Parallelism in Randomized Incremental Algorithms

G. Blelloch, Yan Gu, Julian Shun, Yihan Sun
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引用次数: 41

Abstract

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.
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随机增量算法中的并行性
在本文中,我们证明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、最接近对、最小包围盘、最小元素列表和强连接分量。分析了算法中迭代之间的依赖关系,表明依赖结构很可能是浅的,或者通过违反某些依赖关系,结构很浅而工作量不会显著增加。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。本文展示了第一种具有最优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通分量和最小元素列表的边界,并显著简化了若干问题的并行算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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