Dynamic processor allocation in hypercube computers

Abstract

Recognizing various subcubes in a hypercube computer fully and efficiently is nontrivial because of the specific structure of the hypercube. The authors propose a method that has much less complexity than the multiple-GC strategy in generating the search space, while achieving complete subcube recognition. This method is referred to as a dynamic processor allocation scheme because the search space generated is dependent upon the dimension of the requested subcube dynamically, instead of being predetermined and fixed. The basic idea of this strategy lies in collapsing the binary tree representations of a hypercube successively so that the nodes which form a subcube but are distant would be brought close to each other for recognition. The strategy can be implemented efficiently by using shuffle operations on the leaf node addresses of binary tree representations. Extensive simulation runs are carried out to collect experimental performance measures of interest of different allocation strategies. It is shown from analytic and experimental results that this strategy compares favorably in many situations with any other known allocation scheme capable of achieving complete subcube recognition.<>