|Stability||Alpha 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
the element you are searching for. The distance is determined using
a metric on the type of elements. Therefore all elements must
Metric type class, rather than the more usual
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
- class Eq a => Metric a where
- null :: BKTree a -> Bool
- empty :: BKTree a
- fromList :: Metric a => [a] -> BKTree a
- singleton :: a -> BKTree a
- insert :: Metric a => a -> BKTree a -> BKTree a
- member :: Metric a => a -> BKTree a -> Bool
- memberDistance :: Metric a => Int -> a -> BKTree a -> Bool
- delete :: Metric a => a -> BKTree a -> BKTree a
- union :: Metric a => BKTree a -> BKTree a -> BKTree a
- unions :: Metric a => [BKTree a] -> BKTree a
- elems :: BKTree a -> [a]
- elemsDistance :: Metric a => Int -> a -> BKTree a -> [a]
- closest :: Metric a => a -> BKTree a -> Maybe (a, Int)
distancex y >= 0
if and only if
distancex y == 0
x == y
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.
Inserts an element into the tree. If an element is inserted several times it will be stored several times.
Removes an element from the tree. If an element occurs several times in the only the first occurrence will be deleted.