A Survey of the Data Complexity of Consistent Query Answering under Key Constraints

This paper adopts a very elementary representation of uncertainty. A relational database is called uncertain if it can violate primary key constraints. A repair of an uncertain database is obtained by selecting a maximal number of tuples without selecting two distinct tuples of the same relation that agree on their primary key. For any Boolean queryi¾?q, CERTAINTYq is the problem that takes an uncertain database db on input, and asks whether q is true in every repair of db. The complexity of these problems has been particularly studied for q ranging over the class of Boolean conjunctive queries. A research challenge is to solve the following complexity classification task: given q, determine whether CERTAINTYq belongs to complexity classes FO, P, or coNP-complete. The counting variant of CERTAINTYq, denoted $\sharp$ CERTAINTYq, asks to determine the exact number of repairs that satisfy q. This problem is related to query answering in probabilistic databases. This paper motivates the problems CERTAINTYq and $\sharp$ CERTAINTYq, surveys the progress made in the study of their complexity, and lists open problems. We also show a new result comparing complexity boundaries of both problems with one another.

[1]  Gaëlle Fontaine,et al.  Why is it Hard to Obtain a Dichotomy for Consistent Query Answering? , 2013, 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science.

[2]  Andrei A. Bulatov,et al.  The complexity of the counting constraint satisfaction problem , 2008, JACM.

[3]  Sergio Greco,et al.  Certain Query Answering in Partially Consistent Databases , 2014, Proc. VLDB Endow..

[4]  Leopoldo E. Bertossi,et al.  Database Repairing and Consistent Query Answering , 2011, Database Repairing and Consistent Query Answering.

[5]  Phokion G. Kolaitis,et al.  Efficient Querying of Inconsistent Databases with Binary Integer Programming , 2013, Proc. VLDB Endow..

[6]  Jef Wijsen,et al.  Database repairing using updates , 2005, TODS.

[7]  Jef Wijsen,et al.  Uncertainty That Counts , 2011, FQAS.

[8]  Jef Wijsen,et al.  Charting the tractability frontier of certain conjunctive query answering , 2013, PODS '13.

[9]  Jef Wijsen,et al.  Certain Conjunctive Query Answering in SQL , 2012, SUM.

[10]  Renée J. Miller,et al.  ConQuer: efficient management of inconsistent databases , 2005, SIGMOD '05.

[11]  Jan Chomicki,et al.  Consistent query answers in inconsistent databases , 1999, PODS '99.

[12]  Phokion G. Kolaitis,et al.  On the data complexity of consistent query answering , 2012, ICDT.

[13]  Jef Wijsen,et al.  A remark on the complexity of consistent conjunctive query answering under primary key violations , 2010, Inf. Process. Lett..

[14]  Leonid Libkin,et al.  Elements of Finite Model Theory , 2004, Texts in Theoretical Computer Science.

[15]  Christopher Ré,et al.  Queries and materialized views on probabilistic databases , 2011, J. Comput. Syst. Sci..

[16]  Jef Wijsen,et al.  A dichotomy in the complexity of counting database repairs , 2013, J. Comput. Syst. Sci..

[17]  Leonid Libkin,et al.  Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series) , 2004 .

[18]  Richard E. Ladner,et al.  On the Structure of Polynomial Time Reducibility , 1975, JACM.

[19]  Christopher Ré,et al.  Probabilistic databases: diamonds in the dirt , 2009, CACM.

[20]  Dan Suciu,et al.  A Dichotomy on the Complexity of Consistent Query Answering for Atoms with Simple Keys , 2012, ICDT.

[21]  Thomas Eiter,et al.  Database Theory - Icdt 2005 , 2008 .

[22]  Jef Wijsen,et al.  On the consistent rewriting of conjunctive queries under primary key constraints , 2007, Inf. Syst..

[23]  Jef Wijsen,et al.  On condensing database repairs obtained by tuple deletions , 2005, 16th International Workshop on Database and Expert Systems Applications (DEXA'05).

[24]  Martin E. Dyer,et al.  An Effective Dichotomy for the Counting Constraint Satisfaction Problem , 2010, SIAM J. Comput..

[25]  Jef Wijsen,et al.  Counting Database Repairs that Satisfy Conjunctive Queries with Self-Joins , 2019, ICDT.

[26]  Jef Wijsen,et al.  Certain conjunctive query answering in first-order logic , 2012, TODS.

[27]  Enela Pema.  Consistent Query Answering Of Conjunctive Queries Under Primary Key Constraints , 2014 .

[28]  Jeff Z. Pan,et al.  An Argument-Based Approach to Using Multiple Ontologies , 2009, SUM.

[29]  Catriel Beeri,et al.  On the Desirability of Acyclic Database Schemes , 1983, JACM.

[30]  Phokion G. Kolaitis,et al.  A dichotomy in the complexity of consistent query answering for queries with two atoms , 2012, Inf. Process. Lett..

[31]  Jef Wijsen,et al.  Project-Join-Repair: An Approach to Consistent Query Answering Under Functional Dependencies , 2006, FQAS.

[32]  Andrei A. Bulatov,et al.  Complexity of conservative constraint satisfaction problems , 2011, TOCL.

[33]  Dan Suciu,et al.  The dichotomy of probabilistic inference for unions of conjunctive queries , 2012, JACM.