vp-trees

vp-trees is an implementation of vantage point tree data structure in Common Lisp. It allows to perform fast (O(log N) in the best case) fixed-radius near neighbors searches in some set of a metric space.

Look at the following example. Let's choose the space ℝ²[0, 1] and generate some points belonging to this space:

(defun gen-point ()
  (vector (random 1.0)
          (random 1.0)))

(defun gen-points (n)
  (loop repeat n collect (gen-point)))

Then introduce a metric on this space (usual Euclidean metric):

(defun dist (a b)
  (sqrt
   (reduce #'+
           (map 'vector (lambda (x y) (expt (- x y) 2))
                a b))))

Build a tree consisting of 1000000 items in ℝ²[0, 1]:

(defparameter *tree*
    (vp-trees:make-vp-tree (gen-points 1000000) #'dist))

Now return points which are closer than 0.1 to the origin:

(vp-trees:items-in-ball *tree* #(0.0 0.0) 0.1 #'dist)

The advantage of VP trees is that you don't have to stick to Euclidean metric: you may choose whatever metric you want as long as four metric axioms hold. For example, VP trees can be used for multidimensional spaces.

API list

make-vp-tree
flatten
items-in-ball
nearest-neighbor