Searching dynamic point sets in spaces with bounded doubling dimension

We present a new data structure that facilitates approximate nearest neighbor searches on a dynamic set of points in a metric space that has a bounded doubling dimension. Our data structure has linear size and supports insertions and deletions in O(log n) time, and finds a (1+ε)-approximate nearest neighbor in time O(log n) + (1/ε)O(1). The search and update times hide multiplicative factors that depend on the doubling dimension; the space does not. These performance times are independent of the aspect ratio (or spread) of the points.