Optimal Subcube Assignment for Partitionable Hypercubes

This paper formulates and discusses a processor assignment problem arising in partitionable parallel architectures. A partitionable hypercube multiprocessor can simultaneously execute multiple tasks where each task is independently executed on a subcube. Given a p processor hypercube and n independent tasks, where a task can be assigned a subcube of any size, an assignment determines the size of the subcube — i.e., the number of processors — to be assigned to each task. The objective of our problem is to find the optimal assignment which minimizes the maximum execution time among all tasks. We present an O(n log p max{log log p, log n}) algorithm that determines an optimal assignment. This algorithm can be efficiently parallelized, on the p processor hypercube, to obtain an O((n/p)log p log2(n log p)) parallel assignment algorithm.