Xilinx Fuzzy Match Alveo Product Overview

Levenshtein Distances

Levenshtein edit distance between two strings is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other. Below is the mathematically definition:

where

• tail(x) is a string of all but the first character of x, and x[n] is the nth character of the string x, starting with character 0.

• lev(tail(a), b) is deletion (from a to b).

• lev(a, tail(b) is insertion.

• lev(tail(a), tail(b)) replacement.

For example, the Levenshtein distance between “kitten” and “sitting” is 3, since the following three edits change one into the other, and there is no way to do it with fewer than three edits:

1. kitten → sitten (substitution of “s” for “k”)

2. sitten → sittin (substitution of “i” for “e”)

3. sittin → sitting (insertion of “g” at the end).

Similarity of Two Strings

The similarity of two strings is defined as below, where lev() is the Levenshtein edit distance of the strings:

Two strings are considered as a match if the similarity score is greater than a user programmable threshold.