Modelling of Communication Complexity in Computers

Abstract

We have been oft used to ignore the influence of communication in sequential computers or in better cases we have been supposed that this influence should be included in computation complexity representing performed I/O instructions. Multiple using of high performed CPU (central processor unit) within a single computer (SMP parallel computer) but also multiple using of high performed computers (workstations) as the building computing node of dominant parallel computers nowadays (network of workstations - NOW) or integrated network of NOW modules - Grid).The extended communication steps in parallel computers represent inter process communication (IPC) of decomposed parts of given parallel algorithm (PA) named as parallel processes. Then we can simply say that any PA consists of parallel processes with their sequential character and IPC among parallel processes. In relation to increasing role of communications in parallel computers this paper is devoted to modelling of communication complexity (number of communication steps) in the same way as we use to analyse computation complexity so in sequential algorithms. Based on this extended approach we are able better to optimise performance of all existed parallel computers. Another important problem is to analyse critical parts of communication influence to parallel computer performance and that at first in minimisation of communications at developing stages of any PA and secondly at its whole performance optimisation. Finally we have illustrated from the point of user the important role of communication in parallel computers on the chosen examples.