In the preprocessing model for uncertain data we are given a set of regions R which model the uncertainty associated with an unknown set of points P. In this model there are two phases: a preprocessing phase, in which we have access only to R, followed by a reconstruction phase, in which we have access to points in P at a certain retrieval cost C per point. We study the following algorithmic question: how fast can we construct the pareto front of P in the preprocessing model? We show that if R is a set of pairwise-disjoint axis-aligned rectangles, then we can preprocess R to reconstruct the Pareto front of P efficiently. To refine our algorithmic analysis, we introduce a new notion of algorithmic optimality which relates to the entropy of the uncertainty regions. Our proposed uncertainty-region optimality falls on the spectrum between worst-case optimality and instance optimality. We prove that instance optimality is unobtainable in the preprocessing model, whenever the classic algorithmic problem reduces to sorting. Our results are worst-case optimal in the preprocessing phase; in the reconstruction phase, our results are uncertainty-region optimal with respect to real RAM instructions, and instance optimal with respect to point retrievals.

翻译：在不确定数据的预处理模型中,我们得到了一组区域R,R用来模拟与一组未知点相联的不确定性。在这个模型中,P.有两个阶段:预处理阶段,我们只能接触R,然后是重建阶段,我们能够以一定的检索成本C/每点访问P点。我们研究了以下算法问题:在预处理模型中,我们如何快速地建造P的面部前部?我们证明,如果R是一组对称-分解轴对齐矩形,那么我们就可以先处理R,以高效地重建P的Preto前方。为了改进我们的算法分析,我们引入了一种与不确定区域的酶相关的算法最佳性新概念。我们提议的不确定性区域最佳性存在于最差的情况最佳性与实例最佳性之间。我们证明,在预处理模型中,当典型的算法问题降低到排序时,最优性在预处理阶段,我们的结果是最差的情况最优性;在重建阶段,我们的结果是,最优性区域,最优性地尊重真实性指示和最优性区域。