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\newblock Trio: A system for data, uncertainty, and lineage.
\newblock In {\em VLDB}, pages 1151--1154, 2006.

\bibitem{AB15}
Antoine Amarilli, Pierre Bourhis, and Pierre Senellart.
\newblock Probabilities and provenance via tree decompositions.
\newblock {\em PODS}, 2015.

\bibitem{AD11d}
Yael Amsterdamer, Daniel Deutch, and Val Tannen.
\newblock Provenance for aggregate queries.
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\bibitem{Antova_fastand}
Lyublena Antova, Thomas Jansen, Christoph Koch, and Dan Olteanu.
\newblock Fast and simple relational processing of uncertain data.

\bibitem{AGM}
Albert Atserias, Martin Grohe, and D{\'{a}}niel Marx.
\newblock Size bounds and query plans for relational joins.
\newblock {\em {SIAM} J. Comput.}, 42(4):1737--1767, 2013.
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R.~Iris Bahar, Erica~A. Frohm, Charles~M. Gaona, Gary~D. Hachtel, Enrico Macii,
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\newblock Algebraic decision diagrams and their applications.
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\bibitem{DBLP:journals/pvldb/BeskalesIG10}
George Beskales, Ihab~F. Ilyas, and Lukasz Golab.
\newblock Sampling the repairs of functional dependency violations under hard
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\newblock {\em Proc. {VLDB} Endow.}, 3(1):197--207, 2010.

\bibitem{arith-complexity}
Peter Bürgisser, Michael Clausen, and Mohammad~Amin Shokrollahi.
\newblock {\em Algebraic complexity theory}, volume 315.
\newblock Springer, 1997.

\bibitem{chen-10-cswssr}
Hubie Chen and Martin Grohe.
\newblock Constraint satisfaction with succinctly specified relations.
\newblock {\em J. Comput. Syst. Sci.}, 76(8):847--860, 2010.

\bibitem{CHEN20061346}
Jianer Chen, Xiuzhen Huang, Iyad~A. Kanj, and Ge~Xia.
\newblock Strong computational lower bounds via parameterized complexity.
\newblock {\em Journal of Computer and System Sciences}, 72(8):1346--1367,
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\bibitem{k-match}
Radu Curticapean.
\newblock Counting matchings of size k is w[1]-hard.
\newblock In {\em ICALP}, volume 7965, pages 352--363, 2013.

\bibitem{DS07}
N.~Dalvi and D.~Suciu.
\newblock Efficient query evaluation on probabilistic databases.
\newblock {\em VLDB}, 16(4):544, 2007.

\bibitem{10.1145/1265530.1265571}
Nilesh Dalvi and Dan Suciu.
\newblock The dichotomy of conjunctive queries on probabilistic structures.
\newblock In {\em PODS}, pages 293--302, 2007.

\bibitem{DS12}
Nilesh Dalvi and Dan Suciu.
\newblock The dichotomy of probabilistic inference for unions of conjunctive
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\newblock {\em JACM}, 59(6):30, 2012.

\bibitem{heuvel-19-anappdsd}
Maarten~Van den Heuvel, Peter Ivanov, Wolfgang Gatterbauer, Floris Geerts, and
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\newblock Anytime approximation in probabilistic databases via scaled
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\newblock In {\em SIGMOD}, pages 1295--1312, 2019.

\bibitem{DM14c}
Daniel Deutch, Tova Milo, Sudeepa Roy, and Val Tannen.
\newblock Circuits for datalog provenance.
\newblock In {\em ICDT}, pages 201--212, 2014.

\bibitem{feng:2021:sigmod:efficient}
Su~Feng, Boris Glavic, Aaron Huber, and Oliver Kennedy.
\newblock Efficient uncertainty tracking for complex queries with
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\newblock In {\em SIGMOD}, 2021.

\bibitem{feng:2019:sigmod:uncertainty}
Su~Feng, Aaron Huber, Boris Glavic, and Oliver Kennedy.
\newblock Uncertainty annotated databases - a lightweight approach for
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\newblock In {\em SIGMOD}, 2019.

\bibitem{FH12}
Robert Fink, Larisa Han, and Dan Olteanu.
\newblock Aggregation in probabilistic databases via knowledge compilation.
\newblock {\em PVLDB}, 5(5):490--501, 2012.

\bibitem{FH13}
Robert Fink, Jiewen Huang, and Dan Olteanu.
\newblock Anytime approximation in probabilistic databases.
\newblock {\em VLDBJ}, 22(6):823--848, 2013.

\bibitem{FO16}
Robert Fink and Dan Olteanu.
\newblock Dichotomies for queries with negation in probabilistic databases.
\newblock {\em TODS}, 41(1):4:1--4:47, 2016.

\bibitem{10.5555/645413.652181}
J\"{o}rg Flum and Martin Grohe.
\newblock The parameterized complexity of counting problems.
\newblock In {\em Proceedings of the 43rd Symposium on Foundations of Computer
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\bibitem{param-comp}
J{\"{o}}rg Flum and Martin Grohe.
\newblock {\em Parameterized Complexity Theory}.
\newblock Texts in Theoretical Computer Science. An {EATCS} Series. Springer,
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\bibitem{DBLP:books/daglib/0020812}
Hector Garcia{-}Molina, Jeffrey~D. Ullman, and Jennifer Widom.
\newblock {\em Database systems - the complete book {(2.} ed.)}.
\newblock Pearson Education, 2009.

\bibitem{graetzer-08-un}
George Gr{\"a}tzer.
\newblock {\em Universal algebra}.
\newblock Springer Science \& Business Media, 2008.

\bibitem{DBLP:conf/pods/GreenKT07}
Todd~J. Green, Gregory Karvounarakis, and Val Tannen.
\newblock Provenance semirings.
\newblock In {\em PODS}, pages 31--40, 2007.

\bibitem{GT06}
Todd~J Green and Val Tannen.
\newblock Models for incomplete and probabilistic information.
\newblock In {\em EDBT}, pages 278--296. 2006.

\bibitem{Imielinski1989IncompleteII}
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\newblock Incomplete information in relational databases.
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\bibitem{IL84a}
Tomasz Imieli\'nski and Witold Lipski~Jr.
\newblock Incomplete information in relational databases.
\newblock {\em JACM}, 31(4):761--791, 1984.

\bibitem{jha-12-pdwm}
Abhay~Kumar Jha and Dan Suciu.
\newblock Probabilistic databases with markoviews.
\newblock {\em PVLDB}, 5(11):1160--1171, 2012.

\bibitem{DBLP:journals/jal/KarpLM89}
Richard~M. Karp, Michael Luby, and Neal Madras.
\newblock Monte-carlo approximation algorithms for enumeration problems.
\newblock {\em J. Algorithms}, 10(3):429--448, 1989.

\bibitem{kenig-13-nclexpdc}
Batya Kenig, Avigdor Gal, and Ofer Strichman.
\newblock A new class of lineage expressions over probabilistic databases
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\newblock In {\em SUM}, volume 8078, pages 219--232, 2013.

\bibitem{kennedy:2010:icde:pip}
Oliver Kennedy and Christoph Koch.
\newblock Pip: A database system for great and small expectations.
\newblock In {\em ICDE}, 2010.

\bibitem{DBLP:conf/pods/KhamisNR16}
Mahmoud~Abo Khamis, Hung~Q. Ngo, and Atri Rudra.
\newblock Faq: Questions asked frequently.
\newblock In {\em PODS}, pages 13--28, 2016.

\bibitem{triang-hard}
Tsvi Kopelowitz and Virginia~Vassilevska Williams.
\newblock Towards optimal set-disjointness and set-intersection data
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\newblock In {\em ICALP}, volume 168, pages 74:1--74:16, 2020.

\bibitem{kumari:2016:qdb:communicating}
Poonam Kumari, Said Achmiz, and Oliver Kennedy.
\newblock Communicating data quality in on-demand curation.
\newblock In {\em QDB}, 2016.

\bibitem{ngo-survey}
Hung~Q. Ngo.
\newblock Worst-case optimal join algorithms: Techniques, results, and open
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\newblock In {\em PODS}, 2018.

\bibitem{skew}
Hung~Q. Ngo, Christopher Ré, and Atri Rudra.
\newblock Skew strikes back: new developments in the theory of join algorithms.
\newblock {\em SIGMOD Rec.}, 42(4):5--16, 2013.

\bibitem{DBLP:conf/icde/OlteanuHK10}
Dan Olteanu, Jiewen Huang, and Christoph Koch.
\newblock Approximate confidence computation in probabilistic databases.
\newblock In {\em ICDE}, pages 145--156, 2010.

\bibitem{factorized-db}
Dan Olteanu and Maximilian Schleich.
\newblock Factorized databases.
\newblock {\em SIGMOD Rec.}, 45(2):5--16, 2016.

\bibitem{DBLP:journals/pvldb/RekatsinasCIR17}
Theodoros Rekatsinas, Xu~Chu, Ihab~F. Ilyas, and Christopher R{\'{e}}.
\newblock Holoclean: Holistic data repairs with probabilistic inference.
\newblock {\em Proc. {VLDB} Endow.}, 10(11):1190--1201, 2017.

\bibitem{roy-11-f}
Sudeepa Roy, Vittorio Perduca, and Val Tannen.
\newblock Faster query answering in probabilistic databases using read-once
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\newblock In {\em ICDT}, 2011.

\bibitem{RS07}
C.~Ré and D.~Suciu.
\newblock Materialized views in probabilistic databases: for information
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\newblock In {\em VLDB}, pages 51--62, 2007.

\bibitem{DBLP:journals/vldb/SaRR0W0Z17}
Christopher~De Sa, Alexander Ratner, Christopher R{\'{e}}, Jaeho Shin, Feiran
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\newblock Incremental knowledge base construction using deepdive.
\newblock {\em {VLDB} J.}, 26(1):81--105, 2017.

\bibitem{sen-10-ronfqevpd}
Prithviraj Sen, Amol Deshpande, and Lise Getoor.
\newblock Read-once functions and query evaluation in probabilistic databases.
\newblock {\em PVLDB}, 3(1):1068--1079, 2010.

\bibitem{S18a}
Pierre Senellart.
\newblock Provenance and probabilities in relational databases.
\newblock {\em SIGMOD Record}, 46(4):5--15, 2018.

\bibitem{valiant-79-cenrp}
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\newblock The complexity of enumeration and reliability problems.
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\bibitem{VS17}
Guy Van~den Broeck and Dan Suciu.
\newblock Query processing on probabilistic data: A survey.
\newblock 2017.

\bibitem{virgi-survey}
Virginia~Vassilevska Williams.
\newblock Some open problems in fine-grained complexity.
\newblock {\em {SIGACT} News}, 49(4):29--35, 2018.
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\bibitem{yang:2015:pvldb:lenses}
Ying Yang, Niccolò Meneghetti, Ronny Fehling, Zhen~Hua Liu, Dieter Gawlick,
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\newblock Lenses: An on-demand approach to etl.
\newblock {\em PVLDB}, 8(12):1578--1589, 2015.

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