Model and Algorithmic Scalability

Abstract

This chapter examines running an algorithm designed for a model of a particular size on a different-sized instance of that model or of a different model. In a general setting, this introduces the problem of scaling simulations or self-simulations, in which an instance of a model simulates a differently-sized instance of the same model. Here, we wish to show the flexibility of an implementation of a model in a given size. An algorithm may demand the number of processors to depend on the problem size. For instance, numerous algorithms in earlier chapters claimed N processors or N² processors to solve a problem of size N. An R-Mesh implementation, however, cannot vary its number of processors as the sizes of its problems vary. If a model is scalable, then it can scale down the number of processors that an algorithm specifies to fit an available R-Mesh, at the cost of a corresponding increase in time, while maintaining the same efficiency. This problem is trivial on many models, such as a PRAM or a standard mesh, but is not so for a reconfigurable model.