diff --git a/abstract.tex b/abstract.tex index 607ebc9..56ce867 100644 --- a/abstract.tex +++ b/abstract.tex @@ -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}