high performance computing on graphics processing units: hgpu.org

Many algorithms of practical interest require evaluation of a given function F on each point of a domain consisting of all k-partitions of an N-element set. Because the cardinality of such a domain grows rapidly for fixed k and increasing N, such algorithms are appealing candidates for parallelization; but to implement such parallelization efficiently in a multi-threaded (e.g., GPU/CUDA) architecture requires that each of Stirling2(N,k) threads determine — as a function of thread index alone, in time independent of the thread index, and without recourse to inter-thread communication — a unique corresponding k-partition of the given N-element set. While a number of sequential algorithms are known for recursively enumerating all k-partitions of an N-element set, none of those algorithms can be parallelized while satisfying the requirements above, since each requires that the mth k-partition in the enumeration be known before the (m+1)st k-partition can be computed. This thesis project comprised the design, coding, and testing of a parallel algorithm and corresponding CUDA implementation which do satisfy those requirements.