Well Separated Pair Decomposition

In the previous lecture, we covered an approximation algorithm that answers a (1+ e)-approximate nearest neighbor query in logarithmic time, using only linear space. This algorithm makes use of the compressed quadtree data structure, which clusters the set of distances between query point and the points in the given set, {‖q− pi‖ |1 ≤ i ≤ n}, into O(log n + 1 ed ) clusters. In this lecture, we introduce the notion of well-separated pair decomposition (WSPD) that clusters the set of all pairwise distances in a given point set and discuss a few applications of WSPD.