In this article, we show that many sequential randomized incremental algorithms are in fact parallel. We consider algorithms for several problems, including Delaunay triangulation, linear programming, closest pair, smallest enclosing disk, least-element lists, and strongly connected components. We analyze the dependencies between iterations in an algorithm and show that the dependence structure is shallow with high probability or that, by violating some dependencies, the structure is shallow and the work is not increased significantly. We identify three types of algorithms based on their dependencies and present a framework for analyzing each type. Using the framework gives work-efficient polylogarithmic-depth parallel algorithms for most of the problems that we study. This article shows the first incremental Delaunay triangulation algorithm with optimal work and polylogarithmic depth. This result is important, since most implementations of parallel Delaunay triangulation use the incremental approach. Our results also improve bounds on strongly connected components and least-element lists and significantly simplify parallel algorithms for several problems.

中文翻译：

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随机增量算法中的并行性

在本文中，我们展示了许多顺序随机增量算法实际上是并行的。我们考虑了几个问题的算法，包括 Delaunay 三角剖分、线性规划、最近对、最小封闭圆盘、最小元素列表和强连通分量。我们分析了算法中迭代之间的依赖关系，表明依赖结构很浅，概率很高，或者通过违反一些依赖关系，结构很浅，工作量没有显着增加。我们根据它们的依赖关系确定了三种类型的算法，并提出了一个分析每种类型的框架。使用该框架为我们研究的大多数问题提供了高效的多对数深度并行算法。本文展示了第一个具有最佳工作和多对数深度的增量 Delaunay 三角剖分算法。这个结果很重要，因为并行 Delaunay 三角剖分的大多数实现都使用增量方法。我们的结果还改进了强连接组件和最小元素列表的界限，并显着简化了几个问题的并行算法。