CHAPTER 6: ABSTRACT MODEL

The PRAM Model and Its Variation

PRAM Overview

PRAM Overview

PRAM Operation

PRAM Operation

PRAM Subclasses

Simulating Multiple Accesses on an EREW PRAM

Simulating Concurrent Read on EREW PRAM with 8 Processors Using Algorithm

Broadcast_EREW

Analysis of Parallel Algorithms

The NC-class and P-completeness

The NC-class and P-completeness

Computing Sum and All Sums

Sum of an Array of Numbers on the EREW Model

Example of Algorithm Sum-EREW when n = 8

All Partial Sums of an Array

Computing Partial Sums of an Array of 8 Elements

Matrix MultiplicationUsing n^3 Processors

Complexity Analysis

Multiplying two 2 x 2 matrices using Algorithm MatMult_CREW

Reducing the Number of Processors

Reducing the Number of Processors

SortingThe algorithm consists of 2 steps

Complexity Analysis

Enumeration Sort of [6,1,3] on a CRCW PRAM

Message Passing ModelSynchronous Message Passing Model

Leader Election Problem

Leader Election in Synchronous RingsSimple Leader Election Algorithm

Leader Election in a Synchronous Ring using Algorithm S_Elect_Leader_Simple

Improved Leader Election Algorithm