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Processor Allocation in Hypercube Multiprocessors
June 1995 (vol. 6 no. 6)
pp. 606-616

Abstract—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-down or 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.

Index Terms—Hypercube, processor allocation/deallocation, bit-mapped and available cube strategies, subcube recognition, separation factor, overlap syndrome.

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Suresh Rai, Jerry L. Trahan, Thomas Smailus, "Processor Allocation in Hypercube Multiprocessors," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 6, pp. 606-616, June 1995, doi:10.1109/71.388041
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