Minimization of memory and network contention for accessing arbitrary data patterns in SIMD systems

Finding general XOR-schemes to minimize memory and network contention for accessing arrays with arbitrary sets of data templates is presented. A combined XOR-matrix is proposed together with a necessary and sufficient condition for conflict-free access. We present a new characterization of the baseline network. Finding an XOR-matrix for combined templates is shown to be an NP-complete problem. A heuristic is proposed for finding XOR-matrices by determining the constraints of each template-matrix and solving a set of simultaneous equations for each row. Evaluation shows significant reduction of memory and network contention compared to interleaving and to static row-column-diagonals storage.