Analytical Method of Performance Prediction in Parallel Algorithms

Abstract

With the availability of powerful personal computers, workstations and networking devices, the recent trend in parallel computing is to connect a number of individual workstations (PC, PC SMP) to solve computation-intensive tasks in parallel way on such typical clusters as NOW, SMP, Grid). In this sense it is not more true to consider traditionally evolved parallel computing and distributed computing as two separate research disciplines. Current trends in high performance computing (HPC) are to use networks of workstations (NOW, SMP) as a cheaper alternative to traditionally used massively parallel multiprocessors or supercomputers and to profit from unifying of both mentioned disciplines. The individual workstations could be so single PC (Personal computer) as parallel computers based on modern symmetric multiprocessor systems (SMP) implemented within workstation. To exploit the parallel processing capability of such cluster, the application program must be paralleled. The effective way to do it for (parallelisation strategy) belongs to a most important step in developing effective parallel algorithm (optimisation). For behaviour analysis we have to take into account all overheads that have the influence to performance of parallel algorithms (architecture, computation, communication etc.). In this article we discuss such complex performance evaluation of abstract empty matrix for potential used decomposition strategies. For these decomposition strategies we derived analytical isoefficiency functions, which allow us to predict performance although for hypothetical parallel computer.