Processor allocation in hypercube multiprocessors

The processor allocation problem requires recognizing and locating a free subcube that can accommodate a request for a subcube of a specified size for an incoming task. Methods reported in the literature fall into two strategies: bottom-up or bit mapped technique (BMT) and top-downer available cube technique (ACT). Our algorithm that solves the allocation problem in faulty hypercubes falls into the category of ACT´s which offer the advantage over BMT´s of quickly recognizing whether or not a requested subcube is available in the list of fault-free subcubes. We introduce new algebraic functions and the concept of separation factor to select a subcube for allocation. The notion of overlap-syndrome, defined in the text, quantifies the overlap among free subcubes. Our technique has full subcube recognition ability and thus recognizes more subcubes as compared to bit mapped techniques: Buddy, Gray code and its variants. The advantages of our approach over some of the existing ACT´s in terms of fragmentation and overall completion time are described in the text and in simulation results