  This work focuses on the definition and study of the n-dimensional k-vector,
an algorithm devised to perform orthogonal range searching in static databases
with multiple dimensions. The methodology first finds the order in which to
search the dimensions, and then, performs the search using a modified
projection method. In order to determine the dimension order, the algorithm
uses the k-vector, a range searching technique for one dimension that
identifies the number of elements contained in the searching range. Then, using
this information, the algorithm predicts and selects the best approach to deal
with each dimension. The algorithm has a worst case complexity of
$\mathcal{O}(nd(k/n)^{2/d})$, where $k$ is the number of elements retrieved,
$n$ is the number of elements in the database, and $d$ is the number of
dimensions of the database. This work includes a detailed description of the
methodology as well as a study of the algorithm performance.
