Range-max queries on uncertain data

Let P be a set of n uncertain points in R-d, where each point p(i) is an element of P is associated with a real value v(i) and exists with probability alpha(i) is an element of (0, 1] independently of the other points. We present algorithms for building an index on P so that for a d-dimensional query rectangle rho, the expected maximum value or the most-likely maximum value in rho can be computed quickly. Our main contributions include the following: (i) The first index of sub-quadratic size to achieve a sub-linear query time in any dimension. (ii) A conditional lower bound for most-likely range-max queries, based on the conjectured hardness of the set-intersection problem. (iii) A near-linear-size index for estimating the expected range max value within approximation factor 1/2 in 0 (polylog(n)) time. (iv) Extensions of our algorithm to more general uncertainty models and for computing the top-k values of the range-max. (C) 2017 Published by Elsevier Inc.