ODIn/paper-BagRelationalPDBsAreHard
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Updated Abstract.

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Aaron Huber 2021-08-26 10:17:30 -04:00
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@ -10,8 +10,8 @@ Such factorized representations are
exploited by modern join algorithms (e.g., worst-case optimal joins), and
so our results imply that computing probabilities for Bag-PDB based on the results produced by such algorithms introduces super-linear overhead.
% Such factorized representations are necessary to realize the performance of modern join algorithms (e.g., worst-case optimal joins), and so our results imply that a Bag-PDB doing exact computations (via these factorized representations) can never be as fast as a classical (deterministic) database.
The problem stays hard even for polynomials generated by conjunctive queries (CQs) if all input tuples have a fixed probability $\prob$ (s.t. $\prob \in (0,1)$).
We proceed to study polynomials of result tuples of union of conjunctive queries (UCQs) over TIDBs and for a non-trivial subclass of block-independent databases (BIDBs).
The problem stays hard even for polynomials generated by project-join queries if all input tuples have a fixed probability $\prob$ (s.t. $\prob \in (0,1)$).
We proceed to study polynomials of result tuples of positive relational algebra queries ($\raPlus$) over TIDBs and for a non-trivial subclass of block-independent databases (BIDBs).
We develop a sampling algorithm that computes a $1 \pm \epsilon$-approximation of the expectation of polynomial circuits in linear time in the size of the polynomial.
By removing Bag-PDB's reliance on the sum-of-products representation of polynomials, this result paves the way for future work on PDBs that are competitive with deterministic databases.
\end{abstract}