Geometric Minimum Spanning Trees with GeoFilterKruskal
Let P be a set of points in ℝd. 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 takes one parallel sort plus a linear number of additional steps, with high probability, to compute the minimum spanning tree. Experiments show that our algorithm works better in practice for most data distributions compared to the current state of the art . Our algorithm is easy to parallelize and to our knowledge, is currently the best practical algorithm on multi-core machines for d > 2.
KeywordsComputational Geometry Experimental Algorithmics Minimum spanning tree Well separated pair decomposition Morton ordering multi-core
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