Abstract Machine Models of Computation-Parallel Processing-Lecture Slides, Slides of Parallel Computing and Programming

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Abstract Machine Models of Computation

• RAM : Random Access

Machine

• PRAM : Parallel Random

Access Machine

Random Access Machine (RAM) Model

Abstract Machine Models of Computation

RAM : Random Access Machine - Unbounded memory– Read / Write to any (one) memory location = O (1) - PRAM : Parallel Random Access Machine - Unbounded memory– p processors to p different memory locations simultaneous read / write= O(1)

Categories of PRAM Model PRAM Models: Required for Read/ Write to the same Memory location by many processors

EREW : Exclusive Read, Exclusive Write - CREW : Concurrent Read, Exclusive Write - ERCW : Exclusive Read, Concurrent Write - CRCW : Concurrent Read, Concurrent Write

Matrix Mult Algorithms

Serial Matrix to Matrix Mult - PRAM Matrix to Matrix Mult - CREW– EREW– CRCW

Matrix Multiplication on Sequential Machine T(n) = O(n 3 )

Matrix Multiplication on PRAM-EREW Machine using n 2 processors T(n)= ????? Cost= ????? Optimal???

Matrix Multiplication on PRAM-CRCW Machine using n 2 processors T(n)= ????? Cost= ????? Optimal???

Parallel Prefix Sum on PRAM Machine Num-of-proc , T(n), cost, optimality, speedup, efficiency ????????????