Possible and Certain Answers for Queries over Order-Incomplete Data

TL;DR

This paper introduces a query language for order-incomplete data represented by partial orders, analyzing the complexity of computing possible and certain answers, and identifying tractable cases.

Contribution

It proposes a formal framework for querying order-incomplete data using partial orders and studies the computational complexity of answer problems.

Findings

Possible answers are NP-complete to compute.

Certain answers are coNP-complete to compute.

Many cases are tractable depending on query operators and input data.

Abstract

To combine and query ordered data from multiple sources, one needs to handle uncertainty about the possible orderings. Examples of such "order-incomplete" data include integrated event sequences such as log entries, lists of properties (e.g., hotels and restaurants) ranked by an unknown function reflecting relevance or customer ratings, and documents edited concurrently with an uncertain order on edits. This paper introduces a query language for order-incomplete data, based on the positive relational algebra with order-aware accumulation. We use partial orders to represent order-incomplete data, and study possible and certain answers for queries in this context. We show that these problems are respectively NP-complete and coNP-complete, but identify many tractable cases depending on the query operators or input partial orders.