If you're primarily going to read the tree, it might be advantageous to store pointers to every ancestor instead of just the direct parent. You can query for all the ancestors in one query, and then build the path in Perl. For example,
Nodes
=====
id | node_name | parent
----+------------------+--------
1 | Parent Node1 | 0
2 | Child Node 1 | 1
3 | Sub Child Node 1 | 2
4 | Leaf1 | 3
HasAncestor
===========
child | ancestor
-------+----------
2 | 1
3 | 2
3 | 1
4 | 3
4 | 2
4 | 1
SELECT Nodes.*
FROM Nodes
LEFT JOIN HasAncestor
ON Nodes.id = HasAncestor.child
WHERE Nodes.id = ?
Returns for args (3)
====================
id | node_name | parent
----+------------------+--------
1 | Parent Node1 | 0
2 | Child Node 1 | 1
3 | Sub Child Node 1 | 2
This way, you can easily fetch an entire subtree. For example,
SELECT Nodes.*
FROM Nodes
LEFT JOIN HasAncestor
ON Nodes.id = HasAncestor.child
WHERE HasAncestor.ancestor = ?
Returns for args (2)
====================
id | node_name | parent
----+------------------+--------
3 | Sub Child Node 1 | 2
4 | Leaf1 | 3
You can still fetch only the immediate children. For example,
SELECT Nodes.*
FROM Nodes
WHERE Nodes.parent = ?
Returns for args (2)
====================
id | node_name | parent
----+------------------+--------
3 | Sub Child Node 1 | 2
Similar for the immediate parent.