As Abigail-II says, it would be expensive to get the shortest match, and the following code is expensive, but it does what you want for the examples.

use strict;
use warnings;

my $re = qr/the\b.*?quick\b.*?fox/;
while (<DATA>) {
    chomp($_);
    my $text = $_;
    my $match;
    while ($text =~ /($re)/) {
        $match = $1;
        $text = substr($match, 1);
    }
    print "it matches '$match'\n";
}

__DATA__
the dog and the bear are quick, but the quick white fox is quicker
the quick fox and the brown fox
the quick raven and the quick fox
the quick yellow fox and the quick fox
[download]

Notice that it will return 'the quick yellow fox' in the last case since that's the first "shortest" match.

Hope this helps, -gjb-