K-dimensional trees or k-d trees organize and represent spatial data. These data structures have several applications, particularly in multi-dimensional key searches like nearest neighbor and range searches. Here is how k-d trees operate:

  • Every leaf node of the binary tree is a k-dimensional point
  • Every non-leaf node splits the hyperplane (which is perpendicular to that dimension) into two half-spaces
  • The left subtree of a particular node represents the points to the left of the hyperplane. Similarly, the right subtree of that node denotes the points in the right half.

You can probe one step further and construct a self-balanced k-d tree where each leaf node would have the same distance from the root. Also, you can test it to find whether such balanced trees would prove optimal for a particular kind of application.