LIVE A lineage-supported, versioned DBMS Anish Das Sarma Martin Theobald Jennifer Widom

LIVE

A lineage-supported, versioned DBMS

Anish Das Sarma Martin Theobald Jennifer Widom

ULDB Data Model and the Trio System Uncertainty & Lineage

LIVE Data Model (LDM) Uncertainty, Lineage & Versioning

Data Modifications Insert/Delete Tuples, Update Values, Update

Confidences Query Evaluation

Valid-At vs. Snapshot Queries, Interval Computations, Confidence Computations, Complexity

Experiments/Conclusions

Agenda

21.04.232 LIVE - A lineage-supported, versioned DBMS

ULDB Data Model


Different types of uncertainty: 1. Tuple Alternatives 2. ‘?’ (Maybe) Annotations 3. Confidences

Implementation of the ULDB data model: Trio System

TriQL query language TrioExplorer browser frontend, trioplus client,

API Enhanced PostgreSQL backend (SPI) Search for “Stanford Trio”

ULDBs – Alternatives


1. Alternatives: uncertainty about attribute values

2. ‘?’ (Maybe) Annotations 3. Confidences

Saw (witness, color, car)

Amy red, Honda ∥ red, Toyota ∥ orange, Mazda

Three possibleworlds

ULDBs – Maybe Annotations


Six possibleworlds

1. Alternatives 2. ‘?’ (Maybe): uncertainty about tuple

presence 3. Confidences

?


Amy red, Honda ∥ red, Toyota ∥ orange, Mazda

Betty blue, Acura

ULDBs – Confidences


1. Alternatives 2. ‘?’ (Maybe) Annotations 3. Confidences: weighted uncertainty

Six possible worlds,each with a probability

?


Amy red, Honda 0.5 ∥ red, Toyota 0.3 ∥ orange, Mazda 0.2

Betty blue, Acura 0.6

ULDBs – Closure


Saw (witness, car)

Cathy

Mazda ∥ Honda

Drives (person, car)

Jimmy, Toyota ∥ Jimmy, Mazda

Billy, Honda ∥ Frank, Honda

Hank, Honda

Suspects

Jimmy

Billy ∥ Frank

Hank

Suspects = πperson(Saw ⋈ Drives)

???

Does not correctlycapture possibleworlds in theresult!

CANNOT

ULDBs – Lineage


ID Saw (witness, car)

11

Cathy

Honda ∥ Mazda

ID Drives (person, car)

21

Jimmy, Toyota ∥ Jimmy, Mazda

22

Billy, Honda ∥ Frank, Honda

23

Hank, Honda

ID Suspects

31

Jimmy

32

Billy ∥ Frank

33

Hank

Suspects = πperson(Saw ⋈ Drives)

???

λ(31) = (11,2)(21,2)

λ(32,1) = (11,1)(22,1)

λ(33) = (11,1)23

; λ(32,2) = (11,1)(22,2)

ULDBs – Summary


1. Alternatives2. ‘?’ (Maybe) Annotations3. Confidences4. Lineage

ULDBs are closed and complete

Uncertainty-Lineage Databases (ULDBs)Uncertainty-Lineage Databases (ULDBs)

Can exclusively utilize lineage in order to compute the confidence of a result tuple.

#P-complete for general Boolean formulas Approximation algorithms: Luby-Karp, etc.

Lineage & Confidences


λ(21) = (11 12 13)

ID Saw(witness, car)

11 (Mary, Honda) : 0.8

12 (Susan, Honda) : 0.9

13 (Betty, Honda) : 0.5

ID SuspectCars(car)

21 Honda : ?

Select distinct car from Saw;

P(21) = 1 – (1-0.8) X (1-0.9) X (1-0.5)

0.99

ID Photo(Number,Name)2

11 (1, Amy) [0,1] : 1.0

12 (1, Bob) [0,] : 0.6

13 (2, Carl) [0,1] : 0.314 (3, Dale) [1,1] : 0.1

Versioning (LDM Data Model)


Version intervals for tuples Contiguous version numbers 0,…, Database has current version vD

Tuples have a validity intervals [s, e]

Valid-At Queries: Select * from Photo valid-at 2;

Snapshot Queries: View Photo at 2;

Possible Worlds: LDM databases encode lists of sets of

possible worlds.

ID Photo(Number,Name)2

12 (1, Bob) [0,] : 0.6

ID Photo@2(Number,Name)

12 (1, Bob) : 0.6

Insert Tuple: Insert t with version [vD+1,]

commit; Increase vD

Data Modifications – Insert


ID People(Name, State, Job)0

21 (Bob, NY, Analyst) [0,] : 1.0

22 (Carl, IL, Teacher) [0,] : 1.0

23 (David, PA, Manager)

[0,] : 0.6

24 (Frank, CA, Eng.) [1,] : 0.3



25 (David, PA, CEO) [2,] : 0.3

(1)

(2)

(2)


Delete Tuple: Set end(t) to vD

commit; Increase vD

Data Modifications – Delete



21 (Bob, NY, Analyst) [0,] : 1.0

22 (Carl, IL, Teacher) [0,] : 1.0


[0,] : 0.6

24 (Frank, CA, Eng.) [1,] : 0.325 (David, PA, CEO) [2,] : 0.3

22 (Carl, IL, Teacher) [0,2] : 1.0


(1)

(2)

(3)

(2)



Update Value: Set end(t) to vD

Insert t’ with version [vD+1,]

commit; Increase vD

Data Modifications – Update



21 (Bob, NY, Analyst) [0,] : 1.0

22 (Carl, IL, Teacher) [0,2] : 1.0


[0,] : 0.6

24 (Frank, CA, Eng.) [1,] : 0.325 (David, PA, CEO) [2,] : 0.321 (Bob, CA, Student) [4,] : 0.3

21 (Bob, NY, Analyst) [0,3] : 1.0

(1)

(2)

(3)

(2)

(4)

(4)




Update Value: Set end(t) to vD

Insert t’ with version [vD+1,]

Update Probability: Set end(t) to vD

Insert t’=t with probability p’ and version [vD+1,]

commit; Increase vD

Data Modifications – Update



21 (Bob, NY, Analyst) [0,3] : 1.0

22 (Carl, IL, Teacher) [0,2] : 1.0


[0,] : 0.6


(1)

(2)

(3)

(2)

(4)

(4)21 (Bob, CA, Student) [5,] :

0.7

21 (Bob, CA, Student) [4,4] : 0.3 (5)




Update Value: Set end(t) to vD Insert t’ with version [vD+1,]

Update Probability: Set end(t) to vD Insert t’=t with probability p’ and version

[vD+1,]

Possible worlds: Updates may create duplicate

worlds, which are merged (at any version v).

Data Modifications – Summary



21 (Bob, NY, Analyst) [0,3] : 1.0

22 (Carl, IL, Teacher) [0,2] : 1.0


[0,] : 0.6


(1)

(2)

(3)

(2)

(4)

(4)21 (Bob, CA, Student) [5,] :

0.7

21 (Bob, CA, Student) [4,4] : 0.3 (5)


1) Data Computation (regular SQL, including lineage) 2) Interval Computation (stored procedure)

Query Evaluation


DD

D1, D2, …, Dn1D1, D2, …, Dn1

possibleworlds

at versionsQ on each

world

encodingof possible worlds

Q(D1), Q(D2), …, Q(Dn)Q(D1), Q(D2), …, Q(Dn)

implementation of Q

operational semantics

D + ResultD + Result

D1, D2, …, Dn2D1, D2, …, Dn2

@ (0)

@ (1)

D1, D2, …, DnvD1, D2, …, Dnv @ (vD)

…

…

@ (0)

Can exclusively utilize lineage in order to compute the confidence of any result tuple.

Can exclusively utilize lineage in order to compute the version interval of any result tuple.

Lineage, Confidences & Versions


Positive Lineage (disjunctions & conjunctions) In the lineage formula λ(t)

Replace every tuple t’ by its version interval Replace every with and every with

Version Interval Computation


λ(21) = (11 12 13)

ID Saw(witness, car)3

11 (Mary, Honda) [1,] : 0.8

12 (Susan, Honda) [2,] : 0.9

13 (Betty, Honda) [3,] : 0.5

ID SuspectCars(car)3

21 (Honda) ? : ?


P(21) = 1 – (1-0.8) X (1-0.9) X (1-0.5)

[1,] :

0.99

Positive Lineage (disjunctions & conjunctions) In the lineage formula λ(t)

Replace every tuple t’ by its version interval Replace every with and every with

Version & Confidence Computation


λ(21) = (11 12)

ID Saw(witness, car)3

11 (Mary, Honda) [1,] : 0.8

12 (Susan, Honda) [2,] : 0.9

13 (Betty, Honda) [3,] : 0.5


21 (Honda) [1,] : 0.99


P(21) = 1 – (1-0.8) X (1-0.9)


21 (Honda) ? : ?

Select distinct car from Saw valid-at 2;

[1,] : 0.98

21.04.2321 LIVE - A lineage-supported,

versioned DBMS

Can decouple interval computation from data computation

Or: push interval computation into query plans only when there is no negation.

Interval Computations & Query Plans

Select R.A from R EXCEPT ( Select R.A from R EXCEPT Select S.A from S ); r=(a)[0,10] u=(a)[0,10]

t=(a)[0,10]

r=(a)[0,10] s=(a)[5,15]

–

–

Select R.A from R,SWhere R.A=S.A;

r=(a)[0,10] s=(a)[5,15]

t=(a)[5,10]

Positive Lineage (disjunctions & conjunctions) Version interval computation

PTIME (linear) Confidence computation

#P-complete

Arbitrary Lineage (including negation) Version interval computation

PTIME (linear) if all confidences are known NP-hard if confidences are not known

(need to check for idempotence of negated tuples) Confidence computation

#P-complete

Complexity Results


Probabilistic & versioned TPC-H setting Queries over Lineitem, Orders tables

with varying join selectivity from 0.1% to 1% (6,000-60,000 and1,500-15,000 tuples for Lineitem & Orders)

Update 0.1% to 1% of the input data Assign probabilities within [0,1] uniform-randomly to

tuples

Additional indexes for versioning Two B+-trees on (start, end) and end points of intervals Rewrite valid-at & snapshot queries using

WHERE (start ≤ v ≤ end) predicates

Experiments – Setup


Experiments – Results (I)


Join query Overhead of versioned

system vs. non-versioned system (versions not computed)

Join query Overhead of

computing versions (versioned system)

(%)

Experiments – Results (II)


Join query Progressive data

updates (overwrite multiple times)

Join query Valid-at queries vs. full version

computation

Experiments – Results (III)


Overhead of version computation, different query types (1% data modified)

LDMs are closed and complete Generalizes to full ULDB data

model (including value alternatives & maybe (?) annotations)

Can employ lineage also for update propagations Supports all of

INSERT/DELETE/UPDATE with INTERSECT/UNION/EXCEPT set operations

Conclusions


Lineage

Uncertainty Versioning

DBMS

Documents

LIVE A lineage-supported, versioned DBMS Anish Das Sarma Martin Theobald Jennifer Widom