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README.md

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@@ -22,19 +22,19 @@ The main characteristics of each implemented algorithm are presented below. The
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| | | Normalized? | Metric? | Type | Cost |
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|-------- |------- |------------- |---------- | ------ | ---- |
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| Levenshtein |distance | No | Yes | | O(m.n) <sup>1</sup> |
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| Normalized Levenshtein |distance<br>similarity | Yes | No | | O(m.n) <sup>1</sup> |
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| Weighted Levenshtein |distance | No | No | | O(m.n) <sup>1</sup> |
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| Damerau-Levenshtein <sup>3</sup> |distance | No | Yes | | O(m.n) <sup>1</sup> |
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| [Levenshtein](#levenshtein) |distance | No | Yes | | O(m.n) <sup>1</sup> |
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| [Normalized Levenshtein](#normalized-levenshtein) |distance<br>similarity | Yes | No | | O(m.n) <sup>1</sup> |
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| [Weighted Levenshtein](#weighted-levenshtein) |distance | No | No | | O(m.n) <sup>1</sup> |
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| [Damerau-Levenshtein](#damerau-levenshtein) <sup>3</sup> |distance | No | Yes | | O(m.n) <sup>1</sup> |
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| Optimal String Alignment <sup>3</sup> |not implemented yet | No | No | | O(m.n) <sup>1</sup> |
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| Jaro-Winkler |similarity<br>distance | Yes | No | | O(m.n) |
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| Longest Common Subsequence |distance | No | No | | O(m.n) <sup>1,2</sup> |
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| Metric Longest Common Subsequence |distance | Yes | Yes | | O(m.n) <sup>1,2</sup> |
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| N-Gram (Kondrak) |distance | Yes | No | | O(m.n) |
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| Q-Gram |distance | No | No | Profile | O(m+n) |
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| Cosine |similarity<br>distance | Yes | No | Profile | O(m+n) |
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| Jaccard |similarity<br>distance | Yes | Yes | Set | O(m+n) |
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| Sorensen-Dice |similarity<br>distance | Yes | No | Set | O(m+n) |
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| [Jaro-Winkler](#jaro-winkler) |similarity<br>distance | Yes | No | | O(m.n) |
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| [Longest Common Subsequence](#longest-common-subsequence) |distance | No | No | | O(m.n) <sup>1,2</sup> |
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| [Metric Longest Common Subsequence](#metric-longest-common-subsequence) |distance | Yes | Yes | | O(m.n) <sup>1,2</sup> |
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| [N-Gram](#n-gram) |distance | Yes | No | | O(m.n) |
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| [Q-Gram](#q-gram) |distance | No | No | Profile | O(m+n) |
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| [Cosine similarity](#cosine-similarity) |similarity<br>distance | Yes | No | Profile | O(m+n) |
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| [Jaccard index](#jaccard-index) |similarity<br>distance | Yes | Yes | Set | O(m+n) |
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| [Sorensen-Dice coefficient](#sorensen-dice-coefficient) |similarity<br>distance | Yes | No | Set | O(m+n) |
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[1] In this library, Levenshtein edit distance, LCS distance and their sibblings are computed using the **dynamic programming** method, which has a cost O(m.n). For Levenshtein distance, the algorithm is sometimes called **Wagner-Fischer algorithm** ("The string-to-string correction problem", 1974). The original algorithm uses a matrix of size m x n to store the Levenshtein distance between string prefixes.
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```
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## Metric LCS (Longest Common Subsequence)
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## Metric Longest Common Subsequence
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Distance metric based on Longest Common Subsequence, from the notes "An LCS-based string metric" by Daniel Bakkelund.
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http://heim.ifi.uio.no/~danielry/StringMetric.pdf
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```
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## N-Gram distance (Kondrak)
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## N-Gram
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Normalized N-Gram distance as defined by Kondrak, "N-Gram Similarity and Distance", String Processing and Information Retrieval, Lecture Notes in Computer Science Volume 3772, 2005, pp 115-126.
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