Range Queries on Uncertain Data

TL;DR

This paper develops efficient data structures for range queries on uncertain data points on the real line, enabling quick retrieval of top probabilities, top-k points, or points exceeding a probability threshold within a query interval.

Contribution

It introduces novel data structures with linear or near-linear space complexity for answering various range queries on uncertain data points.

Findings

Data structures support efficient range queries on uncertain data

Linear or near-linear space complexity achieved

Query times are optimized for different query types

Abstract

Given a set $P$ of $n$ uncertain points on the real line, each represented by its one-dimensional probability density function, we consider the problem of building data structures on $P$ to answer range queries of the following three types for any query interval $I$: (1) top-$1$ query: find the point in $P$ that lies in $I$ with the highest probability, (2) top-$k$ query: given any integer $k\leq n$ as part of the query, return the $k$ points in $P$ that lie in $I$ with the highest probabilities, and (3) threshold query: given any threshold $\tau$ as part of the query, return all points of $P$ that lie in $I$ with probabilities at least $\tau$. We present data structures for these range queries with linear or nearly linear space and efficient query time.