Top-k Querying of Unknown Values under Order Constraints (Extended Version)

TL;DR

This paper introduces a novel approach for estimating top-k query results over data with unknown values under order constraints, providing complexity analysis and solutions for specific cases.

Contribution

It is the first to develop a principled scheme for deriving value distributions and expected values in this setting, including tractable solutions for tree-shaped partial orders.

Findings

The problem is generally intractable but can be approximated efficiently.

A polynomial-time solution is provided for tree-shaped partial orders.

The approach enables better top-k estimation under uncertainty.

Abstract

Many practical scenarios make it necessary to evaluate top-k queries over data items with partially unknown values. This paper considers a setting where the values are taken from a numerical domain, and where some partial order constraints are given over known and unknown values: under these constraints, we assume that all possible worlds are equally likely. Our work is the first to propose a principled scheme to derive the value distributions and expected values of unknown items in this setting, with the goal of computing estimated top-k results by interpolating the unknown values from the known ones. We study the complexity of this general task, and show tight complexity bounds, proving that the problem is intractable, but can be tractably approximated. We then consider the case of tree-shaped partial orders, where we show a constructive PTIME solution. We also compare our problem setting to other top-k definitions on uncertain data.