Efficient Serial and Parallel Subcube Recognition in Hypercubes

We develop an efficient subcube recognition algorithm that recognizes all the possible subcubes. The algorithm is based on exploiting more subcubes at different levels of the buddy tree. In exploiting the different levels, the algorithm checks any subcube at most once. Moreover, many unavailable subcubes are not considered as candidates and hence not checked for availability. This makes the algorithm fast in recognizing the subcubes. The number of recognized subcubes, for different subcube sizes, can be easily adjusted by restricting the search level down the buddy tree. The previous known algorithms become a special case of this general approach. When one level is searched, this algorithm perfoms as the original buddy system. When two levels are searched, it will recognized the Same subcubes as the ones in [4] with a faster speed. When all the levels are searched, a complete subcube recognition is obtained. In a multi-processing system, each processor can execute this algorithm on a different tree. Using a given number of processors in a multi-processing system, we give a method of constructing the trees that maximizes the overall number of recognized subcubes. Finally, we introduce an allocation method "best fit" that reduces hypercube fragmentation. Simulation results and performance comparisons between this method and the traditional "first fit" are presented.