<html><!-- Created using the cpp_pretty_printer from the dlib C++ library. See http://dlib.net for updates. --><head><title>dlib C++ Library - graph_utils_abstract.h</title></head><body bgcolor='white'><pre>
<font color='#009900'>// Copyright (C) 2007 Davis E. King (davis@dlib.net)
</font><font color='#009900'>// License: Boost Software License See LICENSE.txt for the full license.
</font><font color='#0000FF'>#undef</font> DLIB_GRAPH_UTILs_ABSTRACT_
<font color='#0000FF'>#ifdef</font> DLIB_GRAPH_UTILs_ABSTRACT_
<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='../directed_graph.h.html'>../directed_graph.h</a>"
<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='../algs.h.html'>../algs.h</a>"
<font color='#0000FF'>namespace</font> dlib
<b>{</b>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> T
<font color='#5555FF'>></font>
<font color='#0000FF'>typename</font> T::edge_type<font color='#5555FF'>&</font> <b><a name='edge'></a>edge</b><font face='Lucida Console'>(</font>
T<font color='#5555FF'>&</font> g,
<font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> i,
<font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> j
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- T is an implementation of graph/graph_kernel_abstract.h
- g.has_edge(i,j)
ensures
- returns a reference to the edge data for the edge connecting nodes i and j
(i.e. returns g.node(i).edge(x) such that g.node(i).neighbor(x).index() == j)
!*/</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> T
<font color='#5555FF'>></font>
<font color='#0000FF'>typename</font> <font color='#0000FF'>const</font> T::edge_type<font color='#5555FF'>&</font> <b><a name='edge'></a>edge</b><font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> T<font color='#5555FF'>&</font> g,
<font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> i,
<font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> j
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- T is an implementation of graph/graph_kernel_abstract.h
- g.has_edge(i,j)
ensures
- returns a const reference to the edge data for the edge connecting nodes i and j
(i.e. returns g.node(i).edge(x) such that g.node(i).neighbor(x).index() == j)
!*/</font>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> T
<font color='#5555FF'>></font>
<font color='#0000FF'>typename</font> T::edge_type<font color='#5555FF'>&</font> <b><a name='edge'></a>edge</b><font face='Lucida Console'>(</font>
T<font color='#5555FF'>&</font> g,
<font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> parent_idx,
<font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> child_idx
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- T is an implementation of directed_graph/directed_graph_kernel_abstract.h
- g.has_edge(parent_idx,child_idx)
ensures
- returns a reference to the edge data for the directed edge connecting parent
node g.node(parent_idx) to child node g.node(child_idx).
!*/</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> T
<font color='#5555FF'>></font>
<font color='#0000FF'>typename</font> <font color='#0000FF'>const</font> T::edge_type<font color='#5555FF'>&</font> <b><a name='edge'></a>edge</b><font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> T<font color='#5555FF'>&</font> g,
<font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> parent_idx,
<font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> child_idx
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- T is an implementation of directed_graph/directed_graph_kernel_abstract.h
- g.has_edge(parent_idx,child_idx)
ensures
- returns a const reference to the edge data for the directed edge connecting
parent node g.node(parent_idx) to child node g.node(child_idx).
!*/</font>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> T
<font color='#5555FF'>></font>
<font color='#0000FF'><u>bool</u></font> <b><a name='graph_has_symmetric_edges'></a>graph_has_symmetric_edges</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> T<font color='#5555FF'>&</font> graph
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- T is an implementation of directed_graph/directed_graph_kernel_abstract.h
ensures
- if (All nodes have either 0 edges between them or 2 edges between them.
That is, if there is an edge pointing from node A to node B then there is
also an edge from B to A) then
- returns true
- else
- returns false
!*/</font>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> T
<font color='#5555FF'>></font>
<font color='#0000FF'><u>bool</u></font> <b><a name='graph_contains_directed_cycle'></a>graph_contains_directed_cycle</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> T<font color='#5555FF'>&</font> graph
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- T is an implementation of directed_graph/directed_graph_kernel_abstract.h
ensures
- if (there is a directed cycle in the given graph) then
- returns true
- else
- returns false
!*/</font>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> T
<font color='#5555FF'>></font>
<font color='#0000FF'><u>bool</u></font> <b><a name='graph_contains_undirected_cycle'></a>graph_contains_undirected_cycle</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> T<font color='#5555FF'>&</font> graph
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- T is an implementation of directed_graph/directed_graph_kernel_abstract.h or
T is an implementation of graph/graph_kernel_abstract.h
ensures
- if (there is an undirected cycle in the given graph) then
- returns true
- else
- returns false
!*/</font>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> T
<font color='#5555FF'>></font>
<font color='#0000FF'><u>bool</u></font> <b><a name='graph_contains_length_one_cycle'></a>graph_contains_length_one_cycle</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> T<font color='#5555FF'>&</font> graph
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- T is an implementation of directed_graph/directed_graph_kernel_abstract.h or
T is an implementation of graph/graph_kernel_abstract.h
ensures
- if (it is the case that graph.has_edge(i,i) == true for some i) then
- returns true
- else
- returns false
!*/</font>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> src_type,
<font color='#0000FF'>typename</font> dest_type
<font color='#5555FF'>></font>
<font color='#0000FF'><u>void</u></font> <b><a name='copy_graph_structure'></a>copy_graph_structure</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> src_type<font color='#5555FF'>&</font> src,
dest_type<font color='#5555FF'>&</font> dest
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- src_type is an implementation of directed_graph/directed_graph_kernel_abstract.h or
src_type is an implementation of graph/graph_kernel_abstract.h
- dest_type is an implementation of directed_graph/directed_graph_kernel_abstract.h or
dest_type is an implementation of graph/graph_kernel_abstract.h
- dest_type is not a directed_graph when src_type is a graph
ensures
- this function copies the graph structure from src into dest
- #dest.number_of_nodes() == src.number_of_nodes()
- for all valid i: #dest.node(i).item has an initial value for its type
- for all valid i and j:
- if (src.has_edge(i,j) == true) then
- #dest.has_edge(i,j) == true
!*/</font>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> src_type,
<font color='#0000FF'>typename</font> dest_type
<font color='#5555FF'>></font>
<font color='#0000FF'><u>void</u></font> <b><a name='copy_graph'></a>copy_graph</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> src_type<font color='#5555FF'>&</font> src,
dest_type<font color='#5555FF'>&</font> dest
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- src_type is an implementation of directed_graph/directed_graph_kernel_abstract.h or
src_type is an implementation of graph/graph_kernel_abstract.h
- dest_type is an implementation of directed_graph/directed_graph_kernel_abstract.h or
dest_type is an implementation of graph/graph_kernel_abstract.h
- src_type and dest_type are both the same kind of graph. That is, they
are either both directed or both undirected.
- the node and edge data in the graphs are copyable via operator=().
ensures
- #dest is a complete duplicate of src.
!*/</font>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> directed_graph_type,
<font color='#0000FF'>typename</font> graph_type
<font color='#5555FF'>></font>
<font color='#0000FF'><u>void</u></font> <b><a name='create_moral_graph'></a>create_moral_graph</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> directed_graph_type<font color='#5555FF'>&</font> g,
graph_type<font color='#5555FF'>&</font> moral_graph
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- directed_graph_type is an implementation of directed_graph/directed_graph_kernel_abstract.h
- graph_type is an implementation of graph/graph_kernel_abstract.h
- graph_contains_directed_cycle(g) == false
ensures
- #moral_graph == the moralized version of the directed graph g
- #moral_graph.number_of_nodes() == g.number_of_nodes()
- for all valid i and j:
- if (g.has_edge(i,j) == true) then
- #moral_graph.has_edge(i,j) == true
(i.e. all the edges that are in g are also in moral_graph)
- for all valid i:
- for all pairs p1 and p2 such that p1 != p2 and g.node(p1) and g.node(p2) are both
parents of node g.node(i):
- #moral_graph.has_edge(p1,p2) == true
(i.e. all the parents of a node are connected in the moral graph)
!*/</font>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> T,
<font color='#0000FF'>typename</font> S
<font color='#5555FF'>></font>
<font color='#0000FF'><u>void</u></font> <b><a name='find_connected_nodes'></a>find_connected_nodes</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> T<font color='#5555FF'>&</font> n,
S<font color='#5555FF'>&</font> visited
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- T is a node_type from an implementation of directed_graph/directed_graph_kernel_abstract.h or
T is a node_type from an implementation of graph/graph_kernel_abstract.h
- S is an implementation of set/set_kernel_abstract.h
ensures
- let G be the graph that contains node n
- #visited.is_member(n.index()) == true
- for all i such that there is an undirected path from n to G.node(i):
- #visited.is_member(i) == true
- for all i such that visited.is_member(i):
- #visited.is_member(i) == true
(i.e. this function doesn't remove anything from visited. So if
it contains stuff when you call this function then it will still
contain those things once the function ends)
!*/</font>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> T
<font color='#5555FF'>></font>
<font color='#0000FF'><u>bool</u></font> <b><a name='graph_is_connected'></a>graph_is_connected</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> T<font color='#5555FF'>&</font> g
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- T is an implementation of directed_graph/directed_graph_kernel_abstract.h or
T is an implementation of graph/graph_kernel_abstract.h
ensures
- every node in g has an undirected path to every other node in g.
I.e. g is a connected graph
!*/</font>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> graph_type,
<font color='#0000FF'>typename</font> sets_of_int
<font color='#5555FF'>></font>
<font color='#0000FF'><u>bool</u></font> <b><a name='is_clique'></a>is_clique</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> graph_type<font color='#5555FF'>&</font> g,
<font color='#0000FF'>const</font> sets_of_int<font color='#5555FF'>&</font> clique
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- graph_type is an implementation of graph/graph_kernel_abstract.h
- sets_of_int is an implementation of set/set_kernel_abstract.h
and it contains unsigned long objects.
- graph_contains_length_one_cycle(g) == false
- for all x such that clique.is_member(x):
- x < g.number_of_nodes()
ensures
- if (it is true that for all i and j such that clique.is_member(i) and
clique.is_member(j) then g.has_edge(i,j) == true) then
- returns true
- else
- returns false
- if (clique.size() == 0) then
- returns true
(this is just a special case of the above condition)
- else
- returns false
!*/</font>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> graph_type,
<font color='#0000FF'>typename</font> sets_of_int
<font color='#5555FF'>></font>
<font color='#0000FF'><u>bool</u></font> <b><a name='is_maximal_clique'></a>is_maximal_clique</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> graph_type<font color='#5555FF'>&</font> g,
<font color='#0000FF'>const</font> sets_of_int<font color='#5555FF'>&</font> clique
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- graph_type is an implementation of graph/graph_kernel_abstract.h
- sets_of_int is an implementation of set/set_kernel_abstract.h
and it contains unsigned long objects.
- graph_contains_length_one_cycle(g) == false
- for all x such that clique.is_member(x):
- x < g.number_of_nodes()
- is_clique(g,clique) == true
ensures
- if (there is no x such that clique.is_member(x) == false
and g.has_edge(i,x) for all i such that cliques.is_member(i)) then
- returns true
- else
- returns false
- if (clique.size() == 0) then
- returns true
(this is just a special case of the above condition)
- else
- returns false
!*/</font>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> graph_type,
<font color='#0000FF'>typename</font> set_of_sets_of_int
<font color='#5555FF'>></font>
<font color='#0000FF'><u>void</u></font> <b><a name='triangulate_graph_and_find_cliques'></a>triangulate_graph_and_find_cliques</b> <font face='Lucida Console'>(</font>
graph_type<font color='#5555FF'>&</font> g,
set_of_sets_of_int<font color='#5555FF'>&</font> cliques
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- graph_type is an implementation of graph/graph_kernel_abstract.h
- set_of_sets_of_int is an implementation of set/set_kernel_abstract.h
and it contains another set object which is comparable by operator< and
itself contains unsigned long objects.
(e.g. set<set<unsigned long>::compare_1a>::kernel_1a)
- graph_contains_length_one_cycle(g) == false
- graph_is_connected(g) == true
ensures
- #g.number_of_nodes() == g.number_of_nodes()
- all this function does to g is add edges to it until g becomes a
chordal graph where a chordal graph is a graph where each cycle
in the graph of 4 or more nodes has an edge joining two nodes
that are not adjacent in the cycle.
- #cliques.size() == the number of maximal cliques in the graph #g
- for all valid sets S such that #cliques.is_member(S):
- for all valid integers i and j such that S.is_member(i) == true
and S.is_member(j) == true and i != j:
- #g.has_edge(i,j) == true
!*/</font>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> graph_type,
<font color='#0000FF'>typename</font> join_tree_type
<font color='#5555FF'>></font>
<font color='#0000FF'><u>bool</u></font> <b><a name='is_join_tree'></a>is_join_tree</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> graph_type<font color='#5555FF'>&</font> g,
<font color='#0000FF'>const</font> join_tree_type<font color='#5555FF'>&</font> join_tree
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- graph_type is an implementation of directed_graph/directed_graph_kernel_abstract.h or
graph_type is an implementation of graph/graph_kernel_abstract.h
- join_tree_type is an implementation of graph/graph_kernel_abstract.h
- join_tree_type::type is an implementation of set/set_compare_abstract.h and
this set type contains unsigned long objects.
- join_tree_type::edge_type is an implementation of set/set_compare_abstract.h and
this set type contains unsigned long objects.
- graph_contains_length_one_cycle(g) == false
- graph_is_connected(g) == true
ensures
- if (join_tree is a valid join tree of graph g. That is, join_tree is a
tree decomposition of g) then
- returns true
- else
- returns false
- a join tree of graph g is defined as follows:
- graph_contains_undirected_cycle(join_tree) == false
- graph_is_connected(join_tree) == true
- for all valid i:
- join_tree.node(i).item == a non-empty set containing node indexes
from g. That is, this set contains all the nodes from g that are
in this cluster in the join tree
- for all valid i and j such that i and j are both < join_tree.number_of_nodes()
- let X be the set of numbers that is contained in both join_tree.node(i).item
and join_tree.node(j).item
- It is the case that all nodes on the unique path between join_tree.node(i)
and join_tree.node(j) contain the numbers from X in their sets.
- edge(join_tree,i,j) == a set containing the intersection of
join_tree.node(i).item and join_tree.node(j).item
- the node index for every node in g appears in some node in join_tree at
least once.
!*/</font>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> graph_type,
<font color='#0000FF'>typename</font> join_tree_type
<font color='#5555FF'>></font>
<font color='#0000FF'><u>void</u></font> <b><a name='create_join_tree'></a>create_join_tree</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> graph_type<font color='#5555FF'>&</font> g,
join_tree_type<font color='#5555FF'>&</font> join_tree
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
requires
- graph_type is an implementation of graph/graph_kernel_abstract.h
- join_tree_type is an implementation of graph/graph_kernel_abstract.h
- join_tree_type::type is an implementation of set/set_compare_abstract.h and
this set type contains unsigned long objects.
- join_tree_type::edge_type is an implementation of set/set_compare_abstract.h and
this set type contains unsigned long objects.
- graph_contains_length_one_cycle(g) == false
- graph_is_connected(g) == true
ensures
- #is_join_tree(g, join_tree) == true
!*/</font>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<b>}</b>
<font color='#0000FF'>#endif</font> <font color='#009900'>// DLIB_GRAPH_UTILs_ABSTRACT_
</font>
</pre></body></html>