MySQL - Какой хэш-алгоритм мне использовать для этого?

Возможно, вы могли бы реализовать алгоритм levenshtein в mysql как хранимую функцию, ниже приведен пример, надеюсь, что это поможет:

DELIMITER //
CREATE FUNCTION levenshtein( s1 VARCHAR(255), s2 VARCHAR(255) )
  RETURNS INT
  DETERMINISTIC
  BEGIN
    DECLARE s1_len, s2_len, i, j, c, c_temp, cost 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;
    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 DO
        SET s1_char = SUBSTRING(s1, i, 1), c = 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;
        END WHILE;
        SET cv1 = cv0, i = i + 1;
      END WHILE;
    END IF;
    RETURN c;
  END; 

Источник http://www.artfulsoftware.com/infotree/queries.php#552 (Исправлено добавлением DELIMITER //)

Пример тестирования script

<?php
//I inserted these test words into a test database
$words = 'back, lack, pack, rack, sack, tack, yak, black, knack, quack, slack, smack, snack, stack, track, whack, attack,bale, fail, hail, mail, male, nail, pail, tale, rail, sail, stale, scale, snail, whale, detail, email,air, bare, care, chair, dare, fair, hair, pair, rare, wear, chair, flare, stare, scare, share, spare, square, there, where, aware, beware, compare, declare, despair, prepare, repair, unfair,ache, bake, fake, lake, make, rake, take, brake, break, flake, quake, snake, steak, awake, mistake,all, ball, call, doll, hall, fall, tall, crawl, small, baseball, football,an, can, fan, man, pan, ran, tan, van, plan, scan, span, began,and, band, hand, land, sand, bland, command, demand, expand, stand, understand,cap, gap, map, nap, tap, zap, chap, clap, flap, slap, snap, strap, trap, wrap,are, bar, car, far, jar, tar, star, scar, afar, guitar,at, bat, fat, mat, pat, rat, sat, flat, that, splat, combat,ate, date, fate, mate, late, gate, rate, wait, crate, great, plate, skate, slate, state, straight, trait, weight, create,bed, dead, fed, head, led, read, red, said, bread, fled, spread, thread, tread, instead,bell, fell, sell, well, yell, shell, smell, spell, farewell, hotel, motel,den, hen, men, pen, ten, glen, then, when, wren, again,bet, get, jet, let, met, pet, set, vet, wet, yet, threat, barrette, reset, upset,bin, chin, in, pin, tin, grin, thin, twin, skin, begin, within,king, ring, sing, wing, zing, bring, cling, fling, sling, spring, sting, string, swing, thing,bit, fit, hit, it, kit, lit, pit, sit, flit, knit, quit, skit, slit, spit, split, admit, commit, permit,bite, kite, bright, fight, fright, knight, night, might, right, tight, white, write, delight, tonight,go, hoe, low, mow, row, sew, toe, blow, crow, dough, flow, know, glow, grow, know, show, slow, snow, stow, though, throw, ago, although, below,cot, dot, got, hot, lot, not, pot, rot, tot, bought, fought, knot, taught, shot, spot, squat, forgot,crowned, found, ground, hound, mound, pound, round, sound, wound, around, surround,bows, hose, nose, rose, toes, blows, flows, froze, grows, those,cub, rub, sub, tub, club, stub, scrub, shrub ,bun, fun, gun, one, run, son, sun, ton, won, done, none, begun, outdone, undone';

//A Class for db connection
Class DB{
    private $db;

    function __construct($host,$dbname,$user,$pass){
        $this->dbhost = $host;
        $this->dbname = $dbname;
        $this->dbuser = $user;
        $this->dbpass = $pass;
    }

    private function connect(){
        if (!$this->db instanceof PDO){
            $this->db = new PDO('mysql:dbname='.$this->dbname.';host='.$this->dbhost, $this->dbuser, $this->dbpass);
            $this->db->setAttribute(PDO::ATTR_ERRMODE, PDO::ERRMODE_EXCEPTION);
        }
    }

    //A Model method for the levenshtein_query.
    public function levenshtein_query($word,$dist){
        $this->connect();
        $sql = "SELECT `word` FROM `words` WHERE levenshtein( :word ,`word` ) BETWEEN 0 AND $dist";
        $statement = $this->db->prepare($sql);
        $statement->bindParam(':word', $word, PDO::PARAM_STR);
        $statement->execute();
        return $statement->fetchAll(PDO::FETCH_ASSOC);
    }
}

//ini the model class
$model = new DB('localhost','test_db','root','');

//The Word posted
$word = 'eet';
$result = $model->levenshtein_query($word,1);

print_r($result);
/*
//The Result
Array
(
    [0] => Array
        (
            [word] => bet
        )

    [1] => Array
        (
            [word] => get
        )

    [2] => Array
        (
            [word] => jet
        )

    [3] => Array
        (
            [word] => let
        )

    [4] => Array
        (
            [word] => met
        )

    [5] => Array
        (
            [word] => pet
        )

    [6] => Array
        (
            [word] => set
        )

    [7] => Array
        (
            [word] => vet
        )

    [8] => Array
        (
            [word] => wet
        )

    [9] => Array
        (
            [word] => yet
        )

    [10] => Array
        (
            [word] => meet
        )

)

*/

Возможно, его интересует...