Parallel algorithms in external memory.

Abstract

External memory (EM) algorithms are designed for computational problems in which the size of the internal memory of the computer is only a small fraction of the problem size. The Parallel Disk Model (PDM) of Vitter and Shriver is widely used to discriminate between external memory algorithms on the basis of input/output (I/O) complexity. Parallel algorithms are designed to efficiently utilize the computing power of multiple processing units, interconnected by a communication mechanism. A popular model for developing and analyzing parallel algorithms is the Bulk Synchronous Parallel (BSP) model due to Valiant. In this work we develop simulation techniques, both randomized and deterministic, which produce efficient EM algorithms from efficient algorithms developed under BSP-like parallel computing models. Our techniques can accommodate one or multiple processors on the EM target machine, each with one or more disks, and they also adapt to the disk blocking factor of the target machine. We propose new, more comprehensive models for EM and parallel algorithms which consider the total costs incurred by the algorithm including computation, I/O and communication. The new EM-BSP, EM-BSP*, and EM-CGM models combine the features of the BSP and PDM and thereby answer to a challenge posed by the ACM Working Group on Storage I/O for Large-Scale Computing. We obtain parallel external memory algorithms for a large number of problems including sorting, permutation, matrix transpose, geometric and GIS problems including 3D convex hulls (2D Voronoi diagrams), and various graph problems.