Fast Algorithms for Constructing Minimal Spanning Trees in Coordinate Spaces

Abstract

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.