A new metric for processor allocation schemes in multiprocessor systems

Recently a number of scalable interconnection networks for connecting multiple processors have been proposed. Though these networks differ in their properties such as bisection bandwidth, node degree, network diameter, and average diameter, there is one common problem that must be addressed by their designers. It should be possible to subdivide the set of processors such that the subset forms a smaller version of the underlying topology. This task is termed as Processor Allocation in general and Subcube allocation for Hypercubes. Various techniques appear in literature, including tree collapsing, free-list based approaches and others. A common metric for evaluating a scheme is the extent to which it can recognize all the possible sub-graphs in a particular network. In this paper are show that recognizability alone is a poor yardstick for predicting the performance of a processor allocation scheme. We introduce the ideas of Search Space and Impact Sets and propose a new, more pragmatic metric to measure the efficiencies of an allocation scheme. We evaluate this metric for a simple buddy strategy and a hypothetical exhaustive scheme for two popular interconnection networks, the Star Graph and the k-ary-n-cube. We support our results by simulation experiments and conclude that a scheme with higher recognizability is unlikely to justify the associated increase in complexity and storage requirements.