Asymptotic Analysis of Parallel Programs

By Sumita Das

Asymptotic Analysis of Parallel Programs

Consider the problem of sorting a list of n numbers.

Given: The fastest serial programs for this problem run in time Θ(n log n).

The objective is to determine which of these four algorithms is the best.

Created by Sumita Das

Comparison of four different algorithms for sorting a given list of numbers. The table shows number of processing elements(p), parallel runtime(Tp), speedup(S), efficiency(E) and the pTP product.

Created by Sumita Das

Asymptotic Analysis

If the metric is speed,Best Algorithm with lowest tpAlgorithm A1 is the best, followed by A3, A4, and A2

If the metric is efficiency, A2 and A4 are the best, followed by A3 and A1.

Created by Sumita Das

If the metric is cost,Algorithms A2 and A4 are cost optimal, A1 and A3 are

not.

It is important to identify the objectives of analysis and to use appropriate metrics.

Created by Sumita Das

References

• Ananth Grama, Anshul Gupta, George Karypis, Vipin Kumar, “Introduction to Parallel Computing: Chapter 5: Analytical Modeling of Parallel Programs”, 2003

• www.parallelcomp.uw.hu/ch05lev1sec6.html

Created by Sumita Das