL

Mini Van

Coupe

Sedan

Blue Red White

ClydeGleason

Carr

COLOR

Mini Van

Blue

Red

WhiteClyde

GleasonCarr

MODEL

Mini Van

Coupe

Sedan

Blue

Red

White

Carr

COLOR

COLOR

DEALERSHIP

View #1 View #2 View #3

DEALERSHIP

Mini Van

CoupeSedan

BlueRedWhite

Clyde

Gleason

Carr

Mini Van Coupe Sedan

Blue

RedWhite

Clyde

Gleason

Carr Mini Van

Coupe

SedanBlue

RedWhite

Clyde Gleason Carr

View #4 View #5 View #6

DEALERSHIP

CoupeSedan

( ROTATE 90o

) ( ROTATE 90o

) ( ROTATE 90o

)

COLOR MODEL

MODEL

DEALERSHIP( ROTATE 90

o ) ( ROTATE 90

o )

Gleason Clyde

Sales Volumes



• All the six views can be obtained by simple rotation

• In MDBs rotations are simple as no rearrangement of data is required

• Rotation is also referred to as “data slicing”

• No. of views

•2D – 2

•3D – 6

•4D - ?24


MDD Features - Ranging

• How sales volume of models painted with new metallic blue compared with the sales of normal blue color models?

• The user knows that only Sports Coupe and Mini Van models have received the new paint treatment

• Also the user knows that only 2 dealers viz, Carr and Clyde have unconstrained supply of these models



• The end user selects the desired positions along each dimension.• Also referred to as "data dicing." • The data is scoped down to a subset grouping

Sales Volumes

DEALERSHIP

Mini Van

Coupe

Metal Blue

MODEL

ClydeCarr

COLOR

Normal Blue

Mini Van

Coupe

Normal Blue

Metal Blue

ClydeCarr



• The reduced array can now be rotated and used in computations in the same was as the parent array

• Referred to as “Data Dicing” as data is scoped down to a subset grouping

• Complex SQL query is required in RDB

• Performance is better in MDB as less resource consuming searches are required


MDD Features – Roll-Up & Drill-Down

• Users want different views of the same data• For eg., Sales Volume by model vs, sales

volume by dealership• Many times views are similar

Sales volume by dealership vs. volume by district

• Natural relationship between Sales Volumes at the DEALERSHIP level and Sales Volumes at the DISTRICT level

• Sales Volumes for all the dealerships in a district sum to the Sales Volumes for that district


MDD Features – Roll-Up & Drill-Down

• Multidimensional database technology is specially designed to facilitate the handling of these natural relationships

• Define two related aggregates on the same dimension

• One aggregation is dealership and the other district

• District is at a higher level of aggregation than dealership


MDD Features - Roll-Ups & Drill Downs

Gary

Gleason Carr Levi Lucas Bolton

Midwest

St. LouisChicago

Clyde

REGION

DISTRICT

DEALERSHIP

ORGANIZATION DIMENSION

• The figure presents a definition of a hierarchy within the organization dimension.• Aggregations perceived as being part of the same dimension.•Moving up and moving down levels in a hierarchy is referred to as “roll-up” and “drill-down.”


MDD Features - Roll-Ups & Drill Downs


MDD Features: Drill-Down Through a Dimension

GaryGleason Carr Levi Lucas Bolton MidwestSt. Louis ChicagoClyde

REGION

DISTRICT

DEALERSHIP

MODEL

COLOR

Sales Volumes


Queries

• High degree of structure in MDB makes the query language very simple and efficient

• Query language is intuitive• Output is immediately useful

to end user


Queries: Example

• Display sales volume by model for each dealershipPRINT TOTAL.(SALES_VOLUME KEEP MODEL DEALERSHIP)

Trends emerge and comparisons are easily made

DEALERSHIPMODEL CLYDE GLEASON CARRMINI VAN 7 5 6SPORTS COUPE 4 6 8

SEDAN 3 8 12


Queries: Example

• Corresponding SQLSELECT MODEL, DEALERSHIP, SUM(SALES_VOLUME)

FROM SALES_VOLUME

GROUP BY MODEL, DEALERSHIP

ORDER BY MODEL, DEALERSHIPMODEL | DEALERSHIP | SUM(SALES_VOLUME)

MINI VAN | CLYDE | 7MINI VAN | GLEASON | 5MINI VAN | CARR | 6SPORTS COUPE| CLYDE | 4SPORTS COUPE| GLEASON | 6SPORTS COUPE| CARR | 8SEDAN | CLYDE | 3SEDAN | GLEASON | 8

SEDAN | CARR | 12


Queries: ExampleUse report writer in addition to SQL and we getMINI VAN

CLYDE 7

GLEASON 5

CARR 6

SPORTS COUPE

CLYDE 4

GLEASON 5

CARR 8

SEDAN

CLYDE 3

GLEASON 8

CARR 12


MDD Features:Multidimensional Computations

• Well equipped to handle demanding mathematical functions.

• Can treat arrays like cells in spreadsheets. For example, in a budget analysis situation, one can divide the ACTUAL array by the BUDGET array to compute the VARIANCE array.

• Applications based on multidimensional database technology typically have one dimension defined as a "business measurements" dimension.

• Integrates computational tools very tightly with the database structure.


MDD Features:Multidimensional Computations

BUSINESS MEASUREMENTS

Mini Van

Coupe

Actual Budget Variance

16 12 0.33

11 10 0.1

8 10 - 0.2

16 16 0.0

Sedan

Sales Volumes


The Time Dimension

• TIME as a predefined hierarchy for rolling-up and drilling-down across days, weeks, months, years and special periods, such as fiscal years.– Eliminates the effort required to build sophisticated

hierarchies every time a database is set up.

– Extra performance advantages


Contrasting Relational Model and MD Model

Criteria Relational Model MultidimensionalDatabases

Focus Data integrity of each pieceof data

Facilitate exploration ofinterrelationships betweendimensions

Organization structure One-dimensional array Multi-dimensional arraysPerspectives Embedded in fields Embedded directly in

MDDB structureComputational power forQuery processing

Joining tables oftenrequired; computationallyexpensive

Structure designed forOLAP; computationallycheap

Cognitive issues inquerying data

Cumbersome Intuitive

Query Languages SQL or SQL front-ends,such as QBE

Point-and-click emphasisNo standardized language

Management of TimeDimension

Not well suited Well suited


RDBMS vs. MDDB

• DO I still use RDBMS for my DW?• MDDBs store data in hypercube, i.e.,

multidimensional array• RDBMS store data as tables with row and

columns that do not map directly to multidimensional view that user have of data

• EDW – RDBMS• Data Marts - MDDB


RDBMS vs. MDDB: Trade-Offs

• SIZE – MDDBs limited by size

• Mid – 1990s 10GB caused problems• Today – 100GB is OK

– Large DWs are still better served by relational front-ends running against high performance and scalable RDBMS

• VOLATILITY– Highly volatile data are better handled by

RDBMS– MDDBs take long to load and update



• AGGREGATE STRATEGY– MDDBs support aggregates better– RDBMSs are catching up with the help of

Aggregate Navigators• INVESTMENT PROTECTION

– Most organizations already have made significant investments in relational technology and skill sets

– Continued use for another purpose (DW) provides additional ROI and lowers technical risk of failure

– MDDBs – need to acquire new software and train staff to use it



TYPE OF USERS– Power users prefer the range of

functionalities available in MOLAP tools– Users that require broad views of enterprise

data require access to DW and therefore better served by a ROLAP tool


INTEGRATED ARCHITECTURE

• DB vendors have integrated their multidimensional and relational database products

• Multidimensional Front-end tools• If queries require data that are not

available in MDDB, the tools retrieve the data from the larger RDB

• Known as “DRILL-THROUGH”

Q & A

Thank You

Multidimensional Databases Prof. Navneet Goyal Computer Science Department BITS, Pilani.

Documents

sales data

multidimensional model

time slide

business data

pilani slide

appropriate data structure

color sales volume

model sales volume