Temporal Databases: Data Models

Temporal Databases: Data Models
Kristian Torp
Department of Computer Science
Aalborg University
people.cs.aau.dk/˜torp
torp@cs.aau.dk
November 2, 2015
daisy.aau.dk
Kristian Torp (Aalborg University) Temporal Databases: Data Models November 2, 2015 1 / 50

Outline
1 State and Event Tables
2 State Tables
Valid Time
3 Uniqueness
4 Temporal Keys
Primary Keys
Foreign Keys
5 Summary

Learning Goals
Learning Goals
Understand event versus state tables
Understand how temporal information is stored
Understand temporal integrity constraints
Note
Core temporal ideas, not speciﬁc DBMS product
We will use integers for timestamps
simply because it takes up less space on slides
Will focus on state tables
Most expressive
Hardest to understand (compared to event)
Supported by IBM, Microsoft, and Teradata

Purpose of Temporal Data Model
Beneﬁts
Understand and measure changes (over time)
Tracking/traceability
Avoid being sued
Predictions (mostly about the future :-))
Legal reasons (Sarbanes-Oxley Act)
Example (Dell/Toyota/VW Recalls)
2006-08-16 Dell recalls 4.1 million lithium-ion batteries
2013-03-19 VW recalls 384,181 vehicles with gearbox issues
2013-10-17 Toyota recalls 885,000 vehicles with airbag issues

Outline
2 State Tables
Valid Time
3 Uniqueness
4 Temporal Keys
Primary Keys
Foreign Keys
5 Summary

Event versus State Tables
Example (Event: Stock Prices)
StockID DateTime Price
IBM 2013-11-11 12:33:44 47
Apple 2013-11-11 12:33:47 161
IBM 2013-11-12 10:20:45 48
IBM 2013-11-13 23:59:00 51
Apple 2013-11-13 08:01:02 148
Example (State: CEO)
StockID CEO DateFrom DateTo
Apple Steve Jobs 1997 2011
Apple Tim Cook 2011 now
IBM Louis V. Gerstner 1993 2002
IBM Samuel J. Palmisano 2002 2011
IBM Virginia M. Rometty 2011 now

Transaction-Time Event (log)
Example (Web-Server Log)
session id url tt
11 main.htm 1
11 main.htm 3
22 main.htm 8
11 about.htm 12
22 order.htm 15
22 download.htm 15
33 about.htm 15
Note
Only a single timestamp column
Append-only, i.e., only inserts and no deletes or updates
Sorted on the timestamp column (tt)

Quiz: Event or State?
Examples
Your IT certifications?
A personal monthly qualification bonus for a year?
A permanent monthly qualification bonus?
The period for your mortgage loans?
The daily police report?
The owner of a land property? (BBR in Denmark)

Summary: Event vs. State Tables
Main Points
State is intervals, e.g., [2015-11-20 08:00:00, 2015-11-26 16:00:00)
State is single timestamps, e.g., 2015-11-20 12:00:00
State is most often used
Can convert between event and state in many cases
The SQL statements are non-trivial!
Note
IBM DB2 uses state data model for both valid-time and
transaction-time
Microsoft uses state data model for transaction time
TeraData uses state data model for both valid-time and
transaction-time

Outline
2 State Tables
Valid Time
3 Uniqueness
4 Temporal Keys
Primary Keys
Foreign Keys
5 Summary

Valid-Time State Tables
Example (AllEmps)
Name Dept vts vte
Joe Shoe 7 10
Kim Toy 7 11
Joe Toy 10 now
Kim Sports 11 13
Kim Shoe 13 now
Note
Name and Dept are explicit columns
vts and vte are implicit columns
Handled like plain columns in the DBMS
In some DBMS modeled as a single column of type period
Explicit and implicit columns pure syntax!
now = the variable now (or nobind-now)

Visualization of the Database Variable now
Example (AllEmps at time 15)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Kim, Shoe
Kim, Sports
Joe, Toy
Kim, Toy
Joe, Shoe

Visualization of the Database Variable now
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Kim, Shoe
Kim, Sports
Joe, Toy
Kim, Toy
Joe, Shoe
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Kim, Shoe
Kim, Sports
Joe, Toy
Kim, Toy
Joe, Shoe

The Database Variable now
Example (Using now)
Name Dept vts vte
Joe Toy 10 now
Kim Shoe 13 now
Note
now indicates that the content of the row is valid
now is a database variable
Variables not supported in relational DBMSs
Uses a value like 9999-12-30 or 9999-12-31
now only allowed in the vte column (not in the vts column)

Explicit Timestamps and now
Example (Explicit Timestamping Current-Time is 8)
Name vts vte
Anna 2 6
Bart 4 12
Curt 14 20
Dan 2 now
Eric 8 now
Finn 14 now
Note
Anna is data in the past
Bart overlaps current-time
Curt and Finn are into the future
Dan is from the past and forward (now)
Eric if from now and forward (now)

Timeslicing and now
Name vts vte
Anna 2 6
Bart 4 12
Curt 14 20
Dan 2 now
Eric 8 now
Finn 14 now
Example (Emp as of Time 8)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Finn
Eric
Dan
Curt
Bart
Anna

Timeslicing and now
Name vts vte
Anna 2 6
Bart 4 12
Curt 14 20
Dan 2 now
Eric 8 now
Finn 14 now
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Finn
Eric
Dan
Curt
Bart
Anna

Quiz: now
Example (Are these two rows the same?)
Name Dept vts vte
Joe Shoe 7 12
Joe Shoe 7 now
Hints
At time 8: How many employees do we have the 14th?
How long will Joe work for us? (Asked at times 5, 10, and 15)
Example (Which Rows are Valid?)
Name Dept vts vte
Ann Toy 10 now
Bar Shoe now 20
Curt Toy 10 30
Dan Shoe now now

Quiz: Any Double Agents?
Example (List of Spies)
SID Country vts vte
007 UK 5 now
008 UK 5 15
008 USSR 15 now
009 UK 5 20
009 USSR 10 20

Quiz: Any Double Agents?
Example (List of Spies)
SID Country vts vte
007 UK 5 now
008 UK 5 15
008 USSR 15 now
009 UK 5 20
009 USSR 10 20
Example (Spies at time 25)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
009, USSR
009, UK
008, USSR
008, UK
007, UK

Interval Types
Deﬁnition (Closed Interval)
An interval i [a, b] is closed if c ∈ i for a ≤ c ≤ b
Deﬁnition (Half-open Interval)
An interval i [a, b) is half-open if c ∈ i for a ≤ c < b
Example (Closed Intervals)
[4, 8] - [2, 6] = [7, 8]
Example (Half-open Intervals)
[4, 8) - [2, 6) = [6, 8)
Note
Half-open intervals are more convenient to work with
You avoid a lot of +/− 1
Do not need to worry about granularity (seconds, hours)
+/- on half-open intervals always results in half-open intervals

Quiz: Conceptual Difference?
Example (Departments)
Name Dept vts vte
Ann HR 1 10
Ann RD 10 20
Ann HR 20 40
Name Dept vts vte
Ann HR 1 15
Ann RD 10 20
Ann HR 20 40

Quiz: Conceptual Difference?
Example (Departments)
Name Dept vts vte
Ann HR 1 10
Ann RD 10 20
Ann HR 20 40
Name Dept vts vte
Ann HR 1 15
Ann RD 10 20
Ann HR 20 40
Example (Salaries)
Name Salary vts vte
Ann 40 1 10
Ann 50 10 20
Ann 70 20 40
Name Salary vts vte
Ann 40 1 15
Ann 50 10 20
Ann 70 20 40

Summary: Valid-Time State
Main Points
Two implicit columns vts and vte
Timestamp value can be
System supplied, called implicit timestamping
User supplied, called explicit timestamping
The vte column can contain the database variable now
The value of now changes with the wall-clock
Impemented using large value, e.g., 9999-12-31
Intervals are typically half-open [4, 10)
Makes computations easier
Timestamp intervals are typically not coalesced

Outline
2 State Tables
Valid Time
3 Uniqueness
4 Temporal Keys
Primary Keys
Foreign Keys
5 Summary

Value-Equivalent Rows
Deﬁnition (Value-Equivalent)
Two rows r1 and r2 are value-equivalent if their explicit columns values are
all equal.
Example
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(Ann, HR)
(Ann, HR)
(Bart, RD)
(Bart, RD)
(Curt, RD)
(Curt, RD)
The Ann rows are value-equivalent
The Bart rows are value-equivalent
The Curt rows are value-equivalent

Quiz: Value-Equivalent Rows
Example (Which Table contains Value-Equivalent Rows?)
Name Dept vts vte
Ann HR 2 8
Ann RD 8 15
Ann HR 15 now
Name Dept vts vte
Ann HR 2 6
Ann RD 6 12
Bart RD 12 now

Quiz: Value-Equivalent Rows
Name Dept vts vte
Ann HR 2 8
Ann RD 8 15
Ann HR 15 now
Name Dept vts vte
Ann HR 2 6
Ann RD 6 12
Bart RD 12 now
Name Dept vts vte
Ann HR 2 8
Ann RD 8 15
Ann AD 15 now
Name Dept vts vte
Ann HR 2 12
Bart HR 2 12
Curt HR 2 12

Sequenced Duplicate
Deﬁnition (Sequenced Duplicate)
Two rows r1 and r2 are sequenced duplicates if they are value-equivalent
in overlapping time periods.
Example
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(Ann, HR)
(Ann, HR)
(Bart, RD)
(Bart, RD)
(Curt, RD)
(Curt, RD)
The Ann rows are sequenced-duplicates in the interval [6, 12)
The Bart rows are not sequenced-duplicates
The Curt rows are value-equivalent in the period [6, 14)

Quiz: Sequenced Duplicate
Example (Which Table contains Sequenced Duplicate Rows?)
Name Dept vts vte
Ann HR 2 8
Ann RD 8 15
Ann HR 5 now
Name Dept vts vte
Ann HR 2 6
Ann RD 2 12
Bart RD 12 now

Quiz: Sequenced Duplicate
Name Dept vts vte
Ann HR 2 8
Ann RD 8 15
Ann HR 5 now
Name Dept vts vte
Ann HR 2 6
Ann RD 2 12
Bart RD 12 now
Name Dept vts vte
Ann HR 2 8
Ann RD 8 15
Ann AD 15 now
Name Dept vts vte
Ann HR 2 12
Bart HR 2 12
Ann HR 2 12

Current-Duplicate Rows
Deﬁnition (Current-Duplicate)
Two rows r1 and r2 are value current-duplicate rows if their explicit columns
values are all equal in the current-time timeslice.

Example (Which Table contains Current-Duplicate Rows?)
Name Dept vts vte
Ann HR 2 8
Ann RD 8 now
Ann HR 5 now
Name Dept vts vte
Ann HR 2 now
Ann HD 16 now
Bart RD 12 now

Name Dept vts vte
Ann HR 2 8
Ann RD 8 now
Ann HR 5 now
Name Dept vts vte
Ann HR 2 now
Ann HD 16 now
Bart RD 12 now
Name Dept vts vte
Ann HR 2 8
Ann RD 8 15
Ann AD 15 now
Name Dept vts vte
Ann HR 2 12
Bart HR 2 12
Curt HR 2 12

Non-Sequenced Duplicate
Deﬁnition (Non-Sequenced Duplicate)
Two rows r1 and r2 are non-sequenced duplicates if all their columns
(explicit and implicit) are identical.
Example
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(Ann, HR)
(Ann, HR)
(Bart, RD)
(Bart, RD)
(Curt, RD)
(Curt, RD)
The Ann rows are not non-sequenced-duplicates
The Bart rows are not non-sequenced-duplicates
The Curt rows are non-sequenced-duplicates

Quiz: Non-Sequenced Duplicate
Example (Which Table contains Non-Sequenced Duplicate Rows?)
Name Dept vts vte
Ann HR 2 8
Ann RD 2 now
Ann HR 2 now
Name Dept vts vte
Ann HR 2 10
Ann RD 2 now
Ann HR 2 10

Quiz: Non-Sequenced Duplicate
Name Dept vts vte
Ann HR 2 8
Ann RD 2 now
Ann HR 2 now
Name Dept vts vte
Ann HR 2 10
Ann RD 2 now
Ann HR 2 10
Name Dept vts vte
Ann HR 2 8
Ann RD 2 8
Ann AD 2 8
Name Dept vts vte
Ann HR 2 12
Ann HR 2 10
Ann HR 10 12

Summary: Uniqueness
Example
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(Ann, HR)
(Ann, HR)
(Bart, RD)
(Bart, RD)
(Curt, RD)
(Curt, RD)
Value Equi. Seq. Duplicate Non-Seq. Duplicate
Ann rows
Bart rows
Curt rows
Note
If non-sequenced duplicates then also sequenced duplicates
It sequenced duplicates then also value equivalent

Outline
2 State Tables
Valid Time
3 Uniqueness
4 Temporal Keys
Primary Keys
Foreign Keys
5 Summary

Uniqueness over Time
Cases
Your DNA proﬁle remains constant over time
Your cell-phone number varies slowly over time, but always one
Your checking balances varies almost daily, but always one
The IBM stock value changes every second but always exactly one
value
Note
The notaion of a primary key caries over to temporal databases
The notaion of a foreign key caries over to temporal databases

Primary Keys Informally
Cases
You have been working for a company for eight years. In this time
interval you salary has changed several times. However, at any point
in time you have always had exactly one salary.
You have been married three times. However at any point in time you
have had either zero or one spouse.
Your car has driven 56,000 kilometers but for all millimeters driven
there has been exactly one driver.
You have a house that is 34 years old. Since the house was build
there has at any time only been one owner of the house.
Note
There is a general concept of time-varying uniqueness

Temporal Primary Key Example
Example (trainer at time 19)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2, Bo, 302, Bo, 20
1, Ann, 251, Ann, 201, Ann, 10
Example (As Valid-Time Table)
tid tname salary vts vte
1 Ann 10 1 7
1 Ann 20 9 15
1 Ann 25 15 now
2 Bo 20 2 13
2 Bo 30 13 18
Note
At any point in time is tid a unique value!

Not Temporal Primary Key
Example (tid not a Temporal Primary Key)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2, Bo, 20
2, Bo, 302, Bo, 20
1, Ann, 25
2, Ann, 20
1, Ann, 10
Example (tid a Temporal Primary Key?)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5, Dan, 20
4, Dan, 20
3, Cho, 40
2, Bo, 402, Bo, 302, Bo, 20
1, Ann, 251, Ann, 10

Summary: Primary Key
Main Points
A temporal primary-key is a straight-forward extension of snapshot
primary keys
A temporal primary-key much more computation intesive
Note
Limited or no support for temporal primary keys in DBMSs

Outline
2 State Tables
Valid Time
3 Uniqueness
4 Temporal Keys
Primary Keys
Foreign Keys
5 Summary

Foreign Keys Informally
Cases
You cannot have a contract to rent a house in the period April to
October if the house is ﬁrst built in September
You cannot call your friend after the subscription of her/his cell-phone
has expired
You expect that the cinema has a copy of the movie Blade Runner II
available during the entire period where you have bought a ticket to
see this movie in the cinema
Note
There is a constraint between the time interval associated with the
phenomenon stored in the database.

Temporal Foreign Key Example
Example (emp and dept at time 19)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2, Bo, 102, Bo, 10
1, Ann, 101, Ann, 201, Ann, 10
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
20, RD20, RD20, RD
10, HR10, HR
Example (As Tables)
tid tname did vts vte
1 Ann 10 1 9
1 Ann 20 10 13
1 Ann 10 16 now
2 Bo 10 2 6
2 Bo 10 13 18
did dname vts vte
10 HR 1 9
10 HR 11 now
20 RD 1 6
20 RD 8 13
20 RD 16 now

Idea in Foreign-Key Solution
Requirements
The emp vts value must be covered by an interval in dept
The emp vte value must be covered by an interval in dept
There cannot be any ”holes” in the coverage of the interval for emp
Example (emp and dept at time 19)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Emp
Dept Dept
“Hole”

Part 1 as a Figure
Example (Overlap of vts)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Emp
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
Case 7
Case 8
Case 9
Case 10
Case 11
Case 12
Case 13
Note
Allen’s operators
13 cases because interval to interval comparison

Part 1 in SQL
Example
where not exists ( select ∗ −− vts i s not covered
from dept as s
where s . did = emp. did
and s . vts <= emp. vts and emp. vts < s . vte )
Note
≤ when comparing vts values
< when comparing a vts value to a vte value

Part 2 as a Figure and SQL
Example (Overlap of vte)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Emp
Case 1
Case 2
Case 3
Case 4
Case 5
Example (Overlap vte in SQL)
or not exists (
select ∗ −− vte i s not covered
from dept as e
where e . did = emp. did
and e . vts < emp. vte and emp. vte <= e . vte )
Note
< when comparing a vts value to a vte value
≤ when comparing vte values

Part 3 Example as a Figure
Example (Overlap of vts)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Emp
s
e
b1
b2
Conditions
s overlaps emp.vts
e overlaps emp.vte
Exist
A b1 that ﬁlls the “holes” towards emp.vte
A b2 that exists the ﬁlling of the “hold” towards emp.vte

Part 3 in SQL
Example
or exists ( −− there i s a hole
select ∗
from dept as b1
where b1 . did = emp. did
and emp. vts < b1 . vte and b1 . vte < emp. vte
and not exists (
select ∗
from dept as b2
and b2 . vts <= b1 . vte and b1 . vte < b2 . vte ) )
Note
There exists a row in dept where the vte is in the interval [emp.vts,
emp.vte),
and there is no row in dept that has an interval that extends towards
emp.vte

Entire Solution
Example
select ∗
from emp
where exists ( select ∗
from dept as s
where s . did = emp. did
and s . vts <= emp. vts and emp. vts < s . vte )
and exists ( select ∗
from dept as e
where e . did = emp. did
and e . vts < emp. vte and emp. vte <= e . vte )
and not exists ( select ∗
from dept as b1
and emp. vts < b1 . vte and b1 . vte < emp. vte
and not exists
( select ∗
from dept as b2
and b2 . vts <= b1 . vte and b1 . vte < b2 . vte ) )

Summary: Foreign Key
Main Points
A temporal foreign-key is a straight-forward extension of non-temporal
foreign-keys
A temporal foreign-key is very expensive to enforce
Note
Limited or no support for temporal foreign-keys in DBMSs

Outline
2 State Tables
Valid Time
3 Uniqueness
4 Temporal Keys
Primary Keys
Foreign Keys
5 Summary

Summary: Temporal Data Model
Main Points
Event single timestamp
State two timestamps (from and to)
What is supported by IBM, Microsoft, and Teradata
now = nobind-now (in column vte)
Implemented by large timestamp, e.g., 9999-12-31
UC = until-changed (in column tte)
Implemented by large timestamp, e.g., 9999-12-31
Temporal primary-key and foreign-key
Can be hard to understand
Note
UC is sometimes all so called now or nobind now

Temporal Databases: Data Models

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