Distinct on two columns (separately) and MIN on another column - sql

Question

I've tried to strip this problem down the the bare bones; I hope I've still captured the essence of what I'm trying to achieve in the original query!
Code to generate the tables and data can be found here.
SQL flavour is Microsoft SQL Server 2000 (although I've been running this stripped down test case on MySQL)
The original table
+-----------+----------+----------+
| master_id | slave_id | distance |
+-----------+----------+----------+
| 1 | 1 | 0.1 |
| 1 | 3 | 10 |
| 2 | 2 | 3 |
| 3 | 2 | 2 |
+-----------+----------+----------+
Description of what is required
I would like to select slave_id master_id pairs with MIN(distance) with no duplicates of either master_id or slave_id.
The desired results table
+-----------+----------+----------+
| master_id | slave_id | distance |
+-----------+----------+----------+
| 1 | 1 | 0.1 |
| 3 | 2 | 2 |
+-----------+----------+----------+
My Attempt
SELECT
join_table.master_id,
join_table.slave_id,
join_table.distance
FROM join_table
INNER JOIN
(
SELECT
slave_id,
MIN(distance) AS distance
FROM join_table
GROUP BY slave_id
) AS self_join
ON self_join.slave_id = join_table.slave_id
AND self_join.distance = join_table.distance
What's wrong with my attempt
This query produces duplicates of master_id
Any help will be very much appreciated.

Answer 1

This should give the correct result:
select distinct t.master_id,
t.slave_id,
t.distance
from join_table t
inner join
(
SELECT ID, min(Distance) dist
FROM
(
SELECT master_ID ID, MIN(distance) AS Distance
FROM join_table
GROUP BY master_ID
UNION
SELECT slave_ID ID, MIN(distance) AS Distance
FROM join_table
GROUP BY slave_ID
) src
GROUP BY ID
) md
on t.distance = md.dist
and (t.master_id = md.id or t.slave_id = md.id)
See SQL Fiddle with Demo

Answer 2

If I got you right, here is what I would do:
SELECT DISTINCT t.master_id
,t.slave_id
,t.distance
FROM your_table t
INNER JOIN
(
SELECT master_id id, min(distance) distance
FROM your_table
GROUP BY master_id
UNION
SELECT slave_id id, min(distance) distance
FROM your_table
GROUP BY slave_id
) sub
ON (sub.id = t.master_id AND sub.distance = t.distance)
OR (sub.id = t.slave_id AND sub.distance = t.distance)