Faster Query Answering in Probabilistic Databases using Read-Once Functions

TL;DR

This paper introduces an efficient method for determining and computing read-once forms of boolean event expressions in probabilistic databases, improving over previous approaches by avoiding disjunctive normal form conversions.

Contribution

The paper presents a novel, efficient algorithm for directly computing read-once forms of boolean expressions generated by conjunctive queries without self-joins, using the new concept of co-table graphs.

Findings

Efficient computation of co-occurrence graphs from provenance graphs.

Successful direct computation of read-once forms using co-table graphs.

Applicable to tuple-independent probabilistic databases with specific query structures.

Abstract

A boolean expression is in read-once form if each of its variables appears exactly once. When the variables denote independent events in a probability space, the probability of the event denoted by the whole expression in read-once form can be computed in polynomial time (whereas the general problem for arbitrary expressions is #P-complete). Known approaches to checking read-once property seem to require putting these expressions in disjunctive normal form. In this paper, we tell a better story for a large subclass of boolean event expressions: those that are generated by conjunctive queries without self-joins and on tuple-independent probabilistic databases. We first show that given a tuple-independent representation and the provenance graph of an SPJ query plan without self-joins, we can, without using the DNF of a result event expression, efficiently compute its co-occurrence graph. From this, the read-once form can already, if it exists, be computed efficiently using existing techniques. Our second and key contribution is a complete, efficient, and simple to implement algorithm for computing the read-once forms (whenever they exist) directly, using a new concept, that of co-table graph, which can be significantly smaller than the co-occurrence graph.