Designing Efficient Parallel Prefix Sum Algorithms for GPUs

This paper presents a novel and efficient method to compute one of the simplest and most useful building block for parallel algorithms: the parallel prefix sum operation. Besides its practical relevance, the problem achieves further interest in parallel-computation theory. We firstly describe step-by-step how parallel prefix sum is performed in parallel on GPUs. Next we propose a more efficient technique properly developed for modern graphics processors and alike processors. Our technique is able to perform the computation in such a way that minimizes both memory conflicts and memory usage. Finally we evaluate theoretically and empirically all the considered solutions in terms of efficiency, space complexity, and computational time. In order to properly conduct the theoretical analysis we used a novel computational model proposed by us in a previous work: K-model. Concerning the experiments, the results show that the proposed solution obtains better performance than the existing ones.