Abstract
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 [31]. Our algorithm is easy to parallelize and to our knowledge, is currently the best practical algorithm on multi-core machines for d > 2.
This research was partially supported by National Science Foundation through CAREER Grant CCF-0643593 and the AFOSR Young Investigator Program. Advanced Micro Devices (AMD) provided the 32-core workstation for experiments. Dr. Giri Narsimhan provided the source code for his Geometric Minimum Spanning tree algorithm [31], which was used as one of the benchmarks for the algorithm implemented in this paper. The source code associated with this paper is part of the STANN library and can be downloaded from www.compgeom.com/~stann
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Chatterjee, S., Connor, M., Kumar, P. (2010). Geometric Minimum Spanning Trees with GeoFilterKruskal . In: Festa, P. (eds) Experimental Algorithms. SEA 2010. Lecture Notes in Computer Science, vol 6049. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13193-6_41
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