The k-th nearest neighbour problem for 3D data has been widely studied, nevertheless, the surge of using GPU (Graphical Processing Unit) as general-purpose computing units opens up the need to design and implement new algorithms, that allow us to get results more rapidly than using conventional algorithms.
The main advantage of GPU is its great computing capacity for parallel computing. This is due to an architecture that contemplates a great number of processing cores originally designed to graphics processing and that can currently be used for other purposes such as high performance cientific calculation.