Toward scalable algorithms for orthogonal shared-memory parallel computers

The problem of developing scalable and near-optimal algorithms for orthogonal shared-memory multiprocessing systems with a multidimensional access (MDA) memory array is considered. An orthogonal shared-memory system consists of 2ⁿ processors and 2^m memory modules accessed in any one of m possible access modes. Data stored in memory modules are available to processors under a mapping rule that allows conflict-free data reads and writes for any given access mode. Scalable algorithms are presented for two well-known computational problems, namely, matrix multiplication and the fast Fourier transform (FFT). A complete analysis of the algorithms based on computational time and the access modes needed is also presented. The algorithms scale very well onto higher dimensional MDA architectures but are not always optimal. This reveals a tradeoff between the scalability of an algorithm and its optimality in the MDA computational model.