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