Computing Geometric Minimum Spanning Trees Using the Filter-Kruskal Method

Let P be a set of points in R. We propose GeoFilterKruskal, an algorithm that computes the minimum spanning tree of P using well separated pair decomposition in combination with a simple modification of Kruskal’s algorithm. When P is sampled from uniform random distribution, we show that our algorithm runs in O(n log n) time with probability at least 1−1/n for a given c > 1. Although this is theoretically worse compared to known O(n) [31] or O(n logn) [27, 11, 15] algorithms, experiments show that our algorithm works better in practice for most data distributions compared to the current state of the art [27]. Our algorithm is easy to parallelize and to our knowledge, is currently the best practical algorithm on multi-core machines for d > 2.