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<p>Two important issues in managing processors in a hypercube are addressed: subcube allocation and task migration to eliminate the system fragmentation caused by allocation and deallocation of subcubes. It is proven that the subcube allocation strategy using a binary reflected Gray code (BRGC), called the GC strategy, possesses the best subcube recognition ability among all strategies using sequential searches. A binary code (BC) is defined as the binary representation of a nonnegative integer, and an extended binary code (EBC) is obtained by permutating the bits of a BC. Similarly, an extended Gray code (EGC) is obtained from a BRGC. The subcube recognition ability of an allocation strategy using multiple EBCs is analyzed and compared to that using multiple EGCs.</p>
task migration; hypercube multiprocessors; subcubes; binary reflected Gray code; BRGC; GC strategy; subcube recognition; binary code; extended binary code; EBC; extended Gray code; EGC; multiprocessing systems.

K. Shin and M. Chen, "Subcube Allocation and Task Migration in Hypercube Multiprocessors," in IEEE Transactions on Computers, vol. 39, no. , pp. 1146-1155, 1990.
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