Computing Possible and Certain Answers over Order-Incomplete Data

TL;DR

This paper analyzes the complexity of computing possible and certain answers for queries over databases with partially ordered relations, identifying NP- and coNP-complete problems and tractable cases.

Contribution

It extends positive relational algebra with aggregates to order-incomplete data and studies the complexity of answer possibility and certainty, including effects of duplicate elimination.

Findings

Possibility problem is NP-complete.

Certainty problem is coNP-complete.

Certain tractable cases depend on query operators and input orders.

Abstract

This paper studies the complexity of query evaluation for databases whose relations are partially ordered; the problem commonly arises when combining or transforming ordered data from multiple sources. We focus on queries in a useful fragment of SQL, namely positive relational algebra with aggregates, whose bag semantics we extend to the partially ordered setting. Our semantics leads to the study of two main computational problems: the possibility and certainty of query answers. We show that these problems are respectively NP-complete and coNP-complete, but identify tractable cases depending on the query operators or input partial orders. We further introduce a duplicate elimination operator and study its effect on the complexity results.