Generic representation of a directed acyclic graph. More...

#include <Directed_acyclic_graph.hpp>

Public Types
enum	Orientation_type
	Orientation of the edges in the Directed Acyclic Graph. More...

typedef boost::adjacency_list< boost::listS, boost::listS, boost::bidirectionalS, VertexProperty, EdgeProperty >	Graph
	Representation of the Directed Acyclic Graph as a adjacency_list of the Boost Graph Library. More...

typedef Graph_traits::vertex_descriptor	Vertex
	Representation of a Vertex of the Directed Acyclic Graph. More...

typedef Graph_traits::edge_descriptor	Edge
	Representation of an Edge of the Directed Acyclic Graph. More...

typedef Graph_traits::vertex_iterator	Vertices_iterator
	Iterator over all the vertices of the Directed Acyclic Graph. More...

typedef Graph_traits::edge_iterator	Edges_iterator
	Iterator over all the edges of the Directed Acyclic Graph. More...

typedef boost::transform_iterator< Get_parent_from_edge, In_edges_iterator >	Parents_iterator
	Iterator over all the parents of a given Vertex. More...

typedef boost::transform_iterator< Get_child_from_edge, Out_edges_iterator >	Children_iterator
	Iterator over all the children of a given Vertex. More...

typedef boost::filter_iterator< Is_maximal_element, Vertices_iterator >	Maximal_elements_iterator
	Iterator over the vertices of the Directed Acyclic Graph that are maximal elements of the corresponding partially ordered set. More...

typedef boost::filter_iterator< Is_minimal_element, Vertices_iterator >	Minimal_elements_iterator
	Iterator over the vertices of the Directed Acyclic Graph that are minimal elements of the corresponding partially ordered set. More...

Constructors
	T_Directed_acyclic_graph (Orientation_type orientation=MAXIMAL_ROOT_ORIENTATION)
	Default constructor creating an empty Directed Acyclic Graph. More...

Graph
const Graph &	get_graph (void) const
	Const Access to the BGL graph. More...

Graph &	get_graph (void)
	Acces to the BGL graph. More...

void	clear (void)

Vertices
unsigned	get_number_of_vertices (void) const
	Access to the number of vertices in the graph. More...

VertexProperty &	operator[] (Vertex v)
	Access to the property associated to a vertex. More...

const VertexProperty &	operator[] (Vertex v) const
	Const access to the property associated to a vertex. More...

bool	is_empty (void) const
	Check that the graph has no vertex. More...

template<class Comparator , class DataType , class OutputIterator >
OutputIterator	find_vertices_compared_to_data (const DataType &data, OutputIterator out, const Comparator &compare=Comparator()) const
	Find all the vertices in the graph having a property that compares equal to the input data. More...

template<class Comparator , class DataType >
bool	find_first_vertex_compared_to_data (const DataType &data, Vertex &v, const Comparator &compare=Comparator()) const
	Find the first vertex in the graph having a property that compares equal to the input data. More...

Vertex	add_vertex (void)
	Add a vertex with no property to the graph. More...

Vertex	add_vertex (const VertexProperty &p)
	Add a vertex with the property p to the graph. More...

void	remove_vertex (Vertex v)
	Remove the vertex v from the graph. More...

Vertices_iterator	vertices_begin (void) const
	Starts the set of vertices of the graph. More...

Vertices_iterator	vertices_end (void) const
	Ends the set of vertices of the graph. More...

Edges
unsigned	get_number_of_edges (void) const
	Access to the number of edges in the graph. More...

Edge	get_edge (Vertex u, Vertex v) const

EdgeProperty &	operator[] (Edge e)
	Access to the property attached to e. More...

const EdgeProperty &	operator[] (Edge e) const
	Const access to the property attached to e. More...

Edge	add_edge (Vertex u, Vertex v)
	Add an edge from u to v, with no property. More...

Edge	add_edge (Vertex u, Vertex v, const EdgeProperty &p)
	Add an edge from u to v, with the property p. More...

void	clear_vertex (Vertex v)
	Remove all edges incident to v. More...

void	remove_edge (Vertex u, Vertex v)
	Remove the edge from u to v. More...

void	remove_edge (Edge e)
	Remove the edge e from the graph. More...

Edges_iterator	edges_begin () const
	Starts the set of edges. More...

Edges_iterator	edges_end () const
	Ends the set of edges. More...

Parent / Child
unsigned	get_number_of_parents (Vertex v) const
	Access to the number of parents of v. More...

unsigned	get_number_of_children (Vertex v) const
	Access to the number of children of v. More...

Vertex	get_parent (Edge e) const
	Access to the source of e. More...

Vertex	get_child (Edge e) const
	Access to the target of e. More...

bool	is_parent (Vertex u, Vertex v) const
	Check that u is a parent of v. More...

bool	is_ancestor (Vertex u, Vertex v) const
	Check that u is an ancestor of v. More...

void	clear_children (Vertex v)
	Remove all out-going edges incident to v. More...

void	clear_parents (Vertex v)
	Remove all in-going edges incident to v. More...

Children_iterator	children_begin (Vertex v) const
	Starts the set of children of v. More...

Children_iterator	children_end (Vertex v) const
	Ends the set of children of v. More...

Parents_iterator	parents_begin (Vertex v) const
	Starts the set of parents of v. More...

Parents_iterator	parents_end (Vertex v) const
	Ends the set of parents of v. More...

Minimal / Maximal Elements
template<class OutputIterator >
OutputIterator	get_minimal_elements_from (Vertex v, OutputIterator out) const
	Access to the set of minimal elements lower or equal to v. More...

template<class OutputIterator >
OutputIterator	get_maximal_elements_from (Vertex v, OutputIterator out) const
	Access to the set of maximal elements greater or equal to v. More...

const Orientation_type &	get_orientation (void) const
	Return the orientation of the DAG. More...

Orientation_type &	get_orientation (void)
	Return a reference to the orientation of the DAG. More...

bool	is_maximal_root_oriented (void) const
	Check that maximal elements are the roots of the graph. More...

bool	is_minimal_element (Vertex u) const
	Check that u is a minimal element. More...

bool	is_maximal_element (Vertex u) const
	Check that u is a maximal element. More...

bool	is_lower (Vertex u, Vertex v) const
	Check that u is lower than v. More...

Maximal_elements_iterator	maximal_elements_begin () const
	Starts the set of maximal elements. More...

Maximal_elements_iterator	maximal_elements_end () const
	Ends the set of maximal elements. More...

Minimal_elements_iterator	minimal_elements_begin () const
	Starts the set of minimal elements. More...

Minimal_elements_iterator	minimal_elements_end () const
	Ends the set of minimal elements. More...

Partial Order Set Builder
template<class PartialOrderPredicate , class InputIterator >
void	build_from_partially_ordered_set (InputIterator begin, InputIterator end, const PartialOrderPredicate &order=PartialOrderPredicate())
	Construct the Directed Acyclic Graph from the partially ordered set in [begin, end). More...

Subgraph Manipulators
template<class InputIterator , class OutputIterator >
OutputIterator	get_induced_subgraph (InputIterator begin, InputIterator end, OutputIterator out) const
	Construct the induced subgraph from the range of vertices in [begin, end). More...

template<class OutputIterator >
OutputIterator	get_descendant_ancestor_subgraph (Vertex u, Vertex v, OutputIterator out) const
	Construct the maximal subgraph such that all vertices are ancestors of u and descendants of v. More...

template<class VertexIterator , class EdgeIterator >
void	get_subgraph (VertexIterator v_begin, VertexIterator v_end, EdgeIterator e_begin, EdgeIterator e_end, Self &subgraph) const
	Construct the subgraph from the range of vertices [v_begin, v_end) and edges in [e_begin, e_end). More...

template<class InputIterator >
void	get_edge_subgraph (InputIterator begin, InputIterator end, Self &subgraph) const
	Construct the edge subgraph from the range of edges in [begin, end). More...

I/O
template<class OutputStream >
void	print_in_dot_format (OutputStream &out) const
	Print in the output stream the graph in DOT format. More...

void	print_in_dot_format (void) const
	Print in the standard output stream the graph in DOT format. More...

Detailed Description

template<class VertexProperty = Directed_acyclic_graph_default_property, class EdgeProperty = Directed_acyclic_graph_default_property>
class SBL::CADS::T_Directed_acyclic_graph< VertexProperty, EdgeProperty >

Generic representation of a directed acyclic graph.

It implements a bidirectional adjacency_list from the Boost Graph Library that uses lists for storing the vertices and the out-going edges. The T_Directed_acyclic_graph class provides:

manipulators for the vertices,

manipulators for the edges,

manipulators for the children or parents of given vertices,

manipulators for the minimal and maximal elements,

constructions for partially ordered set,

subgraphs manipulators.

Template Parameters

VertexProperty	Information attached to the vertices (default is Directed_acyclic_graph_default_property).
EdgeProperty	Information attached to the edges (default is Directed_acyclic_graph_default_property).

Member Typedef Documentation

◆ Children_iterator

typedef boost::transform_iterator<Get_child_from_edge, Out_edges_iterator> Children_iterator

Iterator over all the children of a given Vertex.

◆ Edge

typedef Graph_traits::edge_descriptor Edge

Representation of an Edge of the Directed Acyclic Graph.

◆ Edges_iterator

typedef Graph_traits::edge_iterator Edges_iterator

Iterator over all the edges of the Directed Acyclic Graph.

◆ Graph

typedef boost::adjacency_list<boost::listS, boost::listS, boost::bidirectionalS, VertexProperty, EdgeProperty> Graph

Representation of the Directed Acyclic Graph as a adjacency_list of the Boost Graph Library.

Note that the containers for vertices and out edges are both lists for supoprting the removal.

◆ Maximal_elements_iterator

typedef boost::filter_iterator<Is_maximal_element, Vertices_iterator> Maximal_elements_iterator

Iterator over the vertices of the Directed Acyclic Graph that are maximal elements of the corresponding partially ordered set.

◆ Minimal_elements_iterator

typedef boost::filter_iterator<Is_minimal_element, Vertices_iterator> Minimal_elements_iterator

Iterator over the vertices of the Directed Acyclic Graph that are minimal elements of the corresponding partially ordered set.

◆ Parents_iterator

typedef boost::transform_iterator<Get_parent_from_edge, In_edges_iterator> Parents_iterator

Iterator over all the parents of a given Vertex.

◆ Vertex

typedef Graph_traits::vertex_descriptor Vertex

Representation of a Vertex of the Directed Acyclic Graph.

◆ Vertices_iterator

typedef Graph_traits::vertex_iterator Vertices_iterator

Iterator over all the vertices of the Directed Acyclic Graph.

Member Enumeration Documentation

◆ Orientation_type

enum Orientation_type

Orientation of the edges in the Directed Acyclic Graph.

Options are:

MAXIMAL_ROOT_ORIENTATION : the roots are the maximal elements of the Directed Acyclic Graph.
MINIMAL_ROOT_ORIENTATION : the roots are the minimal elements of the Directed Acyclic Graph.

Constructor & Destructor Documentation

◆ T_Directed_acyclic_graph()

T_Directed_acyclic_graph ( Orientation_type orientation = MAXIMAL_ROOT_ORIENTATION )

inline

Default constructor creating an empty Directed Acyclic Graph.

Parameters

orientation defines the orientation of the edges.

Member Function Documentation

◆ add_edge() [1/2]

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Edge add_edge	(	Vertex	u,
		Vertex	v
	)

inline

Add an edge from u to v, with no property.

Precondition: The edge (u,v) does not exist.; Adding the edge (u,v) do not make any cycle in the graph.

◆ add_edge() [2/2]

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Edge add_edge	(	Vertex	u,
		Vertex	v,
		const EdgeProperty &	p
	)

inline

Add an edge from u to v, with the property p.

Precondition: The edge (u,v) does not exist.; Adding the edge (u,v) do not make any cycle in the graph.

◆ add_vertex() [1/2]

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Vertex add_vertex ( const VertexProperty & p )

inline

Add a vertex with the property p to the graph.

◆ add_vertex() [2/2]

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Vertex add_vertex ( void )

inline

Add a vertex with no property to the graph.

◆ build_from_partially_ordered_set()

void build_from_partially_ordered_set	(	InputIterator	begin,
		InputIterator	end,
		const PartialOrderPredicate &	order = `PartialOrderPredicate()`
	)

inline

Construct the Directed Acyclic Graph from the partially ordered set in [begin, end).

The input order predicate is used as a partial order. Each element of the set is represented by a vertex in the Directed Acyclic Graph. There is an edge from a vertex u to a vertex v if v is compared less than u with the partial order, and if there is no other vertex w such that v is less than w and w is less than u. Note that each element has to be unique (i.e multiplicity is not allowed).

Parameters

begin	Starts the set of elements of the partially ordered set.
end	Ends the set of elements of the partially ordered set.
order	Functor representing a partial ordering over the elements in [begin, end).

◆ children_begin()

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Children_iterator children_begin ( Vertex v ) const

inline

Starts the set of children of v.

◆ children_end()

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Children_iterator children_end ( Vertex v ) const

inline

Ends the set of children of v.

◆ clear_children()

void clear_children ( Vertex v )

inline

Remove all out-going edges incident to v.

◆ clear_parents()

void clear_parents ( Vertex v )

inline

Remove all in-going edges incident to v.

◆ clear_vertex()

void clear_vertex ( Vertex v )

inline

Remove all edges incident to v.

◆ edges_begin()

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Edges_iterator edges_begin ( void ) const

inline

Starts the set of edges.

◆ edges_end()

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Edges_iterator edges_end ( void ) const

inline

Ends the set of edges.

◆ find_first_vertex_compared_to_data()

bool find_first_vertex_compared_to_data	(	const DataType &	data,
		Vertex &	v,
		const Comparator &	compare = `Comparator()`
	)		const

inline

Find the first vertex in the graph having a property that compares equal to the input data.

Note that there is no order on the vertices, so if there are several vertices having properties comparing equal to the input data, only an arbitrary one is found.

Parameters

data	Data to be compared with the properties of the vertices.
v	Vertex with a property that compares equal to data, if any.
compare	Comparator between the data and the properties of vertices.

Returns: true iff a vertex was found.

◆ find_vertices_compared_to_data()

OutputIterator find_vertices_compared_to_data	(	const DataType &	data,
		OutputIterator	out,
		const Comparator &	compare = `Comparator()`
	)		const

inline

Find all the vertices in the graph having a property that compares equal to the input data.

Parameters

data	Data to be compared with the properties of the vertices.
out	Output iterator over a container of vertices.
compare	Comparator between the data and the properties of vertices.

◆ get_child()

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Vertex get_child ( Edge e ) const

inline

Access to the target of e.

◆ get_descendant_ancestor_subgraph()

OutputIterator get_descendant_ancestor_subgraph	(	Vertex	u,
		Vertex	v,
		OutputIterator	out
	)		const

inline

Construct the maximal subgraph such that all vertices are ancestors of u and descendants of v.

Parameters

u	The descendant.
v	The ancestor.
out	Output iterator over a set of edges.

◆ get_edge()

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Edge get_edge	(	Vertex	u,
		Vertex	v
	)		const

inline

Access to the Edge u -> v.

Precondition: u is a parent of v.

◆ get_edge_subgraph()

void get_edge_subgraph	(	InputIterator	begin,
		InputIterator	end,
		Self &	subgraph
	)		const

inline

Construct the edge subgraph from the range of edges in [begin, end).

Parameters

begin	Starts the set of edges.
end	Ends the set of edges.
subgraph	The output edge subgraph.

◆ get_graph() [1/2]

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Graph & get_graph ( void )

inline

Acces to the BGL graph.

◆ get_graph() [2/2]

const T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Graph & get_graph ( void ) const

inline

Const Access to the BGL graph.

◆ get_induced_subgraph()

OutputIterator get_induced_subgraph	(	InputIterator	begin,
		InputIterator	end,
		OutputIterator	out
	)		const

inline

Construct the induced subgraph from the range of vertices in [begin, end).

Parameters

begin	Starts the set of vertices.
end	Ends the set of vertices.
out	Output iterator over a set of edges.

◆ get_maximal_elements_from()

OutputIterator get_maximal_elements_from	(	Vertex	v,
		OutputIterator	out
	)		const

inline

Access to the set of maximal elements greater or equal to v.

◆ get_minimal_elements_from()

OutputIterator get_minimal_elements_from	(	Vertex	v,
		OutputIterator	out
	)		const

inline

Access to the set of minimal elements lower or equal to v.

◆ get_number_of_children()

unsigned get_number_of_children ( Vertex v ) const

inline

Access to the number of children of v.

◆ get_number_of_edges()

unsigned get_number_of_edges ( void ) const

inline

Access to the number of edges in the graph.

◆ get_number_of_parents()

unsigned get_number_of_parents ( Vertex v ) const

inline

Access to the number of parents of v.

◆ get_number_of_vertices()

unsigned get_number_of_vertices ( void ) const

inline

Access to the number of vertices in the graph.

◆ get_orientation() [1/2]

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Orientation_type & get_orientation ( void )

inline

Return a reference to the orientation of the DAG.

◆ get_orientation() [2/2]

const T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Orientation_type & get_orientation ( void ) const

inline

Return the orientation of the DAG.

◆ get_parent()

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Vertex get_parent ( Edge e ) const

inline

Access to the source of e.

◆ get_subgraph()

void get_subgraph	(	VertexIterator	v_begin,
		VertexIterator	v_end,
		EdgeIterator	e_begin,
		EdgeIterator	e_end,
		Self &	subgraph
	)		const

inline

Construct the subgraph from the range of vertices [v_begin, v_end) and edges in [e_begin, e_end).

Parameters

v_begin	Starts the set of vertices.
v_end	Ends the set of vertices.
e_begin	Starts the set of edges.
e_end	Ends the set of edges.
subgraph	The output subgraph.

◆ is_ancestor()

bool is_ancestor	(	Vertex	u,
		Vertex	v
	)		const

inline

Check that u is an ancestor of v.

◆ is_empty()

bool is_empty ( void ) const

inline

Check that the graph has no vertex.

◆ is_lower()

bool is_lower	(	Vertex	u,
		Vertex	v
	)		const

inline

Check that u is lower than v.

◆ is_maximal_element()

bool is_maximal_element ( Vertex u ) const

inline

Check that u is a maximal element.

◆ is_maximal_root_oriented()

bool is_maximal_root_oriented ( void ) const

inline

Check that maximal elements are the roots of the graph.

◆ is_minimal_element()

bool is_minimal_element ( Vertex u ) const

inline

Check that u is a minimal element.

◆ is_parent()

bool is_parent	(	Vertex	u,
		Vertex	v
	)		const

inline

Check that u is a parent of v.

◆ maximal_elements_begin()

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Maximal_elements_iterator maximal_elements_begin ( void ) const

inline

Starts the set of maximal elements.

◆ maximal_elements_end()

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Maximal_elements_iterator maximal_elements_end ( void ) const

inline

Ends the set of maximal elements.

◆ minimal_elements_begin()

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Minimal_elements_iterator minimal_elements_begin ( void ) const

inline

Starts the set of minimal elements.

◆ minimal_elements_end()

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Minimal_elements_iterator minimal_elements_end ( void ) const

inline

Ends the set of minimal elements.

◆ operator[]() [1/4]

EdgeProperty & operator[] ( Edge e )

inline

Access to the property attached to e.

◆ operator[]() [2/4]

const EdgeProperty & operator[] ( Edge e ) const

inline

Const access to the property attached to e.

◆ operator[]() [3/4]

VertexProperty & operator[] ( Vertex v )

inline

Access to the property associated to a vertex.

◆ operator[]() [4/4]

const VertexProperty & operator[] ( Vertex v ) const

inline

Const access to the property associated to a vertex.

◆ parents_begin()

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Parents_iterator parents_begin ( Vertex v ) const

inline

Starts the set of parents of v.

◆ parents_end()

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Parents_iterator parents_end ( Vertex v ) const

inline

Ends the set of parents of v.

◆ print_in_dot_format() [1/2]

void print_in_dot_format ( OutputStream & out ) const

Print in the output stream the graph in DOT format.

◆ print_in_dot_format() [2/2]

void print_in_dot_format ( void ) const

Print in the standard output stream the graph in DOT format.

◆ remove_edge() [1/2]

void remove_edge ( Edge e )

inline

Remove the edge e from the graph.

◆ remove_edge() [2/2]

void remove_edge	(	Vertex	u,
		Vertex	v
	)

inline

Remove the edge from u to v.

◆ remove_vertex()

void remove_vertex ( Vertex v )

inline

Remove the vertex v from the graph.

Precondition: There is no incident edge to v.

◆ vertices_begin()

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Vertices_iterator vertices_begin ( void ) const

inline

Starts the set of vertices of the graph.

◆ vertices_end()

T_Directed_acyclic_graph< VertexProperty, EdgeProperty >::Vertices_iterator vertices_end ( void ) const

inline

Ends the set of vertices of the graph.

Public Types

Constructors

Graph

Vertices

Edges

Parent / Child

Minimal / Maximal Elements

Partial Order Set Builder

Subgraph Manipulators

I/O

Detailed Description

template<class VertexProperty = Directed_acyclic_graph_default_property, class EdgeProperty = Directed_acyclic_graph_default_property> class SBL::CADS::T_Directed_acyclic_graph< VertexProperty, EdgeProperty >

Member Typedef Documentation

◆ Children_iterator

◆ Edge

◆ Edges_iterator

◆ Graph

◆ Maximal_elements_iterator

◆ Minimal_elements_iterator

◆ Parents_iterator

◆ Vertex

◆ Vertices_iterator

Member Enumeration Documentation

◆ Orientation_type

Constructor & Destructor Documentation

◆ T_Directed_acyclic_graph()

Member Function Documentation

◆ add_edge() [1/2]

◆ add_edge() [2/2]

◆ add_vertex() [1/2]

◆ add_vertex() [2/2]

◆ build_from_partially_ordered_set()

◆ children_begin()

◆ children_end()

◆ clear_children()

◆ clear_parents()

◆ clear_vertex()

◆ edges_begin()

◆ edges_end()

◆ find_first_vertex_compared_to_data()

◆ find_vertices_compared_to_data()

◆ get_child()

◆ get_descendant_ancestor_subgraph()

◆ get_edge()

◆ get_edge_subgraph()

◆ get_graph() [1/2]

◆ get_graph() [2/2]

◆ get_induced_subgraph()

◆ get_maximal_elements_from()

◆ get_minimal_elements_from()

◆ get_number_of_children()

◆ get_number_of_edges()

◆ get_number_of_parents()

◆ get_number_of_vertices()

◆ get_orientation() [1/2]

◆ get_orientation() [2/2]

◆ get_parent()

◆ get_subgraph()

◆ is_ancestor()

◆ is_empty()

◆ is_lower()

◆ is_maximal_element()

◆ is_maximal_root_oriented()

◆ is_minimal_element()

◆ is_parent()

◆ maximal_elements_begin()

◆ maximal_elements_end()

◆ minimal_elements_begin()

◆ minimal_elements_end()

◆ operator[]() [1/4]

◆ operator[]() [2/4]

◆ operator[]() [3/4]

◆ operator[]() [4/4]

◆ parents_begin()

◆ parents_end()

◆ print_in_dot_format() [1/2]

◆ print_in_dot_format() [2/2]

◆ remove_edge() [1/2]

◆ remove_edge() [2/2]

◆ remove_vertex()

template<class VertexProperty = Directed_acyclic_graph_default_property, class EdgeProperty = Directed_acyclic_graph_default_property>
class SBL::CADS::T_Directed_acyclic_graph< VertexProperty, EdgeProperty >