Computing expected multiplicities for bag-TIDBs with bounded multiplicities

TL;DR

This paper investigates the complexity of computing and approximating expected tuple multiplicities in probabilistic databases with bounded multiplicities, proposing a sampling algorithm for efficient approximation.

Contribution

It analyzes the complexity of expected multiplicity computation and introduces a linear-time sampling algorithm for approximating these values in certain probabilistic databases.

Findings

Exact computation is super-linear under certain complexity assumptions.

The sampling algorithm provides a 1±ε approximation efficiently.

Applicable to positive relational algebra queries over c-TIDBs.

Abstract

In this work, we study the problem of computing a tuple's expected multiplicity over probabilistic databases with bag semantics (where each tuple is associated with a multiplicity) exactly and approximately. We consider bag-TIDBs where we have a bound $c$ on the maximum multiplicity of each tuple and tuples are independent probabilistic events (we refer to such databases as c-TIDBs. 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 c-TIDBs based on the results produced by such query evaluation algorithms introduces super-linear overhead (under parameterized complexity hardness assumptions/conjectures). We proceed to study approximation of expected result tuple multiplicities for positive relational algebra queries ($RA^+$) over c-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 expected multiplicity of an output tuple in time linear in the runtime of the corresponding deterministic query for any $RA^+$ query.