Using path aliases how to identify node IDs from database and based on these IDs how to publish them?
You can use drupal_get_normal_path() to get the node/id-paths for each of them.

Then you can use the following code to publish them.

// Load the node object.
$node = node_load($nid);
// Set the status property to 1.
$node-&gt;status = 1;
// Re-save the node.
node_save($node);