# $Id: Graph.pm,v 1.5 2004/05/28 13:23:24 jason Exp $
#
# bioperl module for Bio::Coordinate::Graph
#
# Cared for by Heikki Lehvaslaiho <heikki@ebi.ac.uk>
#
# Copyright Heikki Lehvaslaiho
#
# You may distribute this module under the same terms as perl itself

# POD documentation - main docs before the code

=head1 NAME

Bio::Coordinate::Graph - Finds shortest path between nodes in a graph

=head1 SYNOPSIS

  # get a hash of hashes representing the graph. E.g.:
  my $hash= {
	     '1' => {
		     '2' => 1
		    },
	     '2' => {
		     '4' => 1,
		     '3' => 1
		    },
	     '3' => undef,
	     '4' => {
		     '5' => 1
		    },
	     '5' => undef
	    };

  # create the object;
  my $graph = Bio::Coordinate::Graph->new(-graph => $hash);

  # find the shortest path between two nodes
  my $a = 1;
  my $b = 6;
  my @path = $graph->shortest_paths($a);
  print join (", ", @path), "\n";


=head1 DESCRIPTION

This class calculates the shortest path between input and output
coordinate systems in a graph that defines the relationships between
them. This class is primarely designed to analyze gene-related
coordinate systems. See L<Bio::Coordinate::GeneMapper>.

Note that this module can not be used to manage graphs.

Technically the graph implemented here is known as Directed Acyclic
Graph (DAG). DAG is composed of vertices (nodes) and edges (with
optional weights) linking them. Nodes of the graph are the coordinate
systems in gene mapper.

The shortest path is found using the Dijkstra's algorithm. This
algorithm is fast and greedy and requires all weights to be
positive. All weights in the gene coordinate system graph are
currently equal (1) making the graph unweighted. That makes the use of
Dijkstra's algorithm an overkill. A impler and faster breadth-first
would be enough. Luckily the difference for small graphs is not
signigicant and the implementation is capable to take weights into
account if needed at some later time.

=head2 Input format

The graph needs to be primed using a hash of hashes where there is a
key for each node. The second keys are the names of the downstream
neighboring nodes and values are the weights for reaching them. Here
is part of the gene coordiante system graph::


    $hash = {
	     '6' => undef,
	     '3' => {
		     '6' => 1
		    },
	     '2' => {
		     '6' => 1,
		     '4' => 1,
		     '3' => 1
		    },
	     '1' => {
		     '2' => 1
		    },
	     '4' => {
		     '5' => 1
		    },
	     '5' => undef
	    };


Note that the names need to be positive integrers. Root should be '1'
and directness of the graph is taken advantage of to speed
calculations by assuming that downsream nodes always have larger
number as name.

An alternative (shorter) way of describing input is to use hash of
arrays. See L<Bio::Coordinate::Graph::hash_of_arrays>.


=head1 FEEDBACK

=head2 Mailing Lists

User feedback is an integral part of the evolution of this and other
Bioperl modules. Send your comments and suggestions preferably to the
Bioperl mailing lists  Your participation is much appreciated.

  bioperl-l@bioperl.org                         - General discussion
  http://bio.perl.org/MailList.html             - About the mailing lists

=head2 Reporting Bugs

report bugs to the Bioperl bug tracking system to help us keep track
 the bugs and their resolution.  Bug reports can be submitted via
 email or the web:

  bioperl-bugs@bio.perl.org
  http://bugzilla.bioperl.org/

=head1 AUTHOR - Heikki Lehvaslaiho

Email:  heikki@ebi.ac.uk
Address:

     EMBL Outstation, European Bioinformatics Institute
     Wellcome Trust Genome Campus, Hinxton
     Cambs. CB10 1SD, United Kingdom

=head1 APPENDIX

The rest of the documentation details each of the object
methods. Internal methods are usually preceded with a _

=cut


# Let the code begin...

package Bio::Coordinate::Graph;
use vars qw(@ISA );
use strict;

# Object preamble - inherits from Bio::Root::Root
use Bio::Root::Root;

@ISA = qw(Bio::Root::Root);


sub new {
    my($class,@args) = @_;
    my $self = $class->SUPER::new(@args);

    my($graph, $hasharray) =
	$self->_rearrange([qw(
                              GRAPH
                              HASHARRAY
			     )],
			 @args);

    $graph  && $self->graph($graph);
    $hasharray  && $self->hasharray($hasharray);

    $self->{'_root'} = undef;

    return $self; # success - we hope!

}

=head2 Graph structure input methods

=cut

=head2 graph

 Title   : graph
 Usage   : $obj->graph($my_graph)
 Function: Read/write method for the graph structure
 Example : 
 Returns : hash of hashes grah structure
 Args    : reference to a hash of hashes

=cut

sub graph {

  my ($self,$value) = @_;

  if ($value) {
      $self->throw("Need a hash of hashes")
	  unless  ref($value) eq 'HASH' ;
      $self->{'_dag'} = $value;

      # empty the cache
      $self->{'_root'} = undef;

  }

  return $self->{'_dag'};

}


=head2 hash_of_arrays

 Title   : hash_of_arrays
 Usage   : $obj->hash_of_array(%hasharray)
 Function: An alternative method to read in the graph structure.
           Hash arrays are easier to type. This method converts
           arrays into hashes and assigns equal values "1" to
           weights.

 Example : Here is an example of simple structure containing a graph.

           my $DAG = {
	              6  => [],
	              5  => [],
	              4  => [5],
	              3  => [6],
	              2  => [3, 4, 6],
	              1  => [2]
	             };

 Returns : hash of hashes graph structure
 Args    : reference to a hash of arrays

=cut

sub hash_of_arrays {

  my ($self,$value) = @_;

  # empty the cache
  $self->{'_root'} = undef;

  if ($value) {

      $self->throw("Need a hash of hashes")
	  unless  ref($value) eq 'HASH' ;

      #copy the hash of arrays into a hash of hashes;
      my %hash;
      foreach my $start ( keys %{$value}){
	  $hash{$start} = undef;
	  map { $hash{$start}{$_} = 1 } @{$value->{$start}};
      }

      $self->{'_dag'} = \%hash;
  }

  return $self->{'_dag'};

}

=head2 Methods for determining the shortest path in the graph

=cut

=head2 shortest_path

 Title   : shortest_path
 Usage   : $obj->shortest_path($a, $b);
 Function: Method for retrieving the shortest path between nodes.
           If the start node remains the same, the method is sometimes
           able to use cached results, otherwise it will recalculate
           the paths.
 Example : 
 Returns : array of node names, only the start node name if no path
 Args    : name of the start node
         : name of the end node

=cut


sub shortest_path {
    my ($self, $root, $end) = @_;

    $self->throw("Two arguments needed") unless @_ == 3;
    $self->throw("No node name [$root]")
	unless exists $self->{'_dag'}->{$root};
    $self->throw("No node name [$end]")
	unless exists $self->{'_dag'}->{$end};

    my @res;     # results
    my $reverse;

    if ($root > $end) {
	($root, $end) = ($end, $root );
	$reverse++;
    }

    # try to use cached paths
    $self->dijkstra($root) unless
	defined $self->{'_root'} and $self->{'_root'} eq $root;

    return @res unless $self->{'_paths'} ;

    # create the list
    my $node = $end;
    my $prev = $self->{'_paths'}->{$end}{'prev'};
    while ($prev) {
	unshift @res, $node;
	$node = $self->{'_paths'}->{$node}{'prev'};
	$prev = $self->{'_paths'}->{$node}{'prev'};
    }
    unshift @res, $node;

    $reverse ? return reverse @res : return @res;
}


=head2 dijkstra

 Title   : dijkstra
 Usage   : $graph->dijkstra(1);
 Function: Implements Dijkstra's algorithm.
           Returns or sets a list of mappers. The returned path
           description is always directed down from the root.
           Called from shortest_path().
 Example : 
 Returns : Reference to a hash of hashes representing a linked list
           which contains shortest path down to all nodes from the start
           node. E.g.:

            $res = {
                      '2' => {
                               'prev' => '1',
                               'dist' => 1
                             },
                      '1' => {
                               'prev' => undef,
                               'dist' => 0
                             },
                    };

 Args    : name of the start node

=cut

#' keep emacs happy

sub dijkstra {
    my ($self,$root) = @_;

    $self->throw("I need the name of the root node input") unless $root;
    $self->throw("No node name [$root]")
	unless exists $self->{'_dag'}->{$root};

    my %est = ();          # estimate hash
    my %res = ();          # result hash
    my $nodes = keys %{$self->{'_dag'}};
    my $maxdist = 1000000;

    # cache the root value
    $self->{'_root'} = $root;

    foreach my $node ( keys %{$self->{'_dag'}} ){
	if ($node eq $root) {
	    $est{$node}{'prev'} = undef;
	    $est{$node}{'dist'} = 0;
	} else {
	    $est{$node}{'prev'} = undef;
	    $est{$node}{'dist'} = $maxdist;
	}
    }

    # remove nodes from %est until it is empty
    while (keys %est) {

	#select the node closest to current one, or root node
	my $min_node;
	my $min = $maxdist;
	foreach my $node (reverse sort keys %est) {
	    if ( $est{$node}{'dist'} < $min ) {
		$min = $est{$node}{'dist'};
		$min_node = $node;
	    }
	}

	# no more links between nodes
	last unless ($min_node);

	# move the node from %est into %res;
	$res{$min_node} = delete $est{$min_node};

	# recompute distances to the neighbours
	my $dist = $res{$min_node}{'dist'};
	foreach my $neighbour ( keys %{$self->{'_dag'}->{$min_node}} ){
	    next unless $est{$neighbour}; # might not be there any more
	    $est{$neighbour}{'prev'} = $min_node;
	    $est{$neighbour}{'dist'} =
		$dist + $self->{'_dag'}{$min_node}{$neighbour}
		if $est{$neighbour}{'dist'} > $dist + 1 ;
	}
    }
    return $self->{'_paths'} = \%res;
}


1;

