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≤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
Ï„ as part of the query, return all points of P that lie in I with
probabilities at least Ï„. We present data structures for these range
queries with linear or nearly linear space and efficient query time.Comment: 26 pages. A preliminary version of this paper appeared in ISAAC 2014.
In this full version, we also present solutions to the most general case of
the problem (i.e., the histogram bounded case), which were left as open
problems in the preliminary versio