A Pure OCaml implementation of the Wu Manber approximate string matching algorithm for short patterns.
Tagswu-manber baeza-yates-gonnet bitap algorithm levenshtein demarau-levenshtein edit distance approximate fuzzy string search matching
Published: 19 Jan 2022
An OCaml Implementation of the wu-manber fuzzy search algorithm using
Int63 from the
optint package as the underlying bitvectors.
The library can be used to search for a keyword/pattern in a body of text while allowing for spelling errors. We use Levenshtein distances as the notion of spelling errors, and the functions in the library take some error limit
k and searches for substrings in the text with Levenshtein distance less than
k from the pattern.
Wu and Manber variants
I use the shift-or variant of the algorithm to save some bitwise operations. This is also called the
bitap algorithm, and the shift-or version was originally introduced by Baeza-Yates and Gonnet.
Even for the shift-or version, I provide two variants of the algorithm.
The original version from Wu and Manber's technical report.
A right-leaning variant, where delete edits are skipped at the end of the pattern unless at the very end of text. This reports better edit distances is some circumstances.
The right-leaning variant is guaranteed to find a match if and only if the original algorithm finds a match, and the error count reported by the variant is guaranteed to be no worse than the original. But the variant is a little harder to use since extra work is needed to check for matches at the end of the text.
The documentation for the library can be found here.
# #require "wu-manber-fuzzy-search";; # open Wu_Manber;; # StringSearch.(search ~k:2 ~pattern:"abcd" ~text:"abcd" |> report);; - : string = "Pattern matched with 2 errors at character 2 of text" # StringSearch.(search ~k:2 ~pattern:"abcd" ~text:"abd" |> report);; - : string = "Pattern matched with 2 errors at character 2 of text" # StringSearch.(search_right_leaning ~k:2 ~pattern:"abcd" ~text:"abcd" |> report);; - : string = "Pattern matched with 0 errors at character 4 of text" # StringSearch.(search_right_leaning ~k:2 ~pattern:"abcd" ~text:"abd" |> report);; - : string = "Pattern matched with 1 errors at character 3 of text"
The library only supports patterns of length 63. This is unlikely to be extended any time soon.
Runtime and Space Requirements
To search with an edit distance
k, we need to track of an array of
Int63.t of size
k+1. To process a character in the text, we usually need around
6 bitwise operations for every element of the array.
The high-level apis also use some matcher objects, these store patterns, arrays, or hashtables which require additional space.
The shift-and version of the algorithm is described in S. Wu and U. Manber, Fast Text Searching With Errors, tech. rep. TR 91-11, University of Arizona, 1991.
The shift-or version is described in the Wikipedia article for Bitap Algorithm.
agrep implements the shift-and version, but much of it is implmented in C.
There's also the main
agrep unix tool tool itself by Manber and Wu.
PRs are welcome, as long as you are understand that you would be releasing your code under CC0.
Here are extensions that I would like to have in the future.
Add versions of the algorithm that mutate an array instead of creating new arrays all the time.
Add specialized versions for exact matches and small error limits.
Support multi-match and limited expressions.
Full Regular Expressions Support.
Support Demarau-Levenshtein distances.
Support long patterns.
The limited expressions support should not be too difficult, but I haven't thought about if the right-leaning variant has weird interactions with limited expressions.