Conditional Sorting

[monkfan]

Dear all,
Suppose I have the following array and hash:

my @arr = ('foo','bar','qux','foo1','bar1','qux1');

my $hash = {
          '4-5' => '0.750',
          '0-4' => '0.167',
          '0-2' => '0.600',
          '2-3' => '0.200',
          '2-4' => '0.300',
          '0-3' => '0.300',
          '2-5' => '0.400',
          '1-2' => '0.550',
          '1-5' => '0.273',
          '3-4' => '0.300',
          '1-4' => '0.182',
          '0-1' => '0.917',
          '3-5' => '0.400',
          '0-5' => '0.250',
          '1-3' => '0.300'
        };

Now the key and value of $hash represent the following:

    'x-y' => 'VALUE'

     x and y represent the index of the element in @arr
     x and y are reversible

     so for example:

     '0-3' => '0.300', means that
     'foo' and 'foo1' has value 0.300 OR
     'foo1' and 'foo' has value 0.300

Now my question is, how can we sort decendingly @arr_sorted, such that for every index 'z' in @arr, the VALUE of its (z,y) <= (z,y+1)?

Members of @arr_sorted is exactly the same as @arr, only sorted according to the condition above. And yes, every 'z' has its corresponding @arr_sorted.

I'm not sure how to proceed from here:

foreach my $z (0 .. ($#arr-1)) {

   my @arr_sorted = sort{???} @arr;

}

Updated.