lal::graphs::free_tree Class Reference

Free tree graph class. More...

#include <free_tree.hpp>

Inheritance diagram for lal::graphs::free_tree:

Public Member Functions
	free_tree () noexcept
	Empty constructor.
	free_tree (const uint64_t n) noexcept
	Constructor with number of vertices.
	free_tree (const free_tree &t) noexcept
	Copy constructor.
	free_tree (free_tree &&t) noexcept
	Move constructor.
	free_tree (const undirected_graph &t) noexcept
	Copy constructor with undirected graph.
	free_tree (undirected_graph &&t) noexcept
	Move constructor with undirected graph.
	~free_tree () noexcept
	Destructor.
free_tree &	operator= (const free_tree &f) noexcept
	Copy assignment operator.
free_tree &	operator= (free_tree &&f) noexcept
	Copy assignment operator.
free_tree &	add_node () noexcept
	Adds a vertex to the graph.
free_tree &	remove_node (const node u, const bool norm=true, const bool check_norm=true) noexcept
	Remove a node from this graph.
free_tree &	add_edge (const node s, const node t, const bool norm=true, const bool check_norm=true) noexcept
	Adds an edge to the tree.
free_tree &	add_edge_bulk (const node s, const node t) noexcept
	Adds an edge to the tree.
void	finish_bulk_add (const bool norm=true, const bool check=true) noexcept
	Finishes adding edges in bulk.
void	finish_bulk_add_complete (const bool norm=true, const bool check=true) noexcept
	Completes the inner structure of the tree after adding edges in bulk.
free_tree &	add_edges (const std::vector< edge > &edges, const bool norm=true, const bool check_norm=true) noexcept
	Adds a list of edges to the graph.
free_tree &	set_edges (const std::vector< edge > &edges, const bool norm=true, const bool check_norm=true) noexcept
	Sets the edges to the graph.
free_tree &	remove_edge (const node s, const node t, const bool norm=false, const bool check_norm=true) noexcept
	Remove an edge from this graph.
free_tree &	remove_edge_bulk (const node s, const node t) noexcept
	Removes an edge from the tree.
void	finish_bulk_remove (const bool norm=true, const bool check=true) noexcept
	Finishes removing edges in bulk.
void	finish_bulk_remove_complete (const bool norm=true, const bool check=true) noexcept
	Completes the inner structure of the tree after removing edges in bulk.
free_tree &	remove_edges (const std::vector< edge > &edges, const bool norm=true, const bool check_norm=true) noexcept
	Remove an edge from this graph.
free_tree &	remove_edges_incident_to (const node u, const bool norm=true, const bool check_norm=true) noexcept
	Remove all edges incident to a given vertex.
free_tree &	disjoint_union (const free_tree &t) noexcept
	Disjoint union of trees.
void	calculate_tree_type () noexcept
	Calculates the type of tree.
bool	is_rooted () const noexcept
	Returns whether this tree is a rooted tree.
head_vector	get_head_vector (const node r=0, const linear_arrangement &arr={}) const noexcept
	Converts a free tree into a head vector.
void	reserve_degree (const node u, const uint64_t d) noexcept
	Predicts that the degree of node u is d.
std::vector< edge_pair >	get_Q () const noexcept
	Returns all independent pairs of edges of this graph.
std::vector< edge >	get_edges () const noexcept
	Returns all edges of this graph.
const neighbourhood &	get_neighbors (const node u) const noexcept
	Returns the neighbourhood of node u.
uint64_t	get_degree (const node u) const noexcept
	Returns the number of neighbors of u.
bool	has_edge (const node u, const node v) const noexcept
	Returns true if the edge \(\{u,v\}\) exists in the graph.
bool	is_directed () const noexcept
	Returns whether this graph is directed or not.
bool	is_undirected () const noexcept
	Returns whether this graph is undirected or not.
std::vector< undirected_graph >	get_connected_components () const noexcept
	Returns all the connected components of this graph as individual graphs.
bool	is_tree () const noexcept
	Is this graph an actual tree?
virtual bool	can_add_edge (node const s, const node t) const noexcept
	Can this edge be added?
virtual bool	can_add_edges (const std::vector< edge > &edges) const noexcept
	Can these edges be added?
uint64_t	get_component_representative (const node u) const noexcept
	Representative node of the connected component in which u belongs.
bool	are_nodes_in_same_component (const node u, const node v) const noexcept
	Checks if two nodes are in the same connected component.
uint64_t	get_num_nodes_component (const node u) const noexcept
	Amount of nodes in a connected component of the tree.
bool	is_of_tree_type (const tree_type &tt) const noexcept
	Returns whether this tree is of type tt.
bool	is_tree_type_valid () const noexcept
	Is the type of this tree valid?
std::vector< std::string >	get_tree_type_list () const noexcept
	Returns the list of types as a list of strings.
virtual void	init (const uint64_t n) noexcept
	Allocates the necessary memory for this class.
virtual void	clear () noexcept
	Frees the memory occupied by this graph.
virtual void	normalize () noexcept
	Normalizes the graph.
virtual bool	check_normalized () noexcept
	Checks if the graph is normalized.
void	set_normalized (const bool v=true) noexcept
	Sets whether this graph is normalized or not.
bool	has_node (const node u) const noexcept
	Returns true if node u is in this graph.
uint64_t	get_num_nodes () const noexcept
	Returns the number of ndoes.
uint64_t	get_num_edges () const noexcept
	Returns the number of edges.
bool	is_normalized () const noexcept
	Returns whether this graph is normalized or not.

Protected Member Functions
void	_init (const uint64_t n) noexcept
	Initializes the memory in the graph hierarchy.
void	_clear () noexcept
	Clears the memory in the graph hierarchy.
void	actions_after_add_edge (const node u, const node v) noexcept
	Do some extra work after the addition of an edge.
void	actions_after_add_edges (const edge_list &e) noexcept
	Do some extra work after the addition of several edges.
void	actions_after_add_edges_bulk () noexcept
	Do some extra work after the addition of several edges in bulk.
void	actions_after_remove_edge (const node u, const node v) noexcept
	Do some extra work after the removal of an edge.
void	actions_after_remove_edges (const edge_list &e) noexcept
	Do some extra work after the removal of several edges.
void	actions_after_remove_edges_bulk () noexcept
	Do some extra work after the removal of several edges in bulk.
void	actions_after_remove_node (const node u) noexcept
	Do some work before the removal of a vertex.
void	actions_before_remove_edges_incident_to (const node u) noexcept
	Do some work before all edges incident to a node is removed.
void	update_union_find_after_add_edge (const node u, const node v, uint64_t *const root_of, uint64_t *const root_size) const noexcept
	Update the union find data structure after an edge addition.
void	update_union_find_after_add_edges (const edge_list &edges, uint64_t *const root_of, uint64_t *const root_size) const noexcept
	Update the union find data structure after the addition of a set of edges.
void	update_union_find_after_add_edges_bulk (uint64_t *const root_of, uint64_t *const root_size) const noexcept
	Update the union find data structure after the addition of several edges.
void	update_union_find_after_remove_edge (const node u, const node v, uint64_t *const root_of, uint64_t *const root_size) const noexcept
	Update the union find data structure after an edge removal.
void	update_union_find_after_remove_edges (const edge_list &edges, uint64_t *const root_of, uint64_t *const root_size) const noexcept
	Update the union find data structure after the removal of a set of edges.
void	update_union_find_after_remove_edges_bulk (uint64_t *const root_of, uint64_t *const root_size) const noexcept
	Update the union find data structure after the removal of several edges.
void	update_union_find_before_remove_incident_edges_to (const node u, uint64_t *const root_of, uint64_t *const root_size) const noexcept
	Update the union find data structure before the removal of all edges incident to a node.
void	copy_full_free_tree (const free_tree &f) noexcept
	Copies all members of this class and the parent classes.
void	move_full_free_tree (free_tree &&f) noexcept
	Moves all members of this class and the parent classes.
void	copy_full_undirected_graph (const undirected_graph &u) noexcept
	Copies all members of this class and the parent class.
void	move_full_undirected_graph (undirected_graph &&u) noexcept
	Moves all members of this class and the parent class.
void	tree_only_init (const uint64_t n) noexcept
	Initializes only the memory of class tree.
void	tree_only_clear () noexcept
	Clears the memory used by only class tree.
void	tree_only_copy (const tree &t) noexcept
	Copies only members of class tree.
void	tree_only_move (tree &&t) noexcept
	Moves only members of class tree.
void	tree_only_add_node () noexcept
	Adds a node to this tree.
void	tree_only_invalidate () noexcept
	Invalidates the aggregated information of the tree.
void	tree_only_actions_after_add_edge (const node u, const node v) noexcept
	Do some work after the addition of an edge.
void	tree_only_actions_after_add_edges (const edge_list &e) noexcept
	Do some work after the addition of several edges.
void	tree_only_actions_after_add_edges_bulk () noexcept
	Do some work after the addition of several edges in bulk.
void	tree_only_actions_after_add_edges_bulk_complete () noexcept
	Do some work after the addition of several edges in bulk.
void	tree_only_actions_after_remove_edges_bulk () noexcept
	Do some work after the removal of several edges in bulk.
void	tree_only_actions_after_remove_edges_bulk_complete () noexcept
	Do some work after the removal of several edges in bulk.
void	tree_only_actions_after_remove_edge (const node u, const node v) noexcept
	Do some work after the removal of an edge.
void	tree_only_actions_after_remove_edges (const edge_list &e) noexcept
	Do some work after the removal of several edges.
void	tree_only_actions_after_remove_node (const node u) noexcept
	Do some work before the removal of a vertex.
void	tree_only_actions_before_remove_edges_incident_to (const node u) noexcept
	Do some work before the removal of all edges incident to a vertex.
void	tree_only_set_edges () noexcept
	Updates the data structures of a tree after the graph structure has had its set of edges set.
void	tree_only_remove_node (const node u) noexcept
	Removes a vertex from the union-find data structure.
void	fill_union_find () noexcept
void	empty_union_find () noexcept
	Empties the Union-Find data structure assuming that the tree has no edges.
void	copy_full_graph (const graph &g) noexcept
	Copies all members of this class.
void	move_full_graph (graph &&g) noexcept
	Moves all members of this class.
void	__add_node () noexcept
	Adds a node to the graph.
void	__disjoint_union (const graph &g) noexcept
	Disjoint union of graphs.
void	normalize_after_edge_addition (const bool norm, const bool check) noexcept
	Normalize the graph after one (or more) edges have been added.
void	normalize_after_edge_removal (const bool norm, const bool check) noexcept
	Normalize the graph after one (or more) edges have been removed.

Protected Attributes
std::vector< node >	m_union_find__root_of
	The root of every vertex in the union-find data structure.
std::vector< uint64_t >	m_union_find__root_size
	The size of the connected component that a root belongs to.
std::array< bool, __tree_type_size >	m_tree_type
	The type of this tree.
bool	m_is_tree_type_valid = false
	Is the type of this tree valid?
std::vector< neighbourhood >	m_adjacency_list
	Data structure that implements the graph.
uint64_t	m_num_edges = 0
	Amount of edges of this graph.
bool	m_is_normalized = true
	Is this graph normalized?

Private Member Functions
undirected_graph &	disjoint_union (const undirected_graph &g) noexcept
	Disjoint union of graphs.
void	remove_single_edge (const node u, const node v, neighbourhood &out_u, neighbourhood &in_v) noexcept
	Removes a single edge.

Friends
class	rooted_tree

Detailed Description

Free tree graph class.

This class constrains the addition of edges so that the resulting graphs does not contain cycles. Furthermore, the edges added are undirected.

For another type of tree-like graphs, see lal::graphs::rooted_tree.

Constructor & Destructor Documentation

free_tree() [1/5]

lal::graphs::free_tree::free_tree ( const uint64_t n )

inlinenoexcept

Constructor with number of vertices.

Parameters

n	Number of vertices

free_tree() [2/5]

lal::graphs::free_tree::free_tree ( const free_tree & t )

inlinenoexcept

Copy constructor.

Parameters

t	Free tree.

free_tree() [3/5]

lal::graphs::free_tree::free_tree ( free_tree && t )

inlinenoexcept

Move constructor.

Parameters

t	Free tree.

free_tree() [4/5]

lal::graphs::free_tree::free_tree ( const undirected_graph & t )

noexcept

Copy constructor with undirected graph.

Parameters

t	An undirected graph.

Precondition

Graph t is a tree.

free_tree() [5/5]

lal::graphs::free_tree::free_tree ( undirected_graph && t )

noexcept

Move constructor with undirected graph.

Parameters

t	An undirected graph.

Precondition

Graph t is a tree.

Member Function Documentation

__disjoint_union()

void lal::graphs::graph::__disjoint_union ( const graph & g )

protectednoexceptinherited

Disjoint union of graphs.

Given a graph, append it to the current graph.

All the nodes in g are relabelled starting at n, the number of nodes of the current graph.

Parameters

g	Input graph.

Precondition

This graph and g must be of the same type (both must be either undirected, or both directed).

Postcondition

The graph is normalized only if it was normalized before the call and g is also normalized.

_clear()

void lal::graphs::free_tree::_clear ( )

inlineprotectedvirtualnoexcept

Clears the memory in the graph hierarchy.

Clears the memory of lal::graphs::free_tree, lal::graphs::undirected_graph and lal::graphs::graph classes.

Reimplemented from lal::graphs::undirected_graph.

_init()

void lal::graphs::free_tree::_init ( const uint64_t n )

inlineprotectedvirtualnoexcept

Initializes the memory in the graph hierarchy.

Initializes memory of lal::graphs::free_tree, lal::graphs::undirected_graph and lal::graphs::graph classes.

Parameters

n	Number of nodes.

Precondition

The graph is cleared.

Reimplemented from lal::graphs::undirected_graph.

actions_after_add_edge()

void lal::graphs::free_tree::actions_after_add_edge ( const node u, const node v )

protectedvirtualnoexcept

Do some extra work after the addition of an edge.

Parameters

u	Node of the edge
v	Node of the edge

Reimplemented from lal::graphs::undirected_graph.

actions_after_add_edges()

void lal::graphs::free_tree::actions_after_add_edges ( const edge_list & e )

protectedvirtualnoexcept

Do some extra work after the addition of several edges.

Parameters

e	List of edges.

Reimplemented from lal::graphs::undirected_graph.

actions_after_add_edges_bulk()

void lal::graphs::free_tree::actions_after_add_edges_bulk ( )

protectedvirtualnoexcept

Do some extra work after the addition of several edges in bulk.

This method should only be called after several calls to undirected_graph::add_edge_bulk or directed_graph::add_edge_bulk.

Reimplemented from lal::graphs::undirected_graph.

actions_after_remove_edge()

void lal::graphs::free_tree::actions_after_remove_edge ( const node u, const node v )

protectedvirtualnoexcept

Do some extra work after the removal of an edge.

Parameters

u	Node of the edge
v	Node of the edge

Reimplemented from lal::graphs::undirected_graph.

actions_after_remove_edges()

void lal::graphs::free_tree::actions_after_remove_edges ( const edge_list & e )

protectedvirtualnoexcept

Do some extra work after the removal of several edges.

Parameters

e	List of edges.

Reimplemented from lal::graphs::undirected_graph.

actions_after_remove_edges_bulk()

void lal::graphs::free_tree::actions_after_remove_edges_bulk ( )

protectedvirtualnoexcept

Do some extra work after the removal of several edges in bulk.

This method should only be called after several calls to undirected_graph::remove_edge_bulk or directed_graph::remove_edge_bulk.

Reimplemented from lal::graphs::undirected_graph.

actions_after_remove_node()

void lal::graphs::free_tree::actions_after_remove_node ( const node u )

protectedvirtualnoexcept

Do some work before the removal of a vertex.

Parameters

u	Node to be removed.

Reimplemented from lal::graphs::undirected_graph.

actions_before_remove_edges_incident_to()

void lal::graphs::free_tree::actions_before_remove_edges_incident_to ( const node u )

protectedvirtualnoexcept

Do some work before all edges incident to a node is removed.

Parameters

u	Node whose incident edges are to be removed.

Reimplemented from lal::graphs::undirected_graph.

add_edge()

free_tree & lal::graphs::free_tree::add_edge ( const node s, const node t, const bool norm = true, const bool check_norm = true )

virtualnoexcept

Adds an edge to the tree.

This operation checks that the edge added does not produce cycles only in a debug compilation of the library. For a more controlled addition of the edges, see can_add_edge.

For developers: method lal::graphs::graph::actions_after_add_edge is called after the edge has been added.

Parameters

s	Valid node index: \(0 \le s < n\).
t	Valid node index: \(0 \le t < n\).
norm	Should the graph be normalized?
check_norm	If norm is false then, should we check whether the result is normalized or not? This might be useful in case the resulting graph is normalized. If norm is true then check_norm is ignored.

Precondition

\(s \neq t\)

Edge \(\{s,t\}\) is not part of the graph.

Postcondition

If norm is true the graph is guaranteed to be normalized after the addition of the edge.

Reimplemented from lal::graphs::undirected_graph.

add_edge_bulk()

free_tree & lal::graphs::free_tree::add_edge_bulk ( const node s, const node t )

noexcept

Adds an edge to the tree.

This method only adds an edge, and does no other work: normalisation is not checked, and no extra work per edge is done.

Parameters

s	Valid node index: \(0 \le s < n\).
t	Valid node index: \(0 \le t < n\).

Precondition

\(u \neq v\).

The edge \(\{s,t\}\) is not part of the graph.

Postcondition

If norm is true the graph is guaranteed to be normalized after the addition of the edge.

add_edges()

free_tree & lal::graphs::free_tree::add_edges ( const std::vector< edge > & edges, const bool norm = true, const bool check_norm = true )

virtualnoexcept

Adds a list of edges to the graph.

This function checks that edges will not produce cycles only in a debug compilation of the library. Moreover, this operation is faster than calling add_edge since the edges are added in bulk. For a more controlled addition of the edges, see can_add_edges.

Parameters

edges	The edges to be added.
norm	Normalize the graph after the insertions.
check_norm	If norm is false then, should we check whether the result is normalized or not? This might be useful in case the resulting graph is normalized. If norm is true then check_norm is ignored.

Precondition

All the edges in edges must meet the precondition of method add_edge.

None of the subsets of the list of edges can produce cycles when added.

Postcondition

If norm is true the graph is guaranteed to be normalized after the addition of the edges.

Reimplemented from lal::graphs::undirected_graph.

are_nodes_in_same_component()

bool lal::graphs::tree::are_nodes_in_same_component ( const node u, const node v ) const

inlinenodiscardnoexceptinherited

Checks if two nodes are in the same connected component.

Parameters

u	First node.
v	Second node.

Returns

True or false.

calculate_tree_type()

void lal::graphs::free_tree::calculate_tree_type ( )

virtualnoexcept

Calculates the type of tree.

See tree_type for the list of different tree types.

Implements lal::graphs::tree.

can_add_edge()

virtual bool lal::graphs::tree::can_add_edge ( node const s, const node t ) const

nodiscardvirtualnoexceptinherited

Can this edge be added?

In a tree, an edge can only be added if it does not produce cycles, and it has not been added before.

In a rooted tree, an edge can only be added if the in-degree of vertex t (see directed_graph::get_in_degree) is exactly 1 after adding the edge.

Parameters

s	First node of the edge.
t	Second node of the edge.

Returns

Whether or not this edge can be added to the tree without producing cycles.

Reimplemented in lal::graphs::rooted_tree.

can_add_edges()

virtual bool lal::graphs::tree::can_add_edges ( const std::vector< edge > & edges ) const

nodiscardvirtualnoexceptinherited

Can these edges be added?

In a tree, a set of edges can only be added if their addition to the tree do not produce cycles and none of them have been added before.

In a rooted tree, edges \((s,t)\) can only be added if the in-degree of vertex t (see directed_graph::get_in_degree) is exactly 1 after adding the edge.

Parameters

edges

List of edges.

Returns

Whether or not these edges can be added to the tree without producing cycles.

Reimplemented in lal::graphs::rooted_tree.

check_normalized()

virtual bool lal::graphs::graph::check_normalized ( )

virtualnoexceptinherited

Checks if the graph is normalized.

Checks, whether the graph's adjacency structure is normalized or not. In case it is, attribute m_is_normalized is set to true, so method is_normalized evaluates to true.

Reimplemented in lal::graphs::directed_graph.

clear()

virtual void lal::graphs::graph::clear ( )

virtualnoexceptinherited

Frees the memory occupied by this graph.

See _clear for details.

Postcondition

The graph is normalized. The number of edges is 0.

disjoint_union() [1/2]

free_tree & lal::graphs::free_tree::disjoint_union ( const free_tree & t )

noexcept

Disjoint union of trees.

Given a free tree, append it to the current tree. If the current is empty (i.e., size 0), then the new tree is simply copied into the new one.

If the current tree is not empty, all the new nodes in t (appended to the current tree) are relabelled starting at n, the number of nodes of the current tree.

Parameters

t	Input tree.

Postcondition

If the current tree is empty, the whole state of the new tree is copied into the new one.

If the current tree is not empty, then the resulting graph is not a tree since it lacks an edge. Then method is_tree() returns false.

The type of tree (m_is_tree_type_valid) is invalidated.

disjoint_union() [2/2]

undirected_graph & lal::graphs::undirected_graph::disjoint_union ( const undirected_graph & g )

privatenoexcept

Disjoint union of graphs.

Given a graph, append it to the current graph.

All the nodes in g are relabelled starting at n, the number of nodes of the current graph.

Parameters

g	Input graph.

Postcondition

The graph is normalized only if it was normalized before the call and g is also normalized.

fill_union_find()

void lal::graphs::tree::fill_union_find ( )

inlineprotectednoexceptinherited

Fills the Union-Find data structure assuming that the graph structure has all of its edges.

finish_bulk_add()

void lal::graphs::free_tree::finish_bulk_add ( const bool norm = true, const bool check = true )

virtualnoexcept

Finishes adding edges in bulk.

This method updates the Union-Find data structure and all the necessary members after several calls to add_edge_bulk.

Parameters

norm	Normalize the tree.
check	Check whether the tree is normalized or not.

Implements lal::graphs::graph.

finish_bulk_add_complete()

void lal::graphs::free_tree::finish_bulk_add_complete ( const bool norm = true, const bool check = true )

virtualnoexcept

Completes the inner structure of the tree after adding edges in bulk.

This is meant to be used after several calls to undirected_graph::add_edge_bulk, directed_graph::add_edge_bulk.

This method completes the Union-Find data structure and the other necessary members assuming that the tree is now complete.

Parameters

norm	Normalize the graph.
check	Check wether the graph is normalized or not.

Precondition

All edges have been added with method undirected_graph::add_edge_bulk or directed_graph::add_edge_bulk.

Implements lal::graphs::tree.

finish_bulk_remove()

void lal::graphs::free_tree::finish_bulk_remove ( const bool norm = true, const bool check = true )

virtualnoexcept

Finishes removing edges in bulk.

This method updates the Union-Find data structure and all the necessary members after several calls to remove_edge_bulk.

Parameters

norm	Normalize the tree.
check	Check whether the tree is normalized or not.

Implements lal::graphs::graph.

finish_bulk_remove_complete()

void lal::graphs::free_tree::finish_bulk_remove_complete ( const bool norm = true, const bool check = true )

virtualnoexcept

Completes the inner structure of the tree after removing edges in bulk.

This is meant to be used after several calls to undirected_graph::remove_edge_bulk, directed_graph::remove_edge_bulk.

This method completes the Union-Find data structure and the other necessary members assuming that the tree is now empty.

Parameters

norm	Normalize the graph.
check	Check wether the graph is normalized or not.

Precondition

All edges have been added with method undirected_graph::remove_edge_bulk or directed_graph::remove_edge_bulk.

Implements lal::graphs::tree.

get_component_representative()

uint64_t lal::graphs::tree::get_component_representative ( const node u ) const

inlinenodiscardnoexceptinherited

Representative node of the connected component in which u belongs.

If the current graph lacks some edges then it is clearly a forest, i.e., a series of disconnected components. This function returns a representative node of the connected component to which node u belongs.

Further, let \(cc(u)\) be the connected component of vertex u, and \(rep(cc(u))\) be the representative node of \(cc(u)\). For every other node \(v\in cc(u)\), this function will return the same representative node \(rep(cc(u))\). Therefore, \(rep(cc(u))=rep(cc(v))\) for every \(v\in cc(u)\).

Parameters

u	Input node.

Returns

The representative node of node u's component.

get_degree()

uint64_t lal::graphs::undirected_graph::get_degree ( const node u ) const

inlinenodiscardnoexceptinherited

Returns the number of neighbors of u.

Parameters

u	Node to be queried.

Returns

The number of adjacent nodes.

get_head_vector()

head_vector lal::graphs::free_tree::get_head_vector ( const node r = 0, const linear_arrangement & arr = {} ) const

nodiscardnoexcept

Converts a free tree into a head vector.

See Head vector page for a definition of 'head vector'.

Parameters

r	A fictional root to be used to calculate the head vector.
arr	Linear arrangement of the tree.

Returns

The head vector representation of this tree.

Precondition

This tree is a valid free tree (see is_tree).

get_neighbors()

const neighbourhood & lal::graphs::undirected_graph::get_neighbors ( const node u ) const

inlinenodiscardnoexceptinherited

Returns the neighbourhood of node u.

Parameters

u

Node.

Returns

The list of nodes adjacent to node u.

get_num_nodes_component()

uint64_t lal::graphs::tree::get_num_nodes_component ( const node u ) const

inlinenodiscardnoexceptinherited

Amount of nodes in a connected component of the tree.

If the current graph lacks some edges then it is clearly a forest, i.e., a series of disconnected components. This function returns the size of the component node u belongs to.

In rooted trees one has to see this amount as the number of nodes of the component in the underlying undirected forest.

Parameters

u	Input node.

Returns

The size of the connected component of u.

get_Q()

std::vector< edge_pair > lal::graphs::undirected_graph::get_Q ( ) const

nodiscardvirtualnoexceptinherited

Returns all independent pairs of edges of this graph.

The set \(Q(G)\) is defined as the pairs of edges of \(G\), \(E(G) \times E(G)\), that are independent, that is, that share no nodes.

Implements lal::graphs::graph.

get_tree_type_list()

std::vector< std::string > lal::graphs::tree::get_tree_type_list ( ) const

nodiscardnoexceptinherited

Returns the list of types as a list of strings.

Returns

The list of types as a list of strings.

init()

virtual void lal::graphs::graph::init ( const uint64_t n )

virtualnoexceptinherited

Allocates the necessary memory for this class.

See _init for details.

Parameters

n	Number of nodes.

is_normalized()

bool lal::graphs::graph::is_normalized ( ) const

inlinenodiscardnoexceptinherited

Returns whether this graph is normalized or not.

A graph is normalized if every node's adjacency list is sorted increasingly. For this, use method normalize().

Returns

The value of m_is_normalized.

is_of_tree_type()

bool lal::graphs::tree::is_of_tree_type ( const tree_type & tt ) const

inlinenodiscardnoexceptinherited

Returns whether this tree is of type tt.

See method calculate_tree_type to know how to calculate a tree's type.

Parameters

tt	Type of tree (see graphs::tree_type).

Returns

True if this tree is of type tt.

is_tree()

bool lal::graphs::tree::is_tree ( ) const

inlinenodiscardnoexceptinherited

Is this graph an actual tree?

Returns true if the number of edges is one less than the number of nodes.

Note that this would not really be true if the addition of edges was not constrained. That is, since it is constrained (behind the scenes) in a way that no cycles can be produced (for example, see free_tree::add_edge, or free_tree::add_edges), then we only need to check for the number of edges.

For further characterisations of a tree see [29] (chapter 4, pages 32-33).

Returns

True or false depending on whether this graph fits the defintion of tree.

is_tree_type_valid()

bool lal::graphs::tree::is_tree_type_valid ( ) const

inlinenodiscardnoexceptinherited

Is the type of this tree valid?

This function enables users determine when this tree's type should be calculated.

In case this function returns false, users should call function calculate_tree_type in order to obtain a valid tree type. Note, however, that prior to calling the function the type of this tree might be graphs::tree_type::unknown and that the tree type may remain graphs::tree_type::unknown even after the type has been calculated. Nevertheless, users should be suspicious of a tree being of graphs::tree_type::unknown (in fact, of any) type if this method returns false, yet they should be sure of it if the type was calculated via method calculate_tree_type.

Returns

True or false depending on whether the tree type was calculated or not.

normalize()

virtual void lal::graphs::graph::normalize ( )

virtualnoexceptinherited

Normalizes the graph.

Sorts this graph's adjacency list structure in increasing order.

Besides expensive, this method may be unnecessary. Method check_normalized() checks whether the graph is normalized or not; in case it is, using this method is completely unnecessary.

Postcondition

Method is_normalized evaluates to true.

Reimplemented in lal::graphs::directed_graph.

operator=() [1/2]

free_tree & lal::graphs::free_tree::operator= ( const free_tree & f )

inlinenoexcept

Copy assignment operator.

Parameters

f	A lal::graphs::free_tree.

operator=() [2/2]

free_tree & lal::graphs::free_tree::operator= ( free_tree && f )

inlinenoexcept

Copy assignment operator.

Parameters

f	A lal::graphs::free_tree.

remove_edge()

free_tree & lal::graphs::free_tree::remove_edge ( const node s, const node t, const bool norm = false, const bool check_norm = true )

virtualnoexcept

Remove an edge from this graph.

Method lal::graphs::graph::actions_after_remove_edge is called after the edge has been removed.

Parameters

s	Valid node index: \(0 \le s < n\).
t	Valid node index: \(0 \le t < n\).
norm	Normalize the graph after the deletion.
check_norm	If norm is false then, should we check whether the result is normalized or not? This might be useful in case the resulting graph is normalized. If norm is true then check_norm is ignored.

Precondition

The edge must exist.

Postcondition

If norm is true the tree is guaranteed to be normalized after the addition of the edge.

The type of tree (m_is_tree_type_valid) is invalidated.

Reimplemented from lal::graphs::undirected_graph.

remove_edge_bulk()

free_tree & lal::graphs::free_tree::remove_edge_bulk ( const node s, const node t )

virtualnoexcept

Removes an edge from the tree.

This method only removes an edge, and does no other work: normalisation is not checked, and no extra work per edge is done.

Parameters

s	Valid node index: \(0 \le s < n\).
t	Valid node index: \(0 \le t < n\).

Precondition

\(u \neq v\).

The edge \(\{s,t\}\) is not part of the graph.

Postcondition

If norm is true the graph is guaranteed to be normalized after the removal of the edge.

Reimplemented from lal::graphs::undirected_graph.

remove_edges()

free_tree & lal::graphs::free_tree::remove_edges ( const std::vector< edge > & edges, const bool norm = true, const bool check_norm = true )

virtualnoexcept

Remove an edge from this graph.

This operation is faster than removing edges one by one with remove_edge(node,node,bool,bool) since the edges are removed in bulk.

Parameters

edges	The edges to be deleted.
norm	Normalize the graph after the deletion.
check_norm	If norm is false then, should we check whether the result is normalized or not? This might be useful in case the resulting graph is normalized. If norm is true then check_norm is ignored.

Precondition

All the edges in edges must meet the precondition of method add_edge(node,node,bool,bool).

Postcondition

If norm is true the tree is guaranteed to be normalized after the addition of the edge.

The type of tree (m_is_tree_type_valid) is invalidated.

Reimplemented from lal::graphs::undirected_graph.

remove_edges_incident_to()

free_tree & lal::graphs::free_tree::remove_edges_incident_to ( const node u, const bool norm = true, const bool check_norm = true )

virtualnoexcept

Remove all edges incident to a given vertex.

This operation is faster than removing edges one by one with remove_edge(node,node,bool,bool) since the edges are removed in bulk.

Parameters

u	The node whose incident vertices are to be removed.
norm	Normalize the graph after the deletion.
check_norm	If norm is false then, should we check whether the result is normalized or not? This might be useful in case the resulting graph is normalized. If norm is true then check_norm is ignored.

Postcondition

If norm is true the tree is guaranteed to be normalized after the addition of the edge.

The type of tree (m_is_tree_type_valid) is invalidated.

Reimplemented from lal::graphs::undirected_graph.

remove_node()

free_tree & lal::graphs::free_tree::remove_node ( const node u, const bool norm = true, const bool check_norm = true )

virtualnoexcept

Remove a node from this graph.

Parameters

u	Valid node index: \(0 \le u < n\).
norm	Normalize the graph after the deletion.
check_norm	If norm is false then, should we check whether the result is normalized or not? This might be useful in case the resulting graph is normalized. If norm is true then check_norm is ignored.

Precondition

The node must exist.

Postcondition

If norm is true the graph is guaranteed to be normalized after the addition of the edge.

Reimplemented from lal::graphs::undirected_graph.

remove_single_edge()

void lal::graphs::undirected_graph::remove_single_edge ( const node u, const node v, neighbourhood & out_u, neighbourhood & in_v )

privatenoexceptinherited

Removes a single edge.

Parameters

u	First node of edge.
v	Second node of edge.
out_u	Out-neighbourhood of node u.
in_v	In-neighbourhood of node v.

reserve_degree()

void lal::graphs::undirected_graph::reserve_degree ( const node u, const uint64_t d )

inlinenoexceptinherited

Predicts that the degree of node u is d.

Memory of size d is reserved so that adding edges is done more efficiently.

Parameters

u	Node to reserve the degree for.
d	The amount of memory to reserve.

Precondition

The graph must have been initialized.

set_edges()

free_tree & lal::graphs::free_tree::set_edges ( const std::vector< edge > & edges, const bool norm = true, const bool check_norm = true )

virtualnoexcept

Sets the edges to the graph.

Sets the edges of this graph assuming that the nodes indexed in the list are, at most, the number of nodes of this graph.

This list of edges is assumed to be all the edges that are going to be added to this graph. This means that the internal data structures are constructed more efficiently than when adding edges one by one (see add_edge) or in several chunks (see add_edges). For a more controlled addition of the edges, see can_add_edges.

Moreover, the current structure of the graph is cleared before setting the new edges.

Parameters

edges	The edges to be added.
norm	Normalize the graph after the insertions.
check_norm	If norm is false then, should we check whether the result is normalized or not? This might be useful in case the resulting graph is normalized. If norm is true then check_norm is ignored.

Precondition

The graph has been initialized with as many nodes as vertices in the list of edges.

There are no repeated edges in the list.

Postcondition

If norm is true the graph is guaranteed to be normalized after the addition of the edge.

The type of tree (m_is_tree_type_valid) is invalidated.

Reimplemented from lal::graphs::undirected_graph.

tree_only_actions_after_add_edge()

void lal::graphs::tree::tree_only_actions_after_add_edge ( const node u, const node v )

protectednoexceptinherited

Do some work after the addition of an edge.

Parameters

u	First node of the edge.
v	Second node of the edge.

Postcondition

The tree type is invalidated.

Updated union-find.

tree_only_actions_after_add_edges()

void lal::graphs::tree::tree_only_actions_after_add_edges ( const edge_list & e )

protectednoexceptinherited

Do some work after the addition of several edges.

Parameters

e	List of edges.

Postcondition

The tree type is invalidated.

Updated union-find.

tree_only_actions_after_add_edges_bulk()

void lal::graphs::tree::tree_only_actions_after_add_edges_bulk ( )

protectednoexceptinherited

Do some work after the addition of several edges in bulk.

To be called only after veral calls to undirected_graph::add_edge_bulk or directed_graph::add_edge_bulk.

Postcondition

The tree type is invalidated.

Updated union-find.

tree_only_actions_after_add_edges_bulk_complete()

void lal::graphs::tree::tree_only_actions_after_add_edges_bulk_complete ( )

protectednoexceptinherited

Do some work after the addition of several edges in bulk.

To be called only after veral calls to undirected_graph::add_edge_bulk or directed_graph::add_edge_bulk.

Postcondition

The tree type is invalidated.

Updated union-find.

tree_only_actions_after_remove_edge()

void lal::graphs::tree::tree_only_actions_after_remove_edge ( const node u, const node v )

protectednoexceptinherited

Do some work after the removal of an edge.

Parameters

u	First node of the edge.
v	Second node of the edge.

Postcondition

The tree type is invalidated.

Updated union-find.

tree_only_actions_after_remove_edges()

void lal::graphs::tree::tree_only_actions_after_remove_edges ( const edge_list & e )

protectednoexceptinherited

Do some work after the removal of several edges.

Parameters

e	List of edges.

Postcondition

The tree type is invalidated.

Updated union-find.

tree_only_actions_after_remove_edges_bulk()

void lal::graphs::tree::tree_only_actions_after_remove_edges_bulk ( )

protectednoexceptinherited

Do some work after the removal of several edges in bulk.

To be called only after veral calls to undirected_graph::remove_edge_bulk or directed_graph::remove_edge_bulk.

Postcondition

The tree type is invalidated.

Updated union-find.

tree_only_actions_after_remove_edges_bulk_complete()

void lal::graphs::tree::tree_only_actions_after_remove_edges_bulk_complete ( )

protectednoexceptinherited

Do some work after the removal of several edges in bulk.

To be called only after veral calls to undirected_graph::remove_edge_bulk or directed_graph::remove_edge_bulk.

Postcondition

The tree type is invalidated.

Updated union-find.

tree_only_actions_after_remove_node()

void lal::graphs::tree::tree_only_actions_after_remove_node ( const node u )

protectednoexceptinherited

Do some work before the removal of a vertex.

Parameters

u	Node to be removed.

Postcondition

The tree type is invalidated.

Updated union-find.

tree_only_actions_before_remove_edges_incident_to()

void lal::graphs::tree::tree_only_actions_before_remove_edges_incident_to ( const node u )

protectednoexceptinherited

Do some work before the removal of all edges incident to a vertex.

Parameters

u	Node whose incident edges are to be removed.

Postcondition

The tree type is invalidated.

Updated union-find.

tree_only_add_node()

void lal::graphs::tree::tree_only_add_node ( )

inlineprotectednoexceptinherited

Adds a node to this tree.

Updates all the internal data structures.

tree_only_init()

void lal::graphs::tree::tree_only_init ( const uint64_t n )

inlineprotectednoexceptinherited

Initializes only the memory of class tree.

Parameters

n	Number of vertices.

tree_only_invalidate()

void lal::graphs::tree::tree_only_invalidate ( )

inlineprotectednoexceptinherited

Invalidates the aggregated information of the tree.

Invalidates:

• m_is_tree_type_valid.

tree_only_remove_node()

void lal::graphs::tree::tree_only_remove_node ( const node u )

protectednoexceptinherited

Removes a vertex from the union-find data structure.

Parameters

u	Node that was removed.

Postcondition

The tree type is invalidated.

Updated union-find.

tree_only_set_edges()

void lal::graphs::tree::tree_only_set_edges ( )

protectednoexceptinherited

Updates the data structures of a tree after the graph structure has had its set of edges set.

Postcondition

The tree type is invalidated.

Updated union-find.

update_union_find_after_add_edge()

void lal::graphs::free_tree::update_union_find_after_add_edge ( const node u, const node v, uint64_t *const root_of, uint64_t *const root_size ) const

protectedvirtualnoexcept

Update the union find data structure after an edge addition.

This is a helper method to be able to call lal::detail::update_unionfind_after_add_edge which updates the Union-Find data structure under addition of an edge.

Parameters

u	Node that is connected to v.
v	Node that is connected to u.
root_of	Array of n elements relating each vertex to its root in the union find data structure.
root_size	Array of n elements relating each vertex to the size of the connected component it belongs to.

Implements lal::graphs::tree.

update_union_find_after_add_edges()

void lal::graphs::free_tree::update_union_find_after_add_edges ( const edge_list & edges, uint64_t *const root_of, uint64_t *const root_size ) const

protectedvirtualnoexcept

Update the union find data structure after the addition of a set of edges.

This is a helper method to be able to call lal::detail::update_unionfind_after_add_edges which updates the Union-Find data structure under addition of an edge.

Parameters

edges	A set of edges.
root_of	Array of n elements relating each vertex to its root in the union find data structure.
root_size	Array of n elements relating each vertex to the size of the connected component it belongs to.

Implements lal::graphs::tree.

update_union_find_after_add_edges_bulk()

void lal::graphs::free_tree::update_union_find_after_add_edges_bulk ( uint64_t *const root_of, uint64_t *const root_size ) const

protectedvirtualnoexcept

Update the union find data structure after the addition of several edges.

This is a helper method to be able to call lal::detail::update_unionfind_after_add_rem_edges_bulk which updates the Union-Find data structure after addition of several edges.

Parameters

root_of	Array of n elements relating each vertex to its root in the union find data structure.
root_size	Array of n elements relating each vertex to the size of the connected component it belongs to.

Implements lal::graphs::tree.

update_union_find_after_remove_edge()

void lal::graphs::free_tree::update_union_find_after_remove_edge ( const node u, const node v, uint64_t *const root_of, uint64_t *const root_size ) const

protectedvirtualnoexcept

Update the union find data structure after an edge removal.

This is a helper method to be able to call lal::detail::update_unionfind_after_remove_edge which updates the Union-Find data structure under removal of an edge.

Parameters

u	Node that is connected to v.
v	Node that is connected to u.
root_of	Array of n elements relating each vertex to its root in the union find data structure.
root_size	Array of n elements relating each vertex to the size of the connected component it belongs to.

Implements lal::graphs::tree.

update_union_find_after_remove_edges()

void lal::graphs::free_tree::update_union_find_after_remove_edges ( const edge_list & edges, uint64_t *const root_of, uint64_t *const root_size ) const

protectedvirtualnoexcept

Update the union find data structure after the removal of a set of edges.

This is a helper method to be able to call lal::detail::update_unionfind_after_remove_edges which updates the Union-Find data structure under removal of an edge.

Parameters

edges	A set of edges.
root_of	Array of n elements relating each vertex to its root in the union find data structure.
root_size	Array of n elements relating each vertex to the size of the connected component it belongs to.

Implements lal::graphs::tree.

update_union_find_after_remove_edges_bulk()

void lal::graphs::free_tree::update_union_find_after_remove_edges_bulk ( uint64_t *const root_of, uint64_t *const root_size ) const

protectedvirtualnoexcept

Update the union find data structure after the removal of several edges.

This is a helper method to be able to call lal::detail::update_unionfind_after_add_rem_edges_bulk which updates the Union-Find data structure under removal of several edges.

Parameters

root_of	Array of n elements relating each vertex to its root in the union find data structure.
root_size	Array of n elements relating each vertex to the size of the connected component it belongs to.

Implements lal::graphs::tree.

update_union_find_before_remove_incident_edges_to()

void lal::graphs::free_tree::update_union_find_before_remove_incident_edges_to ( const node u, uint64_t *const root_of, uint64_t *const root_size ) const

protectedvirtualnoexcept

Update the union find data structure before the removal of all edges incident to a node.

This is a helper method to be able to call lal::detail::update_unionfind_before_remove_edges_incident_to which updates the Union-Find data structure under removal of all incident edges to a node.

Parameters

u	Node whose incident edges are to be removed.
root_of	Array of n elements relating each vertex to its root in the union find data structure.
root_size	Array of n elements relating each vertex to the size of the connected component it belongs to.

Implements lal::graphs::tree.

Friends And Related Symbol Documentation

rooted_tree

friend class rooted_tree

friend

We want the lal::graphs::rooted_tree class to be a friend of this so as to do move operations.

Member Data Documentation

m_is_normalized

bool lal::graphs::graph::m_is_normalized = true

protectedinherited

Is this graph normalized?

An undirected graph is normalized iff every node's adjacency list is sorted in increasing order.

In directed graphs, however, it is necessary that the adjacency lists of the out-neighbors and in-neighbors of nodes be sorted.

This attribute is set to 'true' in all graph's initialisation and destruction (when clear() method is called).

m_is_tree_type_valid

bool lal::graphs::tree::m_is_tree_type_valid = false

protectedinherited

Is the type of this tree valid?

This attribute keeps track of whether or not the function calculate_tree_type should be called before querying the type of this tree via function is_of_tree_type.

m_union_find__root_size

std::vector<uint64_t> lal::graphs::tree::m_union_find__root_size

protectedinherited

The size of the connected component that a root belongs to.

Formally, m_size_of[v] is the size of the connected component of a root vertex v. A vertex u is a root vertex if there exists a vertex w such that m_union_find__root_of[w] = u.

In this context, root is within the union-find data structure.

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The documentation for this class was generated from the following file:

• lal/graphs/free_tree.hpp