My knowledge about Graphs is quite limited, so I hope this is an easy question for some of you: I need a class that only accepts DAGs (Directed Acyclic Graphs). Based on Graph, the easiest solution is:

package DAG;
    
use strict;
use warnings;

use Graph::Directed;
use Carp;
    
use base 'Graph::Directed';

sub new {
    my ( $self, %args ) = @_;
    $args{multiedged} = 1;
    my $obj = $self->SUPER::new(%args);
    return $obj;
}

sub set_parents {
    my ( $self, $p1, $p2, $c, $checks ) = @_;
    $checks ||=1;

    if ( ( $self->in_degree($c) || 0) > 0) {
        croak "already has parents";
    }
    $self->add_edge_by_id($p1, $c, 1);
    $self->add_edge_by_id($p2, $c, 2);

    if ($checks && !$self->is_dag()) {
        $self->delete_edge_by_id($p1, $c, 1);
        $self->delete_edge_by_id($p2, $c, 2);
        croak 'Not a DAG anymore';
    }    
    
    return $self;
}
[download]

I add always parents-child triples. So add_parents() ist just a method that adds two edges. This code is really slow. My current attempt is a simple breadth first search:

...
sub is_ancestor {
    my ( $self, $v1, $v2 ) = @_;
    for my $child ( $self->get_successors($v1) ) {
        return 1 if $child eq $v2; 
    }
    for my $child ( $self->get_successors($v1) ) {
        my $found = $self->is_ancestor( $child, $v2 );
        return 1 if $found;
    }
    return 0;
}

sub set_parents {
    my ( $self, $p1, $p2, $c, $checks ) = @_;
    $checks ||=1;

    if ( ( $self->in_degree($c) || 0) > 0) {
        croak "already has parents";
    }
    $self->add_edge_by_id($p1, $c, 1);
    if ($checks && $self->is_ancestor($c, $p1)) {
        $self->delete_edge_by_id($p1, $c, 1);
        croak 'Not a DAG anymore';
    }    
    $self->add_edge_by_id($p2, $c, 2);
    if ($checks && $p1 ne $p2 && $self->is_ancestor($c, $p2)) {
        $self->delete_edge_by_id($p2, $c, 2);
        croak 'Not a DAG anymore';
    }    
    return $self;
}
[download]

Which is faster, but still too slow. Do you see how I could improve the performance? My goal is a simple random walk optimization, so I always remove the two incoming edges of a node and then add new ones. The number of nodes is between 100 and 700.

Am I doing something wrong here? Should I use another Graph module as base?

Update: Sorry for writing so unclear :( . What I now have is a big set of parents-child triples:

P1 --+   
     +--> Child
P2 --+
[download]

I start with greedy adding triples to the graph until all nodes are added. Then I start a simple MCMC optimization in the way that I select randomly a node, remove the incoming edges if they exist and then add two new valid incoming edges (another triple where the selected node is a child). So I have a DAG, remove zero or two edges, add two new ones (both directing in the same node) and want that the class very quickly checks whether the two new edges have introduced a directed circle.

With hundred nodes I get only about 50 iterations a second (without any scoring function). I am quite sure that there is a lot to improve.

Update 2: Graph::edges is quite expensive. After removing this in my MCMC iterations,I get about 200 iterations a second, which is at least something I can live with.

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