Dynamic processor allocation in scalable multiprocessors using boolean algebra*

Abstract

In this paper, we study a new model for dynamic processor allocation in k-ary n-dimensional mesh or torus multiprocessors. The model uses Boolean functions to represent free processors and allocates processors by applying Boolean operations on the functions. The processor allocation algorithms based on the Boolean model can be implemented easily using binary decision diagrams(BDDs)and related software packages. To enhance the efficiency of the allocation algorithms, a reordering procedure will be introduced to change the ordering of Boolean variables in the BDD representation and thereby change the free subcube composition. Such a change leads to an improved free processor recognition capability. Complexities of the proposed allocation algorithms will be analyzed. Performance of the algorithms will be evaluated using simulation and compared with other approaches.