chrishowe:

Try changing your expression to:

$sth_get_branch_list = $dbh->prepare(q(
     SELECT branch FROM postgres_database WHERE tree = 'first_tree'
     AND branch ~ '$root\.\d+';
));
[download]

(You don't use slashes for regular expressions in PostgreSQL, see http://www.postgresql.org/docs/8.3/static/functions-matching.html and http://www.oreillynet.com/pub/a/databases/2006/02/02/postgresq_regexes.html.)

Update: Since I don't use PostgreSQL, there are probably other differences as well.

Update 2: In this case, you really don't need regular expressions anyway, you could use:

$sth_get_branch_list = $dbh->prepare(q(
     SELECT branch FROM postgres_database WHERE tree = 'first_tree'
     AND branch like '$root%';
));
[download]

...roboticus