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.

In this note, we outline a very simple algorithm for the following problem: Given a set S of n points p 1

We study the 1-center problem on road networks, an important problem in GIS. Using Euclidean embeddings, and reduction to fast nearest neighbor search, we devise an approximation algorithm for this problem. Our initial experiments on real world data sets indicate fast computation of constant factor approximate solutions for query sets much larger than previously computable using exact techniques.