Slight changes in doc.
5 \file graph_orientation.cc
6 \brief Graph orientation with lower bound requirement on the
7 in-degree of the nodes.
9 This demo shows an adaptation of the well-known "preflow push" algorithm to
10 a simple graph orientation problem.
12 The input of the problem is a(n undirected) graph and an integer value
13 <i>f(n)</i> assigned to each node \e n. The task is to find an orientation
14 of the edges for which the number of edge arriving to each node \e n is at
15 least least <i>f(n)</i>.
17 In fact, the algorithm reads a directed graph and computes a set of edges to
18 be reversed in order to achieve the in-degree requirement.
19 This input is given using
20 \ref graph-io-page ".lgf (Lemon Graph Format)" file. It should contain
21 three node maps. The one called "f" contains the in-degree requirements, while
22 "coordinate_x" and "coordinate_y" indicate the position of the nodes. These
23 latter ones are used to generate the output, which is a <tt>.eps</tt> file.
26 \section go-alg-dec The C++ source file
28 Here you find how to solve the problem above using lemon.
30 \subsection go-alg-head Headers and convenience typedefs
32 First we include some important headers.
34 The first one defines \ref lemon::ListGraph "ListGraph",
35 the "Swiss army knife" graph implementation.
36 \dontinclude graph_orientation.cc
39 The next is to read a \ref graph-io-page ".lgf" (Lemon Graph Format) file.
42 This provides us with some special purpose graph \ref maps "maps".
45 The following header defines a simple data structure to store and manipulate
46 planar coordinates. It will be used to draw the result.
49 And finally, this header contains a simple graph drawing utility.
52 As we don't want to type in \ref lemon "lemon::" million times, the
53 following line seems to be useful.
56 The following <tt>typedef</tt>s will also save a lot of typing.
60 \subsection go-alg-main The main() function
62 Well, we are ready to start <tt>main()</tt>.
66 First we check whether the program is called with exactly one parameter.
67 If it isn't, we print a short help message end exit.
68 The vast majority of people would probably skip this block.
72 Now, we read a graph \c g, and a map \c f containing
73 the in-deg requirements from a \ref graph-io-page ".lgf (Lemon Graph Format)"
74 file. To generate the output picture, we also read the node titles (\c label)
76 coordinates (\c coords).
77 So, first we create the graph
79 and the corresponding NodeMaps.
82 \note The graph must be given to the maps' constructor.
84 Then, the following block will read these data from the file, or exit if
85 the file is missing or corrupt.
90 The algorithm needs an integer value assigned to each node. We call this "level" and the nodes are on level 0 at the
91 beginning of the execution.
95 The deficiency (\c def) of a node is the in-degree requirement minus the
101 A node is \e active if its deficiency is positive (i.e. if it doesn't meet
102 the degree requirement).
106 We also store in a bool map indicating which edges are reverted.
107 Actually this map called \c rev is only
108 used to draw these edges with different color in the output picture. The
109 algorithm updates this map, but will not use it otherwise.
113 The variable \c nodeNum will refer to the number of nodes.
116 Here comes the algorithms itself.
117 In each iteration we choose an active node (\c act will do it for us).
119 no such a node, then the orientation is feasible so we are done.
123 Then we check if there exists an edge leaving this node that steps down exactly
128 If there exists, we decrease the "activity" of the node \c act by reverting
130 Fortunately, \ref lemon::ListGraph "ListGraph"
131 has a special function \ref lemon::ListGraph::reverseEdge() "reverseEdge()"
132 that makes this easy.
133 We also have to update the maps \c def and
138 Otherwise (i.e. if there is no edge stepping down one level). We lift up the
139 current active node \c act. If it reaches level \c nodeNum, then there
140 exists no appropriate orientation so we stop.
148 Believe it or not, this algorithm works and runs fast.
150 Finally, we print the obtained orientation. Note, how the different
152 \c rev are transformed into different \ref lemon::Color "RGB color"s
154 \ref lemon::ColorSet "ColorSet"
155 and the \ref map_adaptors "map adaptor" called
156 \ref lemon::ComposeMap "composeMap".
164 Finally here are again the list of the used include files (because I can't turn