In the noisy primitives model, each primitive comparison performed by an algorithm, e.g., testing whether one value is greater than another, returns the incorrect answer with random, independent probability p < 1/2 and otherwise returns a correct answer. This model was first applied in the context of sorting and searching, and recent work by Eppstein, Goodrich, and Sridhar extends this model to sequential algorithms involving geometric primitives such as orientation and sidedness tests. However, their approaches appear to be inherently sequential; hence, in this paper, we study parallel computational geometry algorithms for 2D and 3D convex hulls in the noisy primitives model. We give the first optimal parallel algorithms in the noisy primitives model for 2D and 3D convex hulls in the CREW PRAM model. The main technical contribution of our work concerns our ability to detect and fix errors during intermediate steps of our algorithm using a generalization of the failure sweeping technique.

翻译：在噪声基本操作模型中，算法执行的每个基本比较（例如测试一个值是否大于另一个值）以随机且独立的概率 p < 1/2 返回错误答案，否则返回正确答案。该模型最初应用于排序与搜索领域，近期 Eppstein、Goodrich 与 Sridhar 的工作将其扩展至涉及方向测试与边侧测试等几何基本操作的串行算法。然而，他们的方法本质上是串行的；因此，本文在噪声基本操作模型下研究二维与三维凸包的并行计算几何算法。我们在 CREW PRAM 模型中首次给出了噪声基本操作模型下二维与三维凸包的最优并行算法。本工作的主要技术贡献在于，我们通过推广故障扫描技术，能够在算法执行过程中检测并修正中间步骤产生的错误。