Range Queries on Uncertain Data

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 <= 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.