On the compatibility of topologies of parallel tasks and computing systems

A.F Zadorozhny,V.A Melent’Ev

doi:10.1088/1742-6596/1864/1/012103

Abstract

Aspects of compatibility of topologies of parallel computing systems and tasks are investigated. The introduction of appropriate indexes based on the original topological model of parallel computations and on the nontraditional description of a graph by its projections is proposed and elucidated. On the example of hypercubic computing system (CS) and tasks with ring and star information topologies, we demonstrate determining the indexes and their use in a comparative analysis of the applicability of interconnect with a given topology for solving tasks with the same and different types of information topologies.

Highlights

Based on Amdahl Law [1], the model allows estimating the limit acceleration of the tasks that have scalarity of separate fragments
Basic provisions and the topologies compatibility concept The real-time implementation of a parallel application on a computing system (CS) can be successful, if: 1) its interconnect operation speed is sufficient to ensure that the delays made by the exchange processes between parallel branches do not exceed the delays allowed by real-time requirements and 2) the system graph of supplemented by edges, corresponding to the preceding condition, contains a subgraph, which is isomorphic to the information graph of the task, with the number of vertices corresponding to the same condition
The topological compatibility of the task with the number of parallel branches of p and CS with a number of processors n > q we is understood as the possibility of isomorphic embedding of the task’s information graph of order p in the system graph transformed according to the specified reachability value ∂ so that the vertices in it are adjacent if the distance between them in the original CS graph of order n does not exceed ∂

Summary

Introduction

Based on Amdahl Law [1], the model allows estimating the limit acceleration of the tasks that have scalarity (nonparallelizability) of separate fragments.

Results

Conclusion