Layouts for improved hierarchical parallel computations

New layouts for the assignment of a set of n parallel processors to perform certain tasks in several hierarchically connected layers are suggested, leading, after some initialization phase, to the full exploitation of all of the processing power all of the time. This framework is useful for a variety of string theoretic problems, ranging from modular arithmetic used, among others, in Karp–Rabin type rolling hashes, as well as in cryptographic applications, and up to data compression and error-correcting codes.