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We present parallel algorithms for constructing and traversing sparse octreeson graphics processing units (GPUs). The algorithms are based on parallel-scanand sort methods. To test the performance and feasibility, we implemented themin CUDA in the form of a gravitational tree-code which completely runs on theGPU.(The code is publicly available at:http://castle.strw.leidenuniv.nl/software.html) The tree construction andtraverse algorithms are portable to many-core devices which have support forCUDA or OpenCL programming languages. The gravitational tree-code outperformstuned CPU code during the tree-construction and shows a performance improvementof more than a factor 20 overall, resulting in a processing rate of more than2.8 million particles per second.

A sparse octree gravitational N-body code that runs entirely on the GPU processor