Fun little problem - just stick the parents in front of the children and clean it up at the end :)

#!/usr/bin/perl

use strict;
use warnings;
use List::Util qw( uniq );

my $data =
  {
  986172 => { cat_name => "Category1", cat_parent_id => "" },
  986176 => { cat_name => "Category2", cat_parent_id => 986172 },
  986177 => { cat_name => "Category3", cat_parent_id => 986176 },
  986178 => { cat_name => "Category4", cat_parent_id => 986177 },
  };

my $string = join ',', find( keys %$data );
print "$string\n";

sub find
  {
  uniq map {
    my $ref = $data->{$_};
    $ref ? ( find( $ref->{cat_parent_id} ), $ref->{cat_name} ) : ()
    } @_;
  }
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Or build a little prerequisite table and topologically extract the names one by one.

#!/usr/bin/perl

use strict;
use warnings;

my $data =
  {
  986172 => { cat_name => "Category1", cat_parent_id => "" },
  986176 => { cat_name => "Category2", cat_parent_id => 986172 },
  986177 => { cat_name => "Category3", cat_parent_id => 986176 },
  986178 => { cat_name => "Category4", cat_parent_id => 986177 },
  };

my $parents = '';
for my $v ( values %$data )
  {
  $parents .= $v->{cat_parent_id}
    ? $v->{cat_name} . ' ' .  $data->{$v->{cat_parent_id}}{cat_name} .
+ "\n"
    : $v->{cat_name} . "\n";
  }
#print "$parents\n";

my @order;
$parents =~ s/\b($1)\b//g, push @order, $1 while $parents =~ s/^(\w+)\
+h*\n//m;
my $answer = join ',', @order;
print "$answer\n";
$parents and die "loop in parents at\n$parents";
[download]