Find path between nodes with SQL

Question

Hi,

i have two mysql tables: nodes and relations

CREATE TABLE `nodes` (
  `id` int(10) unsigned NOT NULL auto_increment,
  PRIMARY KEY  (`id`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8;

CREATE TABLE `relations` (
  `node_id` int(10) unsigned NOT NULL,
  `related_node_id` int(10) unsigned NOT NULL
) ENGINE=InnoDB DEFAULT CHARSET=utf8;

Lets say there are four rows in nodes: Node 1 and 2 share a relation, 2 and 3, 1 and 4, 4 and 3

INSERT INTO `relations` VALUES (1, 2);
INSERT INTO `relations` VALUES (2, 3);
INSERT INTO `relations` VALUES (1, 4);
INSERT INTO `relations` VALUES (4, 3);

Is there any algorithm to get the paths between the related nodes? Like

+---------+------------------+---------+
| node_id | related_node_id  | route   |
+---------+------------------+---------+
|       1 |                2 | 1/2     |
|       2 |                3 | 2/3     |
|       1 |                4 | 1/4     |
|       4 |                3 | 4/3     |
|       1 |                3 | 1/2/3   |
|       1 |                3 | 1/4/3   |
+---------+-----------+------+---------+

Answer 1

I believe you are looking for the all-pairs shortest paths problem. SQL does not seem to be the right tool for solving this - lots of joins - therefore I suggest using a scripting language that interfaces with MySQL.

Answer 2

In vanilla MySQL, there is no easy way to do it.

You can install OQGRAPH (it's a plugin storage engine designed to store the graphs), create a graph table in it and issue a query like this:

SELECT  *
FROM    oqtable
WHERE   latch = 1
        AND origid = 1
        AND destid = 3

which will use Dijkstra's algorithm to find the shortest path between 1 and 3.

Answer 3

I'm looking for all path rather than for the shortest one.