then applying a graph minimum spanning tree algorithm such as the Prim–Dijkstra–Jarník algorithm or Borůvka's algorithm on it. These algorithms can be made to take time on complete graphs, unlike another common choice, Kruskal's algorithm, which is slower because it involves sorting all distances. For points in low-dimensional spaces, the problem may be solved more quickly, as detailed below. Computing Euclidean distances involves a square root calculation. In any comparison of edge weights, comparing the squares of the Euclidean distances, instead of the distances themselves, yields the same ordering, and so does not change the rest of the tree's computation. This shortcut speeds up calculation and allows a minimum spanning tree for points with integer coordinates to be constructed using only integer arithmetic. Two dimensions A faster approach to finding the minimum spanning tree of planar points uses the property that it is a subgraph of the Delaunay triangulation: Compute the Delaunay triangulation, which can be done in time. Because the Delaunay triangulation is a planar graph, it has at most edges. Label each edge with its (squared) length. Run a graph minimum spanning tree algorithm. Since there are edges, this requires time using any of the standard minimum spanning tree algorithms. The result is an algorithm taking time, optimal in certain models of computation (see below). If the input coordinates are integers and can be used as array indices, faster algorithms are possible: the Delaunay triangulation can be constructed by a randomized algorithm in expected time. Additionally, since the Delaunay triangulation is a planar graph, its minimum spanning tree can be found in linear time by a variant of Borůvka's algorithm that removes all but the cheapest edge between each pair of components after each stage of the algorithm. Therefore, the total expected time for this algorithm is . In the other direction, the Delaunay triangulation can be constructed from the minimum spanning tree in the near-linear time bound , where denotes the iterated logarithm. Higher dimensions The problem can also be generalized to points in the -dimensional space . In higher dimensions, the connectivity determined by the Delaunay triangulation (which, likewise, partitions the convex hull into -dimensional simplices) contains the minimum spanning tree; however, the triangulation might contain the complete graph. Therefore, finding the Euclidean minimum spanning tree as a spanning tree of the complete graph or as a spanning tree of the Delaunay triangulation both take time.