Range Queries on Uncertain Data

Jian Li, Haitao Wang

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: (1) top-\(1\) query: find the point in \(P\) that lies in \(I\) with the highest probability, (2) top-\(k\) query: given any integer \(k\le n\) 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 near linear space and efficient query time.