\input{figures/pseudo-code/ball}
A node in a ball tree, even the root node, contains all of that node's children nodes. One benefit of ball trees over KD-trees
is that ball trees do not need to partition the whole
space\cite{BallTrees}. Also, the children's balls are allowed to
intersect with each other. A parent's ball is large enough to encompass
all of its children and their balls. There are two main ways to
construct the ball trees:
\bi
\item Bottom Up: The tree is constructed from the leaves to the root
  node. This provides the optimum trees, but takes the longest to
  construct.
\item Top Down: The tree is constructed from the root to the
  leaves. This provides the fastest construction time, but performs
  worse than trees generated with the Bottom Up method.
\ei
