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paper-BagRelationalPDBsAreHard
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Atri Rudra 2022-05-04 01:03:47 +00:00 committed by node
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introduction.tex
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@ -261,7 +261,7 @@ Bags, as we consider, are sufficient for production use, where bag-relational al
Our results show that bag-\abbrPDB\xplural can be competitive, laying the groundwork for probabilistic functionality in production database engines.
\mypar{Concurrent Work}
In work independent of ours, Grohe, et. al.~\cite{https://doi.org/10.48550/arxiv.2201.11524} investigate bag-\abbrTIDB\xplural allowing for unbounded multiplicities and therefore addressing the concern of a succinct representation of the distribution over infinitely many multiplicities. While the authors observe that computing the expected value of an output tuple multiplicity is in polynomial time, no further analysis of the expected value is considered. The work investigates the query evaluation problem over bag-\abbrTIDB\xplural when computing the probability of an output tuple having at most a multiplicity of $k$, showing that a dichotomy exists for this problem. Our work in contrast assumes a finite bound on the multiplicities where we simply list the finitely many probability values and further looks into the fine-grained analysis of computing the expected multiplicity of an output tuple..
In work independent of ours, Grohe, et. al.~\cite{https://doi.org/10.48550/arxiv.2201.11524} investigate bag-\abbrTIDB\xplural allowing for unbounded multiplicities (which requires them to explicitly address the issue of a succinct representation of the distribution over infinitely many multiplicities). While the authors observe that computing the expected value of an output tuple multiplicity is in polynomial time, no further (fine-grained) analysis of the expected value is considered. The work primarily investigates the query evaluation problem over bag-\abbrTIDB\xplural when computing the probability of an output tuple having at most a multiplicity of $k$, showing that a dichotomy exists for this problem. Our work in contrast assumes a finite bound on the multiplicities where we simply list the finitely many probability values (and hence do not need consider a more succinct representation). Further, our work primarily looks into the fine-grained analysis of computing the expected multiplicity of an output tuple.