Systems and methods for building and utilizing k-dimensional complete pointer-free trees

A computer-implemented method of building a k-dimensional complete pointer-free tree (“KD-CPF tree”) for a plurality of data points, the method comprising:

• determining a number of data points for constructing a KD-CPF tree having a plurality of splitting nodes and a plurality of leaf nodes;
• for each respective splitting node of the plurality of splitting nodes, determining a relative magnitude between (i) half of a high-bit number that is a largest number being a power of two that is less than or equal to the number of data points at the respective splitting node, and (ii) the difference between the number of data points at the respective splitting node and the high-bit number;
• based on the relative magnitude, splitting each of the respective splitting nodes with a hyperplane that places a number of points on a left side of the hyperplane equal to one of (a) the high-bit number or (b) a sum of half of the high-bit number and the difference between the number of data points at the respective splitting node and the high-bit number, until each branch of the KD-CPF tree terminates at a leaf node;
• and
• storing locations of the leaf nodes and the hyperplanes in a memory accessible for a search of data associated with the data points.