Разобраться с процедурой поиска кратчайшего пути в графе

BEGIN
    DECLARE m VARCHAR(250);
    DECLARE n INT;
    SELECT COUNT(*) INTO n FROM vertex;
 
    CREATE TABLE IF NOT EXISTS path 
    (start INT, middle VARCHAR(255), finish INT, weight INT)
    ENGINE=MEMORY;
    INSERT INTO path
    SELECT id, "", id, 0
    FROM vertex;
 
    CREATE TABLE IF NOT EXISTS tmp LIKE path;
 
    WHILE n > 0 DO
        INSERT INTO tmp
        SELECT * FROM path;
 
        INSERT INTO tmp
        SELECT u.start, CONCAT("-",u.finish,v.middle), v.finish, u.weight+v.weight
        FROM edge AS u, path AS v WHERE u.finish=v.start;
 
        TRUNCATE path;
 
        INSERT INTO path 
        SELECT y.* FROM (SELECT start, finish, MIN(weight) AS weight
            FROM tmp GROUP BY start, finish) AS x
        JOIN tmp AS y
        ON x.start=y.start AND x.finish=y.finish AND x.weight=y.weight
        GROUP BY y.start,y.finish,y.weight;
 
        TRUNCATE tmp;
 
        SET n = n - 1;
    END WHILE;
 
    
 
    SELECT middle INTO m FROM path WHERE start=a AND finish=b;
    IF m is NULL THEN
        SELECT "no way" AS way;
    ELSE
        SELECT CONCAT(a,m) AS way;
    END IF;
 
    DROP TABLE IF EXISTS path;
    DROP TABLE IF EXISTS tmp;
END