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343
aaron.bib
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@ -1,343 +0,0 @@
@misc{pdbench,
title = {pdbench},
howpublished = {\url{http://pdbench.sourceforge.net/}},
note = {Accessed: 2020-12-15}
}
@MISC{Antova_fastand,
author = {Lyublena Antova and Thomas Jansen and Christoph Koch and Dan Olteanu},
title = {Fast and Simple Relational Processing of Uncertain Data},
year = {}
}
@book{DBLP:series/synthesis/2011Suciu,
author = {Dan Suciu and
Dan Olteanu and
Christopher R{\'{e}} and
Christoph Koch},
title = {Probabilistic Databases},
series = {Synthesis Lectures on Data Management},
publisher = {Morgan {\&} Claypool Publishers},
year = {2011},
url = {https://doi.org/10.2200/S00362ED1V01Y201105DTM016},
doi = {10.2200/S00362ED1V01Y201105DTM016},
timestamp = {Tue, 16 May 2017 14:24:20 +0200},
biburl = {https://dblp.org/rec/series/synthesis/2011Suciu.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{10.1145/1265530.1265571,
author = {Dalvi, Nilesh and Suciu, Dan},
title = {The Dichotomy of Conjunctive Queries on Probabilistic Structures},
year = {2007},
isbn = {9781595936851},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi-org.gate.lib.buffalo.edu/10.1145/1265530.1265571},
doi = {10.1145/1265530.1265571},
abstract = {We show that for every conjunctive query, the complexity of evaluating it on a probabilistic database is either PTIME or P-complete, and we give an algorithm for deciding whether a given conjunctive query is PTIME or P-complete. The dichotomy property is a fundamental result on query evaluation on probabilistic databases and it gives a complete classification of the complexity of conjunctive queries.},
booktitle = {Proceedings of the Twenty-Sixth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems},
pages = {293–302},
numpages = {10},
keywords = {probabilistic databases, dichotomy, conjunctive queries},
location = {Beijing, China},
series = {PODS '07}
}
@inproceedings{DBLP:conf/icde/OlteanuHK10,
author = {Dan Olteanu and
Jiewen Huang and
Christoph Koch},
editor = {Feifei Li and
Mirella M. Moro and
Shahram Ghandeharizadeh and
Jayant R. Haritsa and
Gerhard Weikum and
Michael J. Carey and
Fabio Casati and
Edward Y. Chang and
Ioana Manolescu and
Sharad Mehrotra and
Umeshwar Dayal and
Vassilis J. Tsotras},
title = {Approximate confidence computation in probabilistic databases},
booktitle = {Proceedings of the 26th International Conference on Data Engineering,
{ICDE} 2010, March 1-6, 2010, Long Beach, California, {USA}},
pages = {145--156},
publisher = {{IEEE} Computer Society},
year = {2010},
url = {https://doi.org/10.1109/ICDE.2010.5447826},
doi = {10.1109/ICDE.2010.5447826},
timestamp = {Wed, 16 Oct 2019 14:14:56 +0200},
biburl = {https://dblp.org/rec/conf/icde/OlteanuHK10.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/icde/AntovaKO07a,
author = {Lyublena Antova and
Christoph Koch and
Dan Olteanu},
editor = {Rada Chirkova and
Asuman Dogac and
M. Tamer {\"{O}}zsu and
Timos K. Sellis},
title = {MayBMS: Managing Incomplete Information with Probabilistic World-Set
Decompositions},
booktitle = {Proceedings of the 23rd International Conference on Data Engineering,
{ICDE} 2007, The Marmara Hotel, Istanbul, Turkey, April 15-20, 2007},
pages = {1479--1480},
publisher = {{IEEE} Computer Society},
year = {2007},
url = {https://doi.org/10.1109/ICDE.2007.369042},
doi = {10.1109/ICDE.2007.369042},
timestamp = {Wed, 16 Oct 2019 14:14:56 +0200},
biburl = {https://dblp.org/rec/conf/icde/AntovaKO07a.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/sigmod/BoulosDMMRS05,
author = {Jihad Boulos and
Nilesh N. Dalvi and
Bhushan Mandhani and
Shobhit Mathur and
Christopher R{\'{e}} and
Dan Suciu},
editor = {Fatma {\"{O}}zcan},
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of Data, Baltimore, Maryland, USA, June 14-16, 2005},
pages = {891--893},
publisher = {{ACM}},
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url = {https://doi.org/10.1145/1066157.1066277},
doi = {10.1145/1066157.1066277},
timestamp = {Tue, 06 Nov 2018 11:07:39 +0100},
biburl = {https://dblp.org/rec/conf/sigmod/BoulosDMMRS05.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/sigmod/SinghMMPHS08,
author = {Sarvjeet Singh and
Chris Mayfield and
Sagar Mittal and
Sunil Prabhakar and
Susanne E. Hambrusch and
Rahul Shah},
editor = {Jason Tsong{-}Li Wang},
title = {Orion 2.0: native support for uncertain data},
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of Data, {SIGMOD} 2008, Vancouver, BC, Canada, June 10-12, 2008},
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publisher = {{ACM}},
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url = {https://doi.org/10.1145/1376616.1376744},
doi = {10.1145/1376616.1376744},
timestamp = {Tue, 06 Nov 2018 11:07:37 +0100},
biburl = {https://dblp.org/rec/conf/sigmod/SinghMMPHS08.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{AF18,
author = {Arab, Bahareh and Feng, Su and Glavic, Boris and Lee, Seokki and Niu, Xing and Zeng, Qitian},
bibsource = {dblp computer science bibliography, https://dblp.org},
biburl = {https://dblp.org/rec/bib/journals/debu/ArabFGLNZ17},
journal = {{IEEE} Data Engineering Bulletin},
keywords = {GProM; Provenance; Annotations},
number = {1},
pages = {51--62},
pdfurl = {http://sites.computer.org/debull/A18mar/p51.pdf},
projects = {GProM; Reenactment},
timestamp = {Fri, 02 Mar 2018 18:50:49 +0100},
title = {{GProM} - {A} Swiss Army Knife for Your Provenance Needs},
venueshort = {Data Eng. Bull.},
volume = {41},
year = {2018},
bdsk-url-1 = {http://sites.computer.org/debull/A18mar/p51.pdf}
}
@article{10.1145/3003665.3003667,
author = {Olteanu, Dan and Schleich, Maximilian},
title = {Factorized Databases},
year = {2016},
issue_date = {June 2016},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {45},
number = {2},
issn = {0163-5808},
url = {https://doi.org/10.1145/3003665.3003667},
doi = {10.1145/3003665.3003667},
abstract = {This paper overviews factorized databases and their application to machine learning. The key observation underlying this work is that state-of-the-art relational query processing entails a high degree of redundancy in the computation and representation of query results. This redundancy can be avoided and is not necessary for subsequent analytics such as learning regression models.},
journal = {SIGMOD Rec.},
month = sep,
pages = {5–16},
numpages = {12}
}
@inproceedings{DBLP:conf/tapp/Zavodny11,
author = {Jakub Z{\'{a}}vodn{\'{y}}},
editor = {Peter Buneman and
Juliana Freire},
title = {On Factorisation of Provenance Polynomials},
booktitle = {3rd Workshop on the Theory and Practice of Provenance, TaPP'11, Heraklion,
Crete, Greece, June 20-21, 2011},
publisher = {{USENIX} Association},
year = {2011},
url = {https://www.usenix.org/conference/tapp11/factorisation-provenance-polynomials},
timestamp = {Wed, 04 Jul 2018 13:06:34 +0200},
biburl = {https://dblp.org/rec/conf/tapp/Zavodny11.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
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author = {Radu Curticapean},
editor = {Fedor V. Fomin and
Rusins Freivalds and
Marta Z. Kwiatkowska and
David Peleg},
title = {Counting Matchings of Size k Is W[1]-Hard},
booktitle = {Automata, Languages, and Programming - 40th International Colloquium,
{ICALP} 2013, Riga, Latvia, July 8-12, 2013, Proceedings, Part {I}},
series = {Lecture Notes in Computer Science},
volume = {7965},
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publisher = {Springer},
year = {2013},
url = {https://doi.org/10.1007/978-3-642-39206-1\_30},
doi = {10.1007/978-3-642-39206-1\_30},
timestamp = {Tue, 14 May 2019 10:00:44 +0200},
biburl = {https://dblp.org/rec/conf/icalp/Curticapean13.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
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author = {Kennedy, Oliver and Koch, Christoph},
title = {PIP: A Database System for Great and Small Expectations},
booktitle = {ICDE},
year = {2010}
}
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Tomoe Sugihara and
Jennifer Widom},
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}
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booktitle = {SIGMOD},
year = {2019}
}
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author = {Robert Fink and
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year = {2013}
}
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Hung Q. Ngo and
Atri Rudra},
title = {{FAQ:} Questions Asked Frequently},
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pages = {13--28},
publisher = {{ACM}},
year = {2016}
}
@inproceedings{DBLP:conf/pods/GreenKT07,
author = {Todd J. Green and
Gregory Karvounarakis and
Val Tannen},
title = {Provenance semirings},
booktitle = {{PODS}},
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publisher = {{ACM}},
year = {2007}
}
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}
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Leonid Libkin},
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Study},
year = {2016}
}
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author = {Jampani, Ravi and Xu, Fei and Wu, Mingxi and Perez, Luis Leopoldo and Jermaine, Christopher and Haas, Peter J},
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year = {2008}
}
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}
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142
atri.bib
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@ -1,142 +0,0 @@
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doi = {10.4230/LIPIcs.ICALP.2020.74},
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Ely Porat and
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Atri Rudra},
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timestamp = {Wed, 21 Nov 2018 12:44:29 +0100},
biburl = {https://dblp.org/rec/journals/jacm/NgoPRR18.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
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author = {Hung Q. Ngo and
Christopher R{\'{e}} and
Atri Rudra},
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journal = {{SIGMOD} Rec.},
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url = {https://doi.org/10.1145/2590989.2590991},
doi = {10.1145/2590989.2590991},
timestamp = {Fri, 06 Mar 2020 21:55:55 +0100},
biburl = {https://dblp.org/rec/journals/sigmod/NgoRR13.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{factorized-db,
author = {Dan Olteanu and
Maximilian Schleich},
title = {Factorized Databases},
journal = {{SIGMOD} Rec.},
volume = {45},
number = {2},
pages = {5--16},
year = {2016},
url = {https://doi.org/10.1145/3003665.3003667},
doi = {10.1145/3003665.3003667},
timestamp = {Fri, 06 Mar 2020 21:56:19 +0100},
biburl = {https://dblp.org/rec/journals/sigmod/OlteanuS16.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{ngo-survey,
author = {Hung Q. Ngo},
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Marcelo Arenas},
title = {Worst-Case Optimal Join Algorithms: Techniques, Results, and Open
Problems},
booktitle = {Proceedings of the 37th {ACM} {SIGMOD-SIGACT-SIGAI} Symposium on Principles
of Database Systems, Houston, TX, USA, June 10-15, 2018},
pages = {111--124},
publisher = {{ACM}},
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url = {https://doi.org/10.1145/3196959.3196990},
doi = {10.1145/3196959.3196990},
timestamp = {Wed, 21 Nov 2018 12:44:18 +0100},
biburl = {https://dblp.org/rec/conf/pods/000118.bib},
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of Database Systems, {PODS} 2016, San Francisco, CA, USA, June 26
- July 01, 2016},
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}
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author = {Albert Atserias and
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biburl = {https://dblp.org/rec/journals/siamcomp/AtseriasGM13.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}

2
experiments.tex
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@ -5,7 +5,7 @@ Recall that by definition of $\abbrBIDB$, a query result cannot be derived by a
We ran our experiments using Windows 10 WSL Operating System with an Intel Core i7 2.40GHz processor and 16GB RAM. All experiments used the PostgreSQL 13.0 database system.
For the data we used the MayBMS data generator~\cite{pdbench} tool to randomly generate uncertain versions of TPCH tables. The queries computed over the database instance are $\query_1$, $\query_2$, and $\query_3$ from~\cite{Antova_fastand}, all of which are modified versions of TPC-H queries $\query_3$, $\query_6$, and $\query_7$ where all aggregations have been dropped.
For the data we used the MayBMS data generator~\cite{pdbench} tool to randomly generate uncertain versions of TPCH tables. The queries computed over the database instance are $\query_1$, $\query_2$, and $\query_3$ from~\cite{4497507}, all of which are modified versions of TPC-H queries $\query_3$, $\query_6$, and $\query_7$ where all aggregations have been dropped.
As written, the queries disallow $\abbrBIDB$ cross terms. We first ran all queries, noting the result size for each. Next the queries were rewritten so as not to filter out the cross terms. The comparison of the sizes of both result sets should then suggest in one way or another whether or not there exist many cross terms in practice. As seen, the experimental query results contain little to no cancelling terms. \Cref{fig:experiment-bidb-cancel} shows the result sizes of the queries, where column CF is the result size when all cross terms are filtered out, column CI shows the number of output tuples when the cancelled tuples are included in the result, and the last column is the value of $\gamma$. The experiments show $\gamma$ to be in a range between $[0, 0.1]\%$, indicating that only a negligible or constant (compare the result sizes of $\query_1 < \query_2$ and their respective $\gamma$ values) amount of tuples are cancelled in practice when running queries over a typical \abbrBIDB instance. Interestingly, only one of the three queries had tuples that violated the \abbrBIDB constraint.

2
introduction.tex
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@ -99,7 +99,7 @@ Further, our approximation algorithm works for a more general notion of bag \abb
(see \Cref{subsec:tidbs-and-bidbs}).
\subsection{Polynomial Equivalence}\label{sec:intro-poly-equiv}
A common encoding of probabilistic databases (e.g., in \cite{IL84a,Imielinski1989IncompleteII,Antova_fastand,DBLP:conf/vldb/AgrawalBSHNSW06} and many others) relies on annotating tuples with lineages or propositional formulas that describe the set of possible worlds that the tuple appears in. The bag semantics analog is a provenance/lineage polynomial (see~\Cref{fig:nxDBSemantics}) $\apolyqdt$~\cite{DBLP:conf/pods/GreenKT07}, a polynomial with non-zero integer coefficients and exponents, over variables $\vct{X}$ encoding input tuple multiplicities. Evaluating a lineage polynomial for a query result tuple $t_{out}$ by, for each tuple $\tup_{in}$, assigning the variable $X_{t_{in}}$ encoding the tuple's multiplicity to the tuple's multiplicity in the possible world yields the multiplicity of the $\tup_{out}$ in the query result for this world.
A common encoding of probabilistic databases (e.g., in \cite{IL84a,Imielinski1989IncompleteII,4497507,DBLP:conf/vldb/AgrawalBSHNSW06} and many others) relies on annotating tuples with lineages or propositional formulas that describe the set of possible worlds that the tuple appears in. The bag semantics analog is a provenance/lineage polynomial (see~\Cref{fig:nxDBSemantics}) $\apolyqdt$~\cite{DBLP:conf/pods/GreenKT07}, a polynomial with non-zero integer coefficients and exponents, over variables $\vct{X}$ encoding input tuple multiplicities. Evaluating a lineage polynomial for a query result tuple $t_{out}$ by, for each tuple $\tup_{in}$, assigning the variable $X_{t_{in}}$ encoding the tuple's multiplicity to the tuple's multiplicity in the possible world yields the multiplicity of the $\tup_{out}$ in the query result for this world.
We drop $\query$, $\tupset$, and $\tup$ from $\apolyqdt$ when they are clear from the context or irrelevant to the discussion. We now specify the problem of computing the expectation of tuple multiplicity in the language of lineage polynomials:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

36
main.bbl
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@ -2,7 +2,7 @@
%%% Do NOT edit. File created by BibTeX with style
%%% ACM-Reference-Format-Journals [18-Jan-2012].
\begin{thebibliography}{48}
\begin{thebibliography}{49}
%%% ====================================================================
%%% NOTE TO THE USER: you can override these defaults by providing
@ -37,16 +37,6 @@
\providecommand\natexlab[1]{#1}
\providecommand\showeprint[2][]{arXiv:#2}
\bibitem[pdb([n.\,d.])]%
{pdbench}
\bibinfo{year}{[n.\,d.]}\natexlab{}.
\newblock \bibinfo{title}{pdbench}.
\newblock \bibinfo{howpublished}{\url{http://pdbench.sourceforge.net/}}.
\newblock
\newblock
\shownote{Accessed: 2020-12-15}.
\bibitem[Agrawal et~al\mbox{.}(2006)]%
{DBLP:conf/vldb/AgrawalBSHNSW06}
\bibfield{author}{\bibinfo{person}{Parag Agrawal}, \bibinfo{person}{Omar
@ -80,6 +70,20 @@
\newblock
\bibitem[Antova et~al\mbox{.}(2008)]%
{4497507}
\bibfield{author}{\bibinfo{person}{Lyublena Antova}, \bibinfo{person}{Thomas
Jansen}, \bibinfo{person}{Christoph Koch}, {and} \bibinfo{person}{Dan
Olteanu}.} \bibinfo{year}{2008}\natexlab{}.
\newblock \showarticletitle{Fast and Simple Relational Processing of Uncertain
Data}. In \bibinfo{booktitle}{\emph{2008 IEEE 24th International Conference
on Data Engineering}}. \bibinfo{pages}{983--992}.
\newblock
\urldef\tempurl%
\url{https://doi.org/10.1109/ICDE.2008.4497507}
\showDOI{\tempurl}
\bibitem[Atserias et~al\mbox{.}(2013)]%
{AGM}
\bibfield{author}{\bibinfo{person}{Albert Atserias}, \bibinfo{person}{Martin
@ -452,6 +456,16 @@
\newblock
\bibitem[pdbench utility([n.\,d.])]%
{pdbench}
pdbench utility \bibinfo{year}{[n.\,d.]}\natexlab{}.
\newblock \bibinfo{title}{pdbench}.
\newblock \bibinfo{howpublished}{\url{http://pdbench.sourceforge.net/}}.
\newblock
\newblock
\shownote{Accessed: 2020-12-15}.
\bibitem[Rekatsinas et~al\mbox{.}(2017)]%
{DBLP:journals/pvldb/RekatsinasCIR17}
\bibfield{author}{\bibinfo{person}{Theodoros Rekatsinas}, \bibinfo{person}{Xu

16
main.bib
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@ -34,10 +34,12 @@ booktitle = {Proceedings of the 43rd Symposium on Foundations of Computer Scienc
pages = {538},
series = {FOCS '02}
}
misc{pdbench,
howpublished = {r̆lhttp://pdbench.sourceforge.net/},
note = {Accessed: 2020-12-15},
title = {pdbench}
@misc{pdbench,
key = {pdbench utility},
title = {pdbench},
howpublished = {\url{http://pdbench.sourceforge.net/}},
note = {Accessed: 2020-12-15}
}
@article{AF18,
@ -580,12 +582,6 @@ Study},
pages = {1578--1589}
}
@misc{pdbench,
title = {pdbench},
howpublished = {\url{http://pdbench.sourceforge.net/}},
note = {Accessed: 2020-12-15}
}
@article{factorized-db,
author = {Dan Olteanu and
Maximilian Schleich},

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