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We study the problem of computing a query result tuple's expected multiplicity for probabilistic databases under bag semantics (where each tuple is associated with a multiplicity) exactly and approximately.
Specifically, we are interested in the fine-grained complexity of this problem for \abbrCTIDB\xplural, i.e., probabilistic databases where tuples are independent probabilistic events and the multiplicity of each tuple is bound by a constant $\bound$.
% We consider bag-\abbrTIDB\xplural where we have a bound $\bound$ on the maximum multiplicity of each tuple and tuples are independent probabilistic events (we refer to such databases as \abbrCTIDB\xplural).
Unfortunately, our results imply that computing expected multiplicities for \abbrCTIDB\xplural 
%based on the output of deterministic query evaluation algorithms 
introduces super-linear overhead over the corresponding deterministic query evaluation algorithms (under certain complexity hardness conjectures).
% We are specifically interested in the fine-grained complexity of computing expected multiplicities and how it compares to the complexity of deterministic query evaluation algorithms --- if these complexities are comparable, it opens the door to practical deployment of probabilistic databases.
% Unfortunately, our results imply that computing expected multiplicities for \abbrCTIDB\xplural based on the results produced by such query evaluation algorithms introduces super-linear overhead (under parameterized complexity hardness assumptions/conjectures).
  Next, we develop a sampling algorithm that computes a $(1 \pm \epsilon)$-approximation of the expected multiplicity of an output tuple in time linear in the runtime of the corresponding deterministic query for any   positive relational algebra ($\raPlus$) query over \abbrCTIDB\xplural and for a non-trivial subclass of block-independent databases. % (\abbrBIDB\xplural).
  % We proceed to study approximation of expected result tuple multiplicities for positive relational algebra queries ($\raPlus$) over \abbrCTIDB\xplural and for a non-trivial subclass of block-independent databases (\abbrBIDB\xplural).
  % We develop a sampling algorithm that computes a $(1 \pm \epsilon)$-approximation of the expected multiplicity of an output tuple in time linear in the runtime of the corresponding deterministic query for any $\raPlus$ query.

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