Parallel algorithms of the hypercube allocation strategies are considered. Although the sequential algorithms of various hypercube allocation strategies are easier to implement, their worst case time complexities exponentially increase as the dimension of the hypercube increases. The authors show that the free processors can be utilized to perform the allocation jobs in parallel to improve the efficiency of the hypercube allocation algorithms. A modified parallel algorithm for the single Gray-Code (GC) strategy is proposed and is shown to be able to recognize more subcubes than the single GC strategy by using the binary reflected Gray code and inverse binary reflected Gray code, without increasing the execution time. Two algorithms for a complete subcube recognition system are also presented and shown to be more efficient and attractive than the sequential one currently used in the hypercube multiprocessor.