Portability | portable |
---|---|

Stability | Alpha quality. Interface may change without notice. |

Maintainer | josef.svenningsson@gmail.com |

Burkhard-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 an 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's not compatible 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
- size :: BKTree a -> Int
- 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)

# Documentation

class Eq a => Metric a whereSource

A type is `Metric`

if is has a function `distance`

which has the following
properties:

`distance`

x y >= 0-

if and only if`distance`

x y == 0`x == y`

`distance`

x y ==`distance`

y x`distance`

x z <=`distance`

x y +`distance`

y z

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.

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.

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

Approximate searching.

will return true if
there is an element in `memberDistance`

n a tree`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 tree then only one occurrence will be deleted.

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

returns all the elements in `elemsDistance`

n a tree`tree`

which are
at a `distance`

less than or equal to `n`

from the element `a`

.