The function given for levenshtein <= 1 above is not right -- it gives incorrect results for e.g., "bed" and "bid".
I modified the "MySQL Levenshtein distance query" given above, in the first answer, to accept a "limit" that will speed it up a little. Basically, if you only care about Levenshtein <= 1, set the limit to "2" and the function will return the exact levenshtein distance if it is 0 or 1; or a 2 if the exact levenshtein distance is 2 or greater.
This mod makes it 15% to 50% faster -- the longer your search word, the bigger the advantage (because the algorithm can bail earlier.) For instance, on a search against 200,000 words to find all matches within distance 1 of the word "giggle," the original takes 3 min 47 sec on my laptop, versus 1:39 for the "limit" version. Of course, these are both too slow for any real-time use.
Code:
DELIMITER $$
CREATE FUNCTION levenshtein_limit_n( s1 VARCHAR(255), s2 VARCHAR(255), n INT)
RETURNS INT
DETERMINISTIC
BEGIN
DECLARE s1_len, s2_len, i, j, c, c_temp, cost, c_min INT;
DECLARE s1_char CHAR;
-- max strlen=255
DECLARE cv0, cv1 VARBINARY(256);
SET s1_len = CHAR_LENGTH(s1), s2_len = CHAR_LENGTH(s2), cv1 = 0x00, j = 1, i = 1, c = 0, c_min = 0;
IF s1 = s2 THEN
RETURN 0;
ELSEIF s1_len = 0 THEN
RETURN s2_len;
ELSEIF s2_len = 0 THEN
RETURN s1_len;
ELSE
WHILE j <= s2_len DO
SET cv1 = CONCAT(cv1, UNHEX(HEX(j))), j = j + 1;
END WHILE;
WHILE i <= s1_len and c_min < n DO -- if actual levenshtein dist >= limit, don't bother computing it
SET s1_char = SUBSTRING(s1, i, 1), c = i, c_min = i, cv0 = UNHEX(HEX(i)), j = 1;
WHILE j <= s2_len DO
SET c = c + 1;
IF s1_char = SUBSTRING(s2, j, 1) THEN
SET cost = 0; ELSE SET cost = 1;
END IF;
SET c_temp = CONV(HEX(SUBSTRING(cv1, j, 1)), 16, 10) + cost;
IF c > c_temp THEN SET c = c_temp; END IF;
SET c_temp = CONV(HEX(SUBSTRING(cv1, j+1, 1)), 16, 10) + 1;
IF c > c_temp THEN
SET c = c_temp;
END IF;
SET cv0 = CONCAT(cv0, UNHEX(HEX(c))), j = j + 1;
IF c < c_min THEN
SET c_min = c;
END IF;
END WHILE;
SET cv1 = cv0, i = i + 1;
END WHILE;
END IF;
IF i <= s1_len THEN -- we didn't finish, limit exceeded
SET c = c_min; -- actual distance is >= c_min (i.e., the smallest value in the last computed row of the matrix)
END IF;
RETURN c;
END$$