I've been chewing on this problem for a day now. This is clearly problem with two logical parts. Part 1 is to generate all legal mappings of N columns of data into M buckets, given the constraints that no bucket can be empty, and that the columns need to stay ordered. The second part is apply these mappings to the input data, and select a mapping that yields a "best fit."

I focused on the first part, looking for a quicker, simpler solution. I think I have one. Here it is. Given a number of columns and a number of buckets, the code below calculates all legal mappings of columns to buckets, and returns these in a hash, where the key is a printable string, and the value is an anonymous array.

{
    # map columns to buckets. key is string, value is anonymous array.
    my %c2bMap;

    sub c2bMappings {
        my($buckets, $columns) = @_;
        die "bogus args" unless $buckets > 1 && $columns > $buckets;
        %c2bMap = ();
        _genFrom(0, (0) x ($columns - $buckets), 1 .. ($buckets - 1));
        return \%c2bMap;
    }

    sub _genFrom {
        my @c2bMap = @_;
        return if exists $c2bMap{"@c2bMap"};
        print "@c2bMap\n";    #DEBUG
        $c2bMap{"@c2bMap"} = \@c2bMap;
    
        foreach my $i ( 2 .. $#c2bMap ) {
            my $n = $c2bMap[$i] - 1;
            if ( $c2bMap[$i - 2] == $n && $c2bMap[$i - 1] == $n ) {
                local $c2bMap[$i-1] = $c2bMap[$i];
                _genFrom(@c2bMap);
            }
        }
    }
}

c2bMappings(4,6);
__END__
0 0 0 1 2 3
0 0 1 1 2 3
0 1 1 1 2 3
0 1 1 2 2 3
0 1 2 2 2 3
0 1 2 2 3 3
0 1 2 3 3 3
0 1 1 2 3 3
0 0 1 2 2 3
0 0 1 2 3 3
[download]

Recursion only happens with valid mappings. Note the selective localization of an element of the array that the code is about to recurse on.