The Euclidean minimum spanning tree or EMST is a minimum spanning tree of a set of n points in the plane (or more generally in ℝd), where the weight of the edge between each pair of points is the Euclidean distance between those two points. In simpler terms, an EMST connects a set of dots using lines such that the total length of all the lines is minimized and any dot can be reached from any other by following the lines. In higher dimensions (d ≥ 3), finding an optimal algorithm remains an open problem.