bktrees-0.1: A set data structure with approximate searching

StabilityAlpha quality. Interface may change without notice.



Burhard-Keller trees provide an implementation of sets which apart from the ordinary operations also has an approximate member search, allowing you to search for elements that are of a distance n from the element you are searching for. The distance is determined using a metric on the type of elements. Therefore all elements must implement the Metric type class, rather than the more usual Ord.

Useful metrics include the manhattan distance between two points, the Levenshtein edit distance between two strings, the number of edges in the shortest path between two nodes in a undirected graph and the Hamming distance between two binary strings. Any euclidean space also has a metric. However, in this module we use int-valued metrics and that doesn't quite with the metrics of euclidean spaces which are real-values.

The worst case complexity of many of these operations is quite bad, but the expected behavior varies greatly with the metric. For example, the discrete metric (distance x y | y == x = 0 | otherwise = 1) makes BK-trees behave abysmally. The metrics mentioned above should give good performance characteristics.



data BKTree a Source

class Eq a => Metric a whereSource

A type is Metric if is has a function distance which has the following properties:

All types of elements to BKTree must implement Metric.

This definition of a metric deviates from the mathematical one in that it returns an integer instead of a real number. The reason for choosing integers is that I wanted to avoid the rather unpredictable rounding of floating point numbers.


distance :: a -> a -> IntSource

null :: BKTree a -> BoolSource

Test if the tree is empty.

empty :: BKTree aSource

The empty tree.

fromList :: Metric a => [a] -> BKTree aSource

Constructs a tree from a list

singleton :: a -> BKTree aSource

The tree with a single element

insert :: Metric a => a -> BKTree a -> BKTree aSource

Inserts an element into the tree. If an element is inserted several times it will be stored several times.

member :: Metric a => a -> BKTree a -> BoolSource

Checks whether an element is in the tree.

memberDistance :: Metric a => Int -> a -> BKTree a -> BoolSource

Approximate searching. memberDistance n a tree will return true if there is an element in tree which has a distance less than or equal to n from a.

delete :: Metric a => a -> BKTree a -> BKTree aSource

Removes an element from the tree. If an element occurs several times in the only the first occurrence will be deleted.

union :: Metric a => BKTree a -> BKTree a -> BKTree aSource

Merges two trees

unions :: Metric a => [BKTree a] -> BKTree aSource

Merges several trees

elems :: BKTree a -> [a]Source

Returns all the elements of the tree

elemsDistance :: Metric a => Int -> a -> BKTree a -> [a]Source

elemsDistance n a tree returns all the elements in tree which are at a distance less than or equal to n from the element a.

closest :: Metric a => a -> BKTree a -> Maybe (a, Int)Source

closest a tree returns the element in tree which is closest to a together with the distance. Returns Nothing if the tree is empty.