Note that I'm not looking for perl speed tricks, but rather algorithmic enhancements. I used the subroutines to make the main algorithm more readable; also, the implementation is not very perlish since that guy wanted to use it for a C++ library.

use strict;
use warnings;

my @sets =
    ([ 0, 1, 2, 3,          7, 8, 9, 10, 11, 12, 13, 14, 15,     ],
     [ 0,       3,          7, 8,    10, 11,     13, 14,     16, ],
     [ 0, 1, 2, 3,    5,    7, 8,    10, 11, 12, 13, 14,     16, ],
     [       2, 3, 4,    6, 7, 8,    10, 11, 12,     14,     16, ],
     [ 0, 1, 2, 3,          7, 8, 9, 10, 11,     13, 14, 15,     ]);

my $numSets = scalar @sets;
my @intersection = ();
my $currentSet = 0;
my @marker = (0, 0, 0, 0, 0);
my $currentItem;

# helper functions 

sub stepMarker {
    $marker[$currentSet]++;
    if ($marker[$currentSet] >= scalar @{$sets[$currentSet]}) {
        # we are at the end of the current set
        # => abort, there cannot be any more common items
        last MAIN;
    }
}

sub nextSet {
    $currentSet++;
    $currentSet %= $numSets;
}

sub getCurrentItem {
    return $sets[$currentSet]->[$marker[$currentSet]];
}


# main intersection algorithm

my $activeItem = getCurrentItem;
my $isPresent = 1;
MAIN: while (1) {
    stepMarker();
    nextSet;

    while (($currentItem = getCurrentItem()) < $activeItem) {
        stepMarker();
    }

    if ($currentItem > $activeItem) {
        $activeItem = $currentItem;
        $isPresent = 1;
    } else {
        $isPresent++;

        if ($isPresent == $numSets) {
            # item has been found present in all sets
            push @intersection, $activeItem;
            stepMarker();
            $activeItem = getCurrentItem;
            $isPresent = 1;
        }
    }
}

print "Common items in the $numSets sets: @intersection\n";
[download]