Chapter

Experimental Algorithms

Volume 6049 of the series Lecture Notes in Computer Science pp 486-500

Geometric Minimum Spanning Trees with GeoFilterKruskal

  • Samidh ChatterjeeAffiliated withDepartment of Computer Science, Florida State University
  • , Michael ConnorAffiliated withDepartment of Computer Science, Florida State University
  • , Piyush KumarAffiliated withDepartment of Computer Science, Florida State University

Abstract

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.

Keywords

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