Subcube recognition, allocation/deallocation and relocation in hypercubes

The paper investigates four different strategies for subcube recognition, allocation/deallocation and relocation in an n-dimensional hypercube multiprocessor: the buddy strategy which recognizes 2^n-k k-cubes in O(N) time, N=2ⁿ, has a relocation cost of O(KlogK) process-moves where K=2^k is the size of subcube requested; the Gray code strategy which recognizes 2^n-k+1 k-cubes in O(N) time is shown to have a relocation cost of O(N) process-moves; the recognizing all strategy can recognize all C_k ⁿ2^n-k k-cubes in O(N^1.58) time with a relocation cost of O(N) process-moves; and the extended buddy strategy which recognizes 2^n-k+(n-k)2^n-k-1 k-cubes in O(NlogN) time is shown to have a relocation cost of O(KlogK) process-moves