Computational Properties of Metaquerying Problems

TL;DR

This paper analyzes the computational complexity of metaquerying, a data mining technique for discovering hidden dependencies in databases, identifying both intractable and tractable cases, and providing algorithms for implementation.

Contribution

It defines all variants of metaquerying, studies their complexity, and identifies tractable cases with algorithms for practical implementation.

Findings

Metaquerying is generally intractable under combined complexity (NP-hard, NP^PP).

Some metaquerying cases are tractable with LOGCFL-complete complexity.

Data complexity of metaquerying is in TC0, with simpler cases in AC0.

Abstract

Metaquerying is a datamining technology by which hidden dependencies among several database relations can be discovered. This tool has already been successfully applied to several real-world applications. Recent papers provide only preliminary results about the complexity of metaquerying. In this paper we define several variants of metaquerying that encompass, as far as we know, all variants defined in the literature. We study both the combined complexity and the data complexity of these variants. We show that, under the combined complexity measure, metaquerying is generally intractable (unless P=NP), lying sometimes quite high in the complexity hierarchies (as high as NP^PP), depending on the characteristics of the plausibility index. However, we are able to single out some tractable and interesting metaquerying cases (whose combined complexity is LOGCFL-complete). As for the data complexity of metaquerying, we prove that, in general, this is in TC0, but lies within AC0 in some simpler cases. Finally, we discuss implementation of metaqueries, by providing algorithms to answer them.