Fast Algorithms for Constructing Minimal Spanning Trees in Coordinate Spaces

Algorithms are presented that construct the shortest connecting network, or minimal spanning tree (MST), of N points embedded in k-dimensional coordinate space. These algorithms take advantage of the geometry of such spaces to substantially reduce the computation from that required to construct MST´s of more general graphs. An algorithm is also presented that constructs a spanning tree that is very nearly minimal with computation proportional to N log N for all k.