  This article proposes an PQR search method for probabilistic objects. The
main idea of our method is to use a strategy called \textit{pre-approximation}
that can reduce the initial problem to a highly simplified version, implying
that it makes the rest of steps easy to tackle. In particular, this strategy
itself is pretty simple and easy to implement. Furthermore, motivated by the
cost analysis, we further optimize our solution. The optimizations are mainly
based on two insights: (\romannumeral 1) the number of \textit{effective
subdivision}s is no more than 1; and (\romannumeral 2) an entity with the
larger \textit{span} is more likely to subdivide a single region. We
demonstrate the effectiveness and efficiency of our proposed approaches through
extensive experiments under various experimental settings.
