Parallelism in Randomized Incremental Algorithms

Author:

Blelloch Guy E.1,Gu Yan2,Shun Julian3,Sun Yihan2

Affiliation:

1. Carnegie Mellon University, Pittsburgh, PA

2. University of California, Riverside, CA

3. MIT CSAIL, Cambridge, MA

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.

Funder

NSF

Miller Institute for Basic Research in Science at UC Berkeley

Intel Science and Technology Center for Cloud Computing

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

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