Cover Tree

A well-documented C++ implementation of the cover tree datastructure for quick k-nearest-neighbor search. Allows single-point insertion and removal. Uses templates.

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 for example code of how to use the cover tree.

Relevant links: - Wikipedia's page on cover trees. - 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 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.

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