Geometric Minimum Spanning Trees with GeoFilterKruskal

  • Samidh Chatterjee
  • Michael Connor
  • Piyush Kumar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6049)


Let P be a set of points in ℝ d . 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.


Computational Geometry Experimental Algorithmics Minimum spanning tree Well separated pair decomposition Morton ordering multi-core 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Samidh Chatterjee
    • 1
  • Michael Connor
    • 1
  • Piyush Kumar
    • 1
  1. 1.Department of Computer ScienceFlorida State UniversityTallahassee

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