Optimal solution to matrix parenthesization problem employing parallel processing approach

Authors:
Muhammad Hafeez;Muhammad Younus;Abdur Rehman;Athar Mohsin
Affiliations:
Computer Science Department, College of Telecommunication Engineering, National University of Sciences and Technology, Rawalpindi, Pakistan;Computer Science Department, College of Telecommunication Engineering, National University of Sciences and Technology, Rawalpindi, Pakistan;Computer Science Department, College of Telecommunication Engineering, National University of Sciences and Technology, Rawalpindi, Pakistan;Computer Science Department, College of Telecommunication Engineering, National University of Sciences and Technology, Rawalpindi, Pakistan
Venue:
EC'07 Proceedings of the 8th Conference on 8th WSEAS International Conference on Evolutionary Computing - Volume 8
Year:
2007

Citing 5
Cited 1

Introduction to algorithms

Introduction to algorithms
Efficient Matrix Chain Ordering in Polylog Time

SIAM Journal on Computing
A scalable parallel Strassen's matrix multiplication algorithm for distributed-memory computers

SAC '95 Proceedings of the 1995 ACM symposium on Applied computing
Multilevel hierarchical matrix multiplication on clusters

Proceedings of the 18th annual international conference on Supercomputing
Memory efficient parallel matrix multiplication operation for irregular problems

Proceedings of the 3rd conference on Computing frontiers

Using parallel signal processing in real-time audio matrix systems

WSEAS Transactions on Computers

Quantified Score

Hi-index	0.00

Visualization

Abstract

Optimal matrix parenthesization problem is an optimization problem that can be solved using dynamic programming. The paper discussed the problem in detail. The results and their analysis reveal that there is considerable amount of time reduction compared with simple left to right multiplication, on applying the matrix parenthesization algorithm. Time reduction varies from 0% to 96%, proportional to the number of matrices and the sequence of dimensions. It is also learnt that on applying parallel matrix parenthesization algorithm, time is reduced proportional to the number of processors at the start, however, after some increase, adding more processors does not yield any more throughput but only increases the overhead and cost. Major advantage of the parallel algorithm used is that it does not depend on the number of matrices. Moreover, work has been evenly distributed between the processors.