Join question

Hey All,

I have a query I'm trying to speed up, and I was hoping someone could
help me.  I have a three tables a and b hold data, and c just references
between a and b:

create table a (  a_id int,  x int
);

create table b (  b_id int,  x int
);

create table c (  a_id int,  b_id int
);

I am doing a query like this:

SELECT a.x, max(b.x) FROM a, b, c WHERE a.a_id = c.a_id AND b.b_id =
c.b_id GROUP by a.x;

I only need to get one row from b for each row in a, and it really
doesn't matter which one.  I use max() to get a single value from table
b.  There are generally be dozens to hundreds of rows in b for each row
in a.  The problem is when I have a query with tens of thousands of rows
in a that the join with b will have millions of rows, and is really
slow.  The group by effectively reduces the results down to what I want,
but it still has to process the millions of rows.  Does anyone know a
way I could restructure this query to get only one b for each a in a
faster way?

Thanks,
Ed Tyrrill