Parallelism in Randomized Incremental Algorithms
Parallelism in Randomized Incremental Algorithms
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DOI：
10.1145/3402819
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发表时间：
2020-10-01
影响因子：
2.5
通讯作者：
Sun, Yihan
中科院分区：
文献类型：
--
作者：
Blelloch, Guy E.;Gu, Yan;Sun, Yihan
在本文中，我们表明许多顺序的随机增量算法实际上是平行的。我们考虑针对多个问题的算法，包括Delaunay三角剖分，线性编程，最接近的一对，最小的封闭磁盘，最小元素列表和紧密连接的组件。我们分析算法中迭代之间的依赖性，并显示依赖性结构很浅，表明依赖性是较高的。概率或通过违反某些依赖性的概率，结构浅，工作没有显着增加。我们根据其依赖项识别三种类型的算法，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工作效率的多层次 - 深度平行算法。本文显示了具有最佳工作和多种层次深度的第一个增量Delaunay三角测量算法。该结果很重要，因为大多数并行Delaunay三角剖分的实现都使用增量方法。我们的结果还提高了牢固连接的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。
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.