COIN-OR::LEMON - Graph Library

source: lemon-0.x/doc/graphs.dox @ 911:89a4fbb99cad

Last change on this file since 911:89a4fbb99cad was 911:89a4fbb99cad, checked in by Alpar Juttner, 15 years ago

Fix many doxygen command bugs.

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[666]1/*!
2
3\page graphs How to use graphs
4
[756]5The primary data structures of HugoLib are the graph classes. They all
6provide a node list - edge list interface, i.e. they have
7functionalities to list the nodes and the edges of the graph as well
8as in incoming and outgoing edges of a given node.
9
10
[873]11Each graph should meet the
[880]12\ref hugo::skeleton::StaticGraph "StaticGraph" concept.
[873]13This concept does not
[756]14makes it possible to change the graph (i.e. it is not possible to add
15or delete edges or nodes). Most of the graph algorithms will run on
16these graphs.
17
[873]18The graphs meeting the
[880]19\ref hugo::skeleton::ExtendableGraph "ExtendableGraph"
[873]20concept allow node and
[756]21edge addition. You can also "clear" (i.e. erase all edges and nodes)
22such a graph.
23
[873]24In case of graphs meeting the full feature
[880]25\ref hugo::skeleton::ErasableGraph "ErasableGraph"
[873]26concept
[756]27you can also erase individual edges and node in arbitrary order.
28
29The implemented graph structures are the following.
30\li \ref hugo::ListGraph "ListGraph" is the most versatile graph class. It meets
[911]31the \ref hugo::skeleton::ErasableGraph "ErasableGraph" concept
[873]32and it also have some convenience features.
[756]33\li \ref hugo::SmartGraph "SmartGraph" is a more memory
34efficient version of \ref hugo::ListGraph "ListGraph". The
[873]35price of it is that it only meets the
[880]36\ref hugo::skeleton::ExtendableGraph "ExtendableGraph" concept,
[756]37so you cannot delete individual edges or nodes.
38\li \ref hugo::SymListGraph "SymListGraph" and
39\ref hugo::SymSmartGraph "SymSmartGraph" classes are very similar to
40\ref hugo::ListGraph "ListGraph" and \ref hugo::SmartGraph "SmartGraph".
41The difference is that whenever you add a
42new edge to the graph, it actually adds a pair of oppositely directed edges.
43They are linked together so it is possible to access the counterpart of an
44edge. An even more important feature is that using these classes you can also
45attach data to the edges in such a way that the stored data
46are shared by the edge pairs.
47\li \ref hugo::FullGraph "FullGraph"
[911]48implements a full graph. It is a \ref hugo::skeleton::StaticGraph, so you cannot
[756]49change the number of nodes once it is constructed. It is extremely memory
50efficient: it uses constant amount of memory independently from the number of
51the nodes of the graph. Of course, the size of the \ref maps "NodeMap"'s and
52\ref maps "EdgeMap"'s will depend on the number of nodes.
53
54\li \ref hugo::NodeSet "NodeSet" implements a graph with no edges. This class
55can be used as a base class of \ref hugo::EdgeSet "EdgeSet".
56\li \ref hugo::EdgeSet "EdgeSet" can be used to create a new graph on
[873]57the node set of another graph. The base graph can be an arbitrary graph and it
[756]58is possible to attach several \ref hugo::EdgeSet "EdgeSet"'s to a base graph.
59
60\todo Don't we need SmartNodeSet and SmartEdgeSet?
61\todo Some cross-refs are wrong.
62
63The graph structures itself can not store data attached
64to the edges and nodes. However they all provide
65\ref maps "map classes"
66to dynamically attach data the to graph components.
67
[666]68The following program demonstrates the basic features of HugoLib's graph
69structures.
70
71\code
72#include <iostream>
73#include <hugo/list_graph.h>
74
75using namespace hugo;
76
77int main()
78{
79  typedef ListGraph Graph;
80\endcode
81
82ListGraph is one of HugoLib's graph classes. It is based on linked lists,
83therefore iterating throuh its edges and nodes is fast.
84
85\code
86  typedef Graph::Edge Edge;
87  typedef Graph::InEdgeIt InEdgeIt;
88  typedef Graph::OutEdgeIt OutEdgeIt;
89  typedef Graph::EdgeIt EdgeIt;
90  typedef Graph::Node Node;
91  typedef Graph::NodeIt NodeIt;
92
93  Graph g;
94 
95  for (int i = 0; i < 3; i++)
96    g.addNode();
97 
[875]98  for (NodeIt i(g); i!=INVALID; ++i)
99    for (NodeIt j(g); j!=INVALID; ++j)
[666]100      if (i != j) g.addEdge(i, j);
101\endcode
102
103After some convenience typedefs we create a graph and add three nodes to it.
104Then we add edges to it to form a full graph.
105
106\code
107  std::cout << "Nodes:";
[875]108  for (NodeIt i(g); i!=INVALID; ++i)
[666]109    std::cout << " " << g.id(i);
110  std::cout << std::endl;
111\endcode
112
113Here we iterate through all nodes of the graph. We use a constructor of the
[875]114node iterator to initialize it to the first node. The operator++ is used to
115step to the next node. Using operator++ on the iterator pointing to the last
116node invalidates the iterator i.e. sets its value to
117\ref hugo::INVALID "INVALID". This is what we exploit in the stop condition.
[666]118
[875]119The previous code fragment prints out the following:
[666]120
121\code
122Nodes: 2 1 0
123\endcode
124
125\code
126  std::cout << "Edges:";
[875]127  for (EdgeIt i(g); i!=INVALID; ++i)
[666]128    std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")";
129  std::cout << std::endl;
130\endcode
131
132\code
133Edges: (0,2) (1,2) (0,1) (2,1) (1,0) (2,0)
134\endcode
135
136We can also iterate through all edges of the graph very similarly. The head and
137tail member functions can be used to access the endpoints of an edge.
138
139\code
140  NodeIt first_node(g);
141
142  std::cout << "Out-edges of node " << g.id(first_node) << ":";
[875]143  for (OutEdgeIt i(g, first_node); i!=INVALID; ++i)
[666]144    std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")";
145  std::cout << std::endl;
146
147  std::cout << "In-edges of node " << g.id(first_node) << ":";
[875]148  for (InEdgeIt i(g, first_node); i!=INVALID; ++i)
[666]149    std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")";
150  std::cout << std::endl;
151\endcode
152
153\code
154Out-edges of node 2: (2,0) (2,1)
155In-edges of node 2: (0,2) (1,2)
156\endcode
157
158We can also iterate through the in and out-edges of a node. In the above
159example we print out the in and out-edges of the first node of the graph.
160
161\code
162  Graph::EdgeMap<int> m(g);
163
[875]164  for (EdgeIt e(g); e!=INVALID; ++e)
[666]165    m.set(e, 10 - g.id(e));
166 
167  std::cout << "Id Edge  Value" << std::endl;
[875]168  for (EdgeIt e(g); e!=INVALID; ++e)
[666]169    std::cout << g.id(e) << "  (" << g.id(g.tail(e)) << "," << g.id(g.head(e))
170      << ") " << m[e] << std::endl;
171\endcode
172
173\code
174Id Edge  Value
1754  (0,2) 6
1762  (1,2) 8
1775  (0,1) 5
1780  (2,1) 10
1793  (1,0) 7
1801  (2,0) 9
181\endcode
182
[873]183As we mentioned above, graphs are not containers rather
[666]184incidence structures which are iterable in many ways. HugoLib introduces
185concepts that allow us to attach containers to graphs. These containers are
186called maps.
187
188In the example above we create an EdgeMap which assigns an int value to all
189edges of the graph. We use the set member function of the map to write values
190into the map and the operator[] to retrieve them.
191
192Here we used the maps provided by the ListGraph class, but you can also write
193your own maps. You can read more about using maps \ref maps "here".
194
195*/
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