The Dichotomy of Conjunctive Queries on Probabilistic Structures

TL;DR

This paper establishes a clear complexity classification for evaluating conjunctive queries on probabilistic databases, showing they are either efficiently solvable or computationally hard, and provides an algorithm to determine which case applies.

Contribution

It proves a dichotomy theorem for conjunctive query evaluation on probabilistic databases and offers an algorithm to classify queries as polynomial-time or #P-complete.

Findings

Every conjunctive query is either in PTIME or #P-complete for evaluation.

An algorithm is provided to decide the complexity class of a given query.

The result offers a complete classification of conjunctive query evaluation complexity.

Abstract

We show that for every conjunctive query, the complexity of evaluating it on a probabilistic database is either \PTIME or #\P-complete, and we give an algorithm for deciding whether a given conjunctive query is \PTIME or #\P-complete. The dichotomy property is a fundamental result on query evaluation on probabilistic databases and it gives a complete classification of the complexity of conjunctive queries.