README

This is a C++ implementation of the cover tree datastructure. Implements the
cover tree algorithms for insert, removal, and k-nearest-neighbor search.

To build simply type make in the terminal from the project directory. Do
./test to run the tests. Look in test.cc for example code of how to use the
cover tree.

Relevant links:
https://secure.wikimedia.org/wikipedia/en/wiki/Cover_tree - Wikipedia's page
on cover trees.
http://hunch.net/~jl/projects/cover_tree/cover_tree.html - John Langford's (one
of the inventors of cover trees) page on cover trees with links to papers.

To use the Cover Tree, you must implement your own Point class. CoverTreePoint
is provided for testing and as an example. Your Point class must implement the
following functions:

double YourPoint::distance(const YourPoint& p);
bool YourPoint::operator==(const YourPoint& p);
and optionally (for debugging/printing only):
void YourPoint::print();

The distance function must be a Metric, meaning (from Wikipedia):
1: d(x, y) = 0   if and only if   x = y
2: d(x, y) = d(y, x)     (symmetry)
3: d(x, z) =< d(x, y) + d(y, z)     (subadditivity / triangle inequality).

See https://secure.wikimedia.org/wikipedia/en/wiki/Metric_%28mathematics%29
for details.

Actually, 1 does not exactly need to hold for this implementation; you can
provide, for example, names for your points which are unrelated to distance
but important for equality. You can insert multiple points with distance 0 to
each other and the tree will keep track of them, but you cannot insert multiple
points that are equal to each other; attempting to insert a point that
already exists in the tree will not alter the tree at all.

If you do not want to allow multiple nodes with distance 0, then just make
your equality operator always return true when distance is 0.

TODO:
-The papers describe batch insert and batch-nearest-neighbors algorithms which
may be worth implementing.
-Try using a third "upper bound" argument for distance functions, beyond which
the distance does not need to be calculated, to improve efficiency in practice.