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.
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