A Novel Computational Model for GPUs with Application to I/O Optimal Sorting Algorithms

We propose a novel computational model for GPU. Known parallel computational models such as the PRAM model are not appropriate for evaluating GPU algorithms. Our model, called AGPU, abstracts the essence of current GPU architectures such as global and shared memory, memory coalescing and bank conflicts. We can therefore evaluate asymptotic behavior of GPU algorithms more accurately than known models and we can develop algorithms that are efficient on many real architectures. As a showcase, we first analyze known comparison-based sorting algorithms using the AGPU model and show that they are not I/O optimal, that is, the number of global memory accesses is more than necessary. Then we propose a new algorithm which uses an asymptotically optimal number of global memory accesses and whose time complexity is also nearly optimal.