Efficient Partitioning of a Multi-dimensional Axis-Aligned Space into Uniform Non-overlapping Sub-spaces for Diverse Applications

This research presents an algorithm for efficiently subdividing an N-dimensional axis-aligned space into 2N sub-spaces, as if it is sliced by N, N-1 dimensional constructs which are each perpendicular to any one of the N axes and parallel to the rest. The resulting subdivision allows for efficient partitioning of the space into 2N equal N dimensional sub-spaces which are evenly distributed inside the original space and also are not intersecting with each other. This algorithm can be used in several data structures like kd-trees, etc. and can be applied in a variety of fields like computer graphics, physics simulations, machine learning, statistics to name a few.