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\begin{abstract}
\AH{High-level intution}
Most people think that computing expected multiplicity of an output tuple in a probabilistic database (PDB) is easy.  Due to the fact that most modern implementations of PDBs represent tuple lineage in their expanded form, it has to be the case that such a computation is linear in the size of the lineage.  This follows since, when we have an uncompressed lineage, linearity allows for expectation to be pushed through the sum.
\AH{Low-level why-would-an-expert-read-this}
However, when we consider compressed representations of the tuple lineage, the complexity landscape changes.  If we use a lineage computed over a factorized database, we find in general that computation time is not linear in the size of the compressed lineage.
\AH{Key technical contributions}
This work theoretically demonstrates that bags are not easy in general, and in the case of compressed lineage forms, the computation can be greater than linear.  As such, it is then desirable to have an approximation algorithm to approximate the expected multiplicity in linear time.  We introduce such an algorithm and give theoretical guarentees on its efficiency and accuracy.  It then follows that computing an approximate value of the tuple's expected multiplicity on a bag PDB is equivalent to deterministic query processing complexity.
\end{abstract}
