Modelling of Parallel Processing Tasks by Combinatorial Designs

Combinatorial Designs, also known as experimental designs, historically first were used in agriculture. With the advent of electronic computers together with the significant advancement of combinatorics, combinatorial structures have become an often used means in computer science. At present, massively parallel computers become more and more reliable so that they can be used as production systems. Thus, understanding the theoretical foundations of parallel processing becomes essential. In this paper we will show how combinatorial designs can be used in modelling parallel architectures as well as parallel algorithms. With the existence of combinatorial representations of parallel objects, problems and tasks from parallel processing can be transferred to combinatorics. While parallel processing suffers from the lack of theoretical concepts, combinatorics (of experimental designs) is full of structures, theoremes, lemmata and methods. So by the application of a transformation from parallel processing to combinatorics, for a lot of difficult tasks within parallel processing new ways for solution evolve from the combinatorics of experimental designs.