package Bio::Coordinate::Graph;
use utf8;
use strict;
use warnings;
use parent qw(Bio::Root::Root);
# ABSTRACT: Finds shortest path between nodes in a graph.
# AUTHOR: Heikki Lehvaslaiho
# OWNER: Heikki Lehvaslaiho
# LICENSE: Perl_5
=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.
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 simpler and faster breadth-first
would be enough. Luckily the difference for small graphs is not
significant and the implementation is capable of taking 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:
$hash = {
'6' => undef,
'3' => {
'6' => 1
},
'2' => {
'6' => 1,
'4' => 1,
'3' => 1
},
'1' => {
'2' => 1
},
'4' => {
'5' => 1
},
'5' => undef
};
Note that the names need to be positive integers. Root should be '1'
and directness of the graph is taken advantage of to speed
calculations by assuming that downsream nodes always have larger
number as name.
An alternative (shorter) way of describing input is to use hash of
arrays. See L.
=cut
=head2 new
=cut
sub new {
my($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
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 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.:
$res = {
'2' => {
'prev' => '1',
'dist' => 1
},
'1' => {
'prev' => undef,
'dist' => 0
},
};
Args : name of the start node
=cut
sub dijkstra {
my ($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;