Pack the data into a big vector and then sort it inplace using Sort::Packed. Memory requirements will get reduced to ~1/4 of your data set. 
#!/usr/bin/perl

use strict;
use warnings;

use Sort::Packed qw(sort_packed);

my $packed = '';
my ($len);

my %val = (A => 0, C => 1, G => 2, T => 3);
my %rev = reverse %val;

sub compress {
    my @data = split //, scalar(reverse shift);
    my $out = '';
    for (my $i = 0; $i < @data; $i++) {
    my $bits = $val{$data[$i]};
    defined $bits or die "bad data";
    vec($out, $i, 2) = $bits;
    }
    scalar reverse $out
}

sub decompress {
    my $data = reverse shift;
    my $len = shift;
    my $out;
    for (my $i = 0; $i< $len; $i++) {
    $out .= $rev{vec($data, $i, 2)}
    }
    scalar reverse $out;
}

while(<DATA>) {
    chomp;
    ($len ||= length) == length or die "bad data";
    $packed .= compress $_;
}

my $bytes = int(($len * 2 + 7) / 8);
my $n = length($packed) / $bytes;

sort_packed "C$bytes" => $packed;

for (my $i = 0; $i < $n; $i++) {
    print decompress(substr($packed, $i * $bytes, $bytes), $len), "\n"
+;
}

__DATA__
AAACGAGAAGTAATATCAGTATCGTATGCTTCAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAC
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
TTTTCGCCTTCCGGGTGCCGCTGGGGTCTTTCTC
GCACACTCGGAGCCCGGGGAGCCAGAGGAAACAA
GATCATGACACAGTTGATAAAATTGTTGTTCAGA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACC
AAACGAGAAGTAATATCAGTATCGTATGCTTCAC
AAACGAGAAGTAATATCAGTATCGTATGCTTCGA
AAACGAGAAGTAATATCAGTATCGTATGTTTCAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAATA

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Preallocating the vector will also further reduce memory comsumption.

In reply to Re: Sorting Gigabytes of Strings Without Storing Them by salva
in thread Sorting Gigabytes of Strings Without Storing Them by neversaint

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