are you confined to representing your tree that way? i've done some basic relationship traversals using a hash of node objects, each referring to it's parent. you can then just lookup the node you want and do a recursive call up the parent chain like so:

package Node;

use strict;
use warnings;


sub new
{
    my $self  = bless( {}, shift );
    my $name = shift;
    $self->name($name);
    return $self;
}

sub name
{
    my $self = shift;
    @_ ? $self->{name} = shift : $self->{name};
}

sub parent
{
    my $self = shift;
    @_ ? $self->{parent} = shift : $self->{parent};
}

sub ancestory
{
    my $self = shift;
    my $decendants = shift || ();
    my $name = $self->name();
    unshift @{$decendants}, $self->name();
    my $parent = $self->parent();
    $parent ? $parent->ancestory($decendants) : $decendants;
}



my %Nodes;

sub GetNode
{
    my $nodeName = shift;
    if ( ! $Nodes{$nodeName} )
    {
        $Nodes{$nodeName} = new Node($nodeName);
    }
    return $Nodes{$nodeName};
    
}

#
#   load relationships
#
while (<DATA>)
{
    chomp;
    my ($parentName,$childName) = split ",",$_ ;
    my $parentNode = GetNode($parentName);
    my $childNode = GetNode($childName);
    $childNode->parent($parentNode)
}

#
#   print path to the node you are looking for
#
print join " ", @{GetNode("managedApplication")->ancestory()};
print "\n";
print join " ", @{GetNode("personnel")->ancestory()};
print "\n";


__DATA__
top,inetUser
top,person
top,application
person,organizationalPerson
application,managedApplication
organizationalPerson,managedPerson
managedPerson,personnel
[download]

produces:

top application managedApplication
top person organizationalPerson managedPerson personnel
[download]