A note on computing the center of uncertain data on the real line

We consider the one-dimensional one-center problem on uncertain data. We are given a set PP of nn (weighted) uncertain points on a real line LL and each uncertain point is specified by a probability density function that is a piecewise-uniform function (i.e., a histogram). The goal is to find a point cc (the center  ) on LL such that the maximum expected distance from cc to all uncertain points of PP is minimized. We present a linear-time algorithm for this problem.