database tuples play cooperative games
TRANSCRIPT
Database Tuples Play Cooperative Games
Ester Livshits
Joint work with:
Leopoldo Bertossi, Benny Kimelfeld, Alon Reshef, Moshe Sebag
Ester Livshits Oxford Data and Knowledge Seminar 2
AUTHOR
Name Affiliation
Alice UCLA
Bob NYU
Cathy MIT
David UCSD
Ellen NYU
INSTITUTE
Name STATE
UCLA CA
UCSD CA
NYU NY
MIT MA
PUBLICAION
Author Paper
Alice A
Alice B
Bob C
Cathy C
Cathy D
David C
CITATIONS
PAPER CITS
A 18
B 2
C 8
D 12
𝑞 𝑧, 𝑤 :−AUTHOR 𝑥, 𝑦 , INSTITUE 𝑦, ′CA′ , PUBLICATION 𝑥, 𝑧 , CITATIONS 𝑧, 𝑤
PAPER CITS
A 18
B 2
C 8
Why we obtained a
particular answer?
Why we did not obtain
some other answer?
Ester Livshits Oxford Data and Knowledge Seminar 3
AUTHOR
Name Affiliation
Alice UCLA
Bob NYU
Cathy MIT
David UCSD
Ellen NYU
INSTITUTE
Name STATE
UCLA CA
UCSD CA
NYU NY
MIT MA
PUBLICAION
Author Paper
Alice A
Alice B
Bob C
Cathy C
Cathy D
David C
CITATIONS
PAPER CITS
A 18
B 2
C 8
D 12
𝑞 𝑧, 𝑤 :−AUTHOR 𝑥, 𝑦 , INSTITUE 𝑦, ′CA′ , PUBLICATION 𝑥, 𝑧 , CITATIONS 𝑧, 𝑤
PAPER CITS
A 18
B 2
C 8
Why we obtained a
particular answer?
Why we did not obtain
some other answer?
Ester Livshits Oxford Data and Knowledge Seminar 4
Which tuples in the database
explain the query result?
Measuring Contribution
➢ Causal responsibility [Meliou et al. 2010]
❖ 𝑡 is a counterfactual cause for 𝑞 if 𝐷 ⊨ 𝑞 and 𝐷 ∖ {𝑡} ⊨ 𝑞
❖ 𝑡 is an actual cause for 𝑞 if 𝐷 ∖ Γ ⊨ 𝑞 and 𝐷 ∖ {Γ ∪ {𝑡}} ⊨ 𝑞for some Γ ⊆ 𝐷 ∖ {𝑡}
❖ The responsibility of 𝑡 is 1
1+|Γmin|
➢ Not extendable to aggregate queries
➢ May be counterintuitive
Ester Livshits Oxford Data and Knowledge Seminar 5
Is there a path from a to b?
Contingency
set
Measuring Contribution
➢ Causal effect [Salimi et al. 2016]
❖ See the database as a probabilistic database
❖ CE 𝑡 = E 𝑞 𝑡 ∈ 𝐷) − E 𝑞 𝑡 ∉ 𝐷)
Ester Livshits Oxford Data and Knowledge Seminar 6
What makes the choice of a contribution score a good one?
Shapley Value
➢ A widely known profit-sharing formula in cooperative game theory
➢ Introduced by Lloyd Shapley in 1953
➢ Applied in various areas beyond cooperative game theory:
❖ Pollution responsibility in environmental management
❖ Influence measurement in social network analysis
❖ Identifying candidate autism genes
❖ Bargaining foundations in economics
❖ Takeover corporate rights in law
❖ Explanations in machine learning
Ester Livshits Oxford Data and Knowledge Seminar 7
Shapley Value
Ester Livshits 8
Set 𝐴 of players: Wealth function 𝑣:𝒫 𝐴 → ℝ:
3
7
42
How to distribute the total
wealth among the players?
Machine learning
Query answering
Inconsistency
Features Prediction
Tuples Answer
Tuples Measure
[Lundberg, Lee 2017]
[L, Kimelfeld 2021]
[L et al. 2020]
Oxford Data and Knowledge Seminar
Shapley Value
Ester Livshits Oxford Data and Knowledge Seminar 9
Shapley 𝐴, 𝑣, 𝑎 =
𝐵⊆𝐴∖{𝑎}
𝐵 ! 𝐴 − 𝐵 − 1 !
𝐴 !𝑣 𝐵 ∪ 𝑎 − 𝑣 𝐵
72
21 25
+4
The Shapley value is the expected delta
due to the addition in a random permutation
Shapley Value for Database Queries
➢ Which tuples in the database explain the query result?
Ester Livshits Oxford Data and Knowledge Seminar 10
AUTHOR
Name Affiliation
Alice UCLA
Bob NYU
Cathy MIT
David UCSD
Ellen NYU
INSTITUTE
Name STATE
UCLA CA
UCSD CA
NYU NY
MIT MA
PUBLICAION
Author Paper
Alice A
Alice B
Bob C
Cathy C
Cathy D
David C
CITATIONS
PAPER CITS
A 18
B 2
C 8
D 12
𝑞 𝑧, 𝑤 :−AUTHOR 𝑥, 𝑦 , PUBLICATION 𝑥, 𝑧 , CITATIONS(𝑧, 𝑤)
SUM𝑤⟨𝑞 𝑧, 𝑤 ⟩
Players
Wealth function
𝑆𝑉 𝐴𝑙𝑖𝑐𝑒 = 20𝑆𝑉 𝐶𝑎𝑡ℎ𝑦 = 14.67𝑆𝑉 𝐵𝑜𝑏 = 2.67𝑆𝑉 𝐷𝑎𝑣𝑖𝑑 = 2.67𝑆𝑉 𝐸𝑙𝑙𝑒𝑛 = 0
Ester Livshits Oxford Data and Knowledge Seminar 11
AUTHOR
Name Affiliation
Alice UCLA
Bob NYU
Cathy MIT
David UCSD
Ellen NYU
INSTITUTE
Name STATE
UCLA CA
UCSD CA
NYU NY
MIT MA
PUBLICAION
Author Paper
Alice A
Alice B
Bob C
Cathy C
Cathy D
David C
CITATIONS
PAPER CITS
A 18
B 2
C 8
D 12
𝑞 𝑧, 𝑤 :−AUTHOR 𝑥, 𝑦 , INSTITUE 𝑦, ′CA′ , PUBLICATION 𝑥, 𝑧 , CITATIONS 𝑧, 𝑤
PAPER CITS
A 18
B 2
C 8
Ester Livshits Oxford Data and Knowledge Seminar 12
AUTHOR
Name Affiliation
Alice UCLA
Bob NYU
Cathy MIT
David UCSD
Ellen NYU
INSTITUTE
Name STATE
UCLA CA
UCSD CA
NYU NY
MIT MA
PUBLICAION
Author Paper
Alice A
Alice B
Bob C
Cathy C
Cathy D
David C
CITATIONS
PAPER CITS
A 18
B 2
C 8
D 12
𝑞 𝑧, 𝑤 :−AUTHOR 𝑥, 𝑦 , INSTITUE 𝑦, ′CA′ , PUBLICATION 𝑥, 𝑧 , CITATIONS 𝑧, 𝑤
PAPER CITS
A 18
B 2
C 8
𝑞():−AUTHOR 𝑥, 𝑦 , INSTITUE 𝑦, ′CA′ , PUBLICATION 𝑥, ′A′ , CITATIONS ′A′, 18
➢ Explaining Query Answers
➢ Computational Complexity
➢ Responsibility to Inconsistency
Outline
Ester Livshits Oxford Data and Knowledge Seminar 13
Computational Complexity
Ester Livshits Oxford Data and Knowledge Seminar 14
➢ A CQ 𝑞 is hierarchical if for every two existential variables 𝑥 and 𝑦:
❖ 𝐴𝑡𝑜𝑚𝑠 𝑥 ⊆ 𝐴𝑡𝑜𝑚𝑠 𝑦 or
❖ 𝐴𝑡𝑜𝑚𝑠 𝑦 ⊆ 𝐴𝑡𝑜𝑚𝑠 𝑥 or
❖ 𝐴𝑡𝑜𝑚𝑠 𝑥 ∩ 𝐴𝑡𝑜𝑚𝑠 𝑦 = ∅
𝑞1():−𝑅 𝑥, 𝑦 , 𝑆(𝑥, 𝑧)
Query Hierarchical Non-hierarchical
SJFCQ PTIME FP#P-complete
SJFCQ with
negationsPTIME FP#P-complete
sum \ count PTIME FP#P-complete
[L et al.
ICDT 2020]
[Reshef et al.
PODS 2020]
𝑞():−AUTHOR 𝑥, 𝑦 , INSTITUTE 𝑦, ′CA′ , PUBLICATION 𝑥, 𝑧
𝑦 𝑧
𝑥
Computational Complexity
Ester Livshits Oxford Data and Knowledge Seminar 15
➢ A CQ 𝑞 is hierarchical if for every two existential variables 𝑥 and 𝑦:
❖ 𝐴𝑡𝑜𝑚𝑠 𝑥 ⊆ 𝐴𝑡𝑜𝑚𝑠 𝑦 or
❖ 𝐴𝑡𝑜𝑚𝑠 𝑦 ⊆ 𝐴𝑡𝑜𝑚𝑠 𝑥 or
❖ 𝐴𝑡𝑜𝑚𝑠 𝑥 ∩ 𝐴𝑡𝑜𝑚𝑠 𝑦 = ∅
Query Hierarchical Non-hierarchical
SJFCQ PTIME FP#P-complete
SJFCQ with
negationsPTIME FP#P-complete
sum \ count PTIME FP#P-complete
𝑞2():−𝑅 𝑥 , 𝑆 𝑥, 𝑦 , 𝑇(𝑦)
[L et al.
ICDT 2020]
[Reshef et al.
PODS 2020]
𝑞():−AUTHOR 𝑥, 𝑦 , INSTITUTE 𝑦, ′CA′ , PUBLICATION 𝑥, 𝑧
𝑦
𝑥
Conjunctive Queries
➢ To prove hardness, we consider the simplest non-hierarchical query
𝑞𝑅𝑆𝑇(): −𝑅 𝑥 , 𝑆 𝑥, 𝑦 , 𝑇(𝑦)
➢ Reduction from counting independent sets in a bipartite graph
Ester Livshits Oxford Data and Knowledge Seminar 16
R S T
Conjunctive Queries
➢ Each instance provides us with an equation over |IS(𝑔, 𝑘)|
➢ |IS(𝑔, 𝑘)| - number of independent sets of size 𝑘 in 𝑔
Ester Livshits Oxford Data and Knowledge Seminar 17
Computational Complexity
Ester Livshits Oxford Data and Knowledge Seminar 18
➢ A CQ 𝑞 is hierarchical if for every two existential variables 𝑥 and 𝑦:
❖ 𝐴𝑡𝑜𝑚𝑠 𝑥 ⊆ 𝐴𝑡𝑜𝑚𝑠 𝑦 or
❖ 𝐴𝑡𝑜𝑚𝑠 𝑦 ⊆ 𝐴𝑡𝑜𝑚𝑠 𝑥 or
❖ 𝐴𝑡𝑜𝑚𝑠 𝑥 ∩ 𝐴𝑡𝑜𝑚𝑠 𝑦 = ∅
Query Hierarchical Non-hierarchical
SJFCQ PTIME FP#P-complete
SJFCQ with
negationsPTIME FP#P-complete
sum \ count PTIME FP#P-complete
[L et al.
ICDT 2020]
[Reshef et al.
PODS 2020]
𝑞():−AUTHOR 𝑥, 𝑦 , ¬INSTITUTE 𝑦, ′CA′ , PUBLICATION 𝑥, 𝑧
Computational Complexity
Ester Livshits Oxford Data and Knowledge Seminar 19
➢ A CQ 𝑞 is hierarchical if for every two existential variables 𝑥 and 𝑦:
❖ 𝐴𝑡𝑜𝑚𝑠 𝑥 ⊆ 𝐴𝑡𝑜𝑚𝑠 𝑦 or
❖ 𝐴𝑡𝑜𝑚𝑠 𝑦 ⊆ 𝐴𝑡𝑜𝑚𝑠 𝑥 or
❖ 𝐴𝑡𝑜𝑚𝑠 𝑥 ∩ 𝐴𝑡𝑜𝑚𝑠 𝑦 = ∅
Query Hierarchical Non-hierarchical
SJFCQ PTIME FP#P-complete
SJFCQ with
negationsPTIME FP#P-complete
sum \ count PTIME FP#P-complete
[L et al.
ICDT 2020]
[Reshef et al.
PODS 2020]
𝑞 𝑧, 𝑤 :−AUTHOR 𝑥, 𝑦 , PUBLICATION 𝑥, 𝑧 , CITATIONS(𝑧, 𝑤)SUM𝑤⟨𝑞 𝑧, 𝑤 ⟩
Computational Complexity
Ester Livshits Oxford Data and Knowledge Seminar 20
➢ A CQ 𝑞 is hierarchical if for every two existential variables 𝑥 and 𝑦:
❖ 𝐴𝑡𝑜𝑚𝑠 𝑥 ⊆ 𝐴𝑡𝑜𝑚𝑠 𝑦 or
❖ 𝐴𝑡𝑜𝑚𝑠 𝑦 ⊆ 𝐴𝑡𝑜𝑚𝑠 𝑥 or
❖ 𝐴𝑡𝑜𝑚𝑠 𝑥 ∩ 𝐴𝑡𝑜𝑚𝑠 𝑦 = ∅
Query Hierarchical Non-hierarchical
SJFCQ PTIME FP#P-complete
SJFCQ with
negationsPTIME FP#P-complete
sum \ count PTIME FP#P-complete
[L et al.
ICDT 2020]
[Reshef et al.
PODS 2020]
𝑞 𝑧, 𝑤 :−AUTHOR 𝑥, 𝑦 , PUBLICATION 𝑥, 𝑧 , CITATIONS(𝑧, 𝑤)MAX𝑤⟨𝑞 𝑧, 𝑤 ⟩, MIN𝑤⟨𝑞 𝑧, 𝑤 ⟩, AVERAGE𝑤⟨𝑞 𝑧, 𝑤 ⟩
Hardness can be extended to
general numerical queries
➢ Computing the Shapley value is often hard
➢ The picture is more positive when allowing approximation
➢ Generalizes to unions of CQs
Approximation Complexity
Ester Livshits Oxford Data and Knowledge Seminar 21
Pr𝑓(𝑥)
1 + 𝜖≤ 𝐴 𝑥, 𝜖, 𝛿 ≤ (1 + 𝜖)𝑓(𝑥) ≥ 1 − 𝛿
Query Hierarchical Non-hierarchical
SJFCQ PTIME FPRAS
sum \ count PTIME FPRAS
➢ Additive approximation via Monte Carlo sampling
➢ Also a multiplicative approximation due to the “gap property”
➢ Does not hold when allowing negation
➢ Negation fundamentally changes the complexity picture!
Approximation Complexity
Ester Livshits Oxford Data and Knowledge Seminar 22
Pr 𝑓 𝑥 − 𝜖 ≤ 𝐴 𝑥, 𝜖, 𝛿 ≤ 𝑓 𝑥 + 𝜖 ≥ 1 − 𝛿
For every tuple 𝑡 in the database 𝐷:
Shapley(𝑡)=0 or Shapley(𝑡)≥1
𝑝(|𝐷|)
➢ With negation, the contribution can be negative
Approximation Complexity
Ester Livshits Oxford Data and Knowledge Seminar 23
Register
Student Course
Alice OS
Alice AI
Bob OS
Cathy DB
Cathy IC
Student
Name
Alice
Bob
Cathy
David
TA
Name
Alice
Bob
David
𝑞(): −Student 𝑥 , ¬TA 𝑥 , Register(𝑥, 𝑦)
In some cases, deciding whether Shapley(𝑡)≠0 is hard
➢ Causal effect [Salimi et al. 2016]
❖ See the database as a probabilistic database
❖ CE 𝑡 = E 𝑞 𝑡 ∈ 𝐷) − E 𝑞 𝑡 ∉ 𝐷)
➢ Coincides with the Banzhaf Power Index [Banzhaf 1965]
➢ Our complexity results extend to this measure
Ester Livshits Oxford Data and Knowledge Seminar
Banzhaf Power Index
24
➢ Explaining Query Answers
➢ Computational Complexity
➢ Responsibility to Inconsistency
Outline
Ester Livshits Oxford Data and Knowledge Seminar 25
Inconsistent Databases➢ A database is inconsistent if it violates integrity constraints
Ester Livshits Oxford Data and Knowledge Seminar 26
Cullen Douglas
dbo:birthPlace
▪ dbr:California
▪ dbr:Florida
Marion Jones
dbo:height
▪ 1.524
▪ 1.778
Irene Tedrow
dbo:deathPlace
▪ dbr:California
▪ dbr:Hollywood,_Los_Angeles
▪ dbr:New_York_City
Inconsistent Databases
Ester Livshits Oxford Data and Knowledge Seminar 27
➢ Imprecise data sources
❖ Crowd, Web pages, social encyclopedias, sensors, …
➢ Imprecise data generation
❖ natural-language processing, sensor/signal processing, image recognition, …
➢ Conflicts in data integration
❖ Crowd + enterprise data + KB + Web + ...
➢ Data staleness
❖ Entities change address, status, ...
➢ And so on…
Ester Livshits Oxford Data and Knowledge Seminar 28
Idea:
Quantify the extent to which
integrity constraints are violated
Reliability estimationHow reliable is a new data source?
Progress indicationProgress bar for data repairing
Action prioritizationWhich tuples are mostly
responsible for inconsistency?
Ester Livshits Oxford Data and Knowledge Seminar 29
How can we quantify the
responsibility of individual tuples
to inconsistency?
Inconsistency measure
Responsibility sharing
mechanism
Ester Livshits Oxford Data and Knowledge Seminar 30
How can we quantify the
responsibility of individual tuples
to inconsistency?
Inconsistency measure
Responsibility sharing
mechanism
How to Measure Inconsistency?
➢ Several measures proposed by the KR and DB communities
❖ The drastic measure – 1 if inconsistent, 0 otherwise [Thimm 2017]
❖ #minimal inconsistent subsets [Hunter and Konieczny 2008]
❖ #problematic tuples [Grant and Hunter 2011]
❖ Minimal #tuples to remove to satisfy the constraints [Grant and Hunter 2013], [Bertossi 2018]
❖ #maximal consistent subsets [Grant and Hunter 2011]
➢ What makes a measure a good one? [L et al. SIGMOD 2021]
Ester Livshits Oxford Data and Knowledge Seminar 31
Ester Livshits Oxford Data and Knowledge Seminar 32
How can we quantify the
responsibility of individual tuples
to inconsistency?
Inconsistency measure
Responsibility sharing
mechanism
Shapley Value
Computational Complexity
Ester Livshits Oxford Data and Knowledge Seminar 33
Measure lhs chainNo lhs chain,
tractable c-repairother
drastic PTIME FP#P-complete
#min-
inconsistentPTIME
#problematic
tuplesPTIME
cardinality
repairPTIME Open NP-hard
#repairs PTIME FP#P-complete
FD: birthCity → birthState
Tractable Measures
Ester Livshits Oxford Data and Knowledge Seminar 34
➢ 𝐼𝑀𝐼 - Number of minimal inconsistent subsets
𝑓4
Train Departs Arrives Time Duration
𝑓1 16 NYP BBY 1030 315
𝑓2 16 NYP PVD 1030 250
𝑓3 16 PHL WIL 1030 20
𝑓4 16 PHL BAL 1030 70
𝑓5 16 PHL WAS 1030 120
𝑓6 16 BBY PHL 1030 260
𝑓7 16 BBY NYP 1030 260
𝑓8 16 BBY WAS 1030 420
𝑓9 16 WAS PVD 1030 390
Train Time → Departs
Train Time Duration → Arrives
𝑓7 𝑓1 𝑓3 𝑓9 𝑓2 𝑓5 𝑓8 𝑓6
Tractable Measures
Ester Livshits Oxford Data and Knowledge Seminar 35
➢ 𝐼𝑀𝐼 - Number of minimal inconsistent subsets
𝑓4
Train Departs Arrives Time Duration
𝑓1 16 NYP BBY 1030 315
𝑓2 16 NYP PVD 1030 250
𝑓3 16 PHL WIL 1030 20
𝑓4 16 PHL BAL 1030 70
𝑓5 16 PHL WAS 1030 120
𝑓6 16 BBY PHL 1030 260
𝑓7 16 BBY NYP 1030 260
𝑓8 16 BBY WAS 1030 420
𝑓9 16 WAS PVD 1030 390
Train Time → Departs
Train Time Duration → Arrives
𝑓7 𝑓1 𝑓3 𝑓9 𝑓2 𝑓5 𝑓8 𝑓6
+2
𝑓 increases the value of 𝐼𝑀𝐼 by 𝑘 if
𝑘 of the previous tuples conflict with it
Tractable Measures
Ester Livshits Oxford Data and Knowledge Seminar 36
➢ 𝐼𝑃 - Number of problematic tuples
𝑓4
Train Departs Arrives Time Duration
𝑓1 16 NYP BBY 1030 315
𝑓2 16 NYP PVD 1030 250
𝑓3 16 PHL WIL 1030 20
𝑓4 16 PHL BAL 1030 70
𝑓5 16 PHL WAS 1030 120
𝑓6 16 BBY PHL 1030 260
𝑓7 16 BBY NYP 1030 260
𝑓8 16 BBY WAS 1030 420
𝑓9 16 WAS PVD 1030 390
Train Time → Departs
Train Time Duration → Arrives
𝑓7 𝑓1 𝑓3 𝑓9 𝑓2 𝑓5 𝑓8 𝑓6
+1
𝑓 increases the value of 𝐼𝑝 by 𝑘 if
(𝑘 − 1) of the previous tuples:
(1) conflict with 𝑓,
(2) do not conflict with other
tuples that occur before 𝑓.
Computational Complexity
Ester Livshits Oxford Data and Knowledge Seminar 37
Measure lhs chainNo lhs chain,
tractable c-repairother
drastic PTIME FP#P-complete
#min-
inconsistentPTIME
#problematic
tuplesPTIME
cardinality
repairPTIME Open NP-hard
#repairs PTIME FP#P-complete
{𝑩 → 𝐴,𝑩𝑪 → 𝐷,𝑩𝑪𝑮 → 𝐸,𝑩𝑪𝑭 → 𝐻}
𝐵 ⊆ 𝐵, 𝐶 ⊆ {𝐵, 𝐶, 𝐹} 𝐵, 𝐶, 𝐺 ⊈ 𝐵, 𝐶, 𝐹 , {𝐵, 𝐶, 𝐹}⊈ 𝐵, 𝐶, 𝐺
{𝑩 → 𝐴,𝑩𝑪 → 𝐷,𝑩𝑪𝑭 → 𝐸}
Left-Hand Side Chain
Ester Livshits Oxford Data and Knowledge Seminar 38
Train Departs Arrives Time Duration
𝑓1 16 NYP BBY 1030 315
𝑓2 16 NYP PVD 1030 250
𝑓3 16 PHL WIL 1030 20
𝑓4 16 PHL BAL 1030 70
𝑓5 16 PHL WAS 1030 120
𝑓6 16 BBY PHL 1030 260
𝑓7 16 BBY NYP 1030 260
𝑓8 16 BBY WAS 1030 420
𝑓9 16 WAS PVD 1030 390
Train Time → Departs
Train Time Duration → Arrives
PVD
Train, Time
Departs
Duration
NYP PHL BBY WAS
16, 1030
315 250 20 70 120 260 420 390
BBY PVD WIL BAL WAS PHL NYP WAS
Arrives
Independent
branchesConflicting
branches
Computational Complexity
Ester Livshits Oxford Data and Knowledge Seminar 39
Measure lhs chainNo lhs chain,
tractable c-repairother
drastic PTIME FP#P-complete
#min-
inconsistentPTIME
#problematic
tuplesPTIME
cardinality
repairPTIME Open NP-hard
#repairs PTIME FP#P-complete
{𝑩 → 𝐴,𝑩𝑪 → 𝐷,𝑩𝑪𝑮 → 𝐸,𝑩𝑪𝑭 → 𝐻}
𝐵 ⊆ 𝐵𝐶 ⊆ {𝐵𝐶𝐹} 𝐵𝐶𝐺 ⊈ 𝐵𝐶𝐹 , {𝐵𝐶𝐹}⊈ 𝐵𝐶𝐺
{𝑩 → 𝐴,𝑩𝑪 → 𝐷,𝑩𝑪𝑭 → 𝐸}
Efficiency: σ𝑎∈𝐴 Shapley 𝐴, 𝑣, 𝑎 = 𝑣(𝐴)
Approximation Complexity
Ester Livshits Oxford Data and Knowledge Seminar 40
Measure lhs chainNo lhs chain,
tractable c-repairother
drastic PTIME FPRAS
#min-
inconsistentPTIME
#problematic
tuplesPTIME
cardinality
repairPTIME FPRAS No FPRAS
#repairs PTIME Open
Would imply an FPRAS for #MIS in a bipartite
graph – long standing open problem
➢ Two situations where we wish to quantify the responsibility of tuples:
❖ Query answering
❖ Database inconsistency
➢ We treat the contribution from the viewpoint of game theory
➢ We investigated the computational complexity
Ester Livshits Oxford Data and Knowledge Seminar
Concluding Remarks
41
Ester Livshits Oxford Data and Knowledge Seminar 42
Thank you for listening!
Questions?