1. A multi-dimensional and geographic-search system comprising: a search-region-receiving component that receives a number i of sets of coordinates that define a region to be searched, the number i greater than 1 and each of the i sets of coordinates including d coordinates associated with a multidimensional space, each of the d coordinates represented by an ordered sequence of n bits; an indexing component that generates, by a bit-permutation mapping, i integer indexes that include an integer index for each of the i sets of the received coordinates, the bit-permutation mapping grouping, for each of the n bits used to represent each of the d coordinates of a set of coordinates, the bits of the d coordinates at each bit position within the ordered-bit-sequence representations of the d coordinates together into a subsequence of bits within an ordered sequence of subsequences of bits that together compose the integer index; a recursive-decomposition component that decomposes the region into sub-regions based on the integer indices generated by the indexing component; and a search component that selects points of interest from a points-of-interest database by comparing integer indices computed for the regular sub-regions to indices computed and stored in the database for each point of interest.