namespace lemon { /** \ingroup demos \file graph_orientation.cc \brief Graph orientation with lower bound requirement on the in-degree of the nodes. This demo shows an adaptation of the well-known "preflow push" algorithm to a simple graph orientation problem. The input of the problem is a(n undirected) graph and an integer value f(n) assigned to each node \e n. The task is to find an orientation of the edges for which the number of edge arriving to each node \e n is at least least f(n). In fact, the algorithm reads a directed graph and computes a set of edges to be reversed in order to achieve the in-degree requirement. This input is given using \ref graph-io-page ".lgf (Lemon Graph Format)" file. It should contain three node maps. The one called "f" contains the in-degree requirements, while "coordinate_x" and "coordinate_y" indicate the position of the nodes. These latter ones are used to generate the output, which is a .eps file. \section go-alg-dec The C++ source file Here you find how to solve the problem above using lemon. \subsection go-alg-head Headers and convenience typedefs First we include some important headers. The first one defines \ref lemon::ListGraph "ListGraph", the "Swiss army knife" graph implementation. \dontinclude graph_orientation.cc \skipline list_graph The next is to read a \ref graph-io-page ".lgf" (Lemon Graph Format) file. \skipline reader This provides us with some special purpose graph \ref maps "maps". \skipline iterable The following header defines a simple data structure to store and manipulate planar coordinates. It will be used to draw the result. \skipline xy And finally, this header contains a simple graph drawing utility. \skipline eps As we don't want to type in \ref lemon "lemon::" million times, the following line seems to be useful. \skipline namespace The following typedefs will also save a lot of typing. \skip typedef \until InEdgeIt \subsection go-alg-main The main() function Well, we are ready to start main(). \skip main \until { First we check whether the program is called with exactly 1 parameter. If it isn't, we print a short help message end exit. The vast majority of people would probably skip this block. \skip if \until } Now, we read a graph \c g, and a map \c f containing the in-deg requirements from a \ref graph-io-page ".lgf (Lemon Graph Format)" file. To generate the output picture, we also read the node titles (\c id) and coordinates (\c coords). So, first we create the graph \skipline ListGraph and the corresponding NodeMaps. \skipline NodeMap \until coords \note The graph must be given to the maps' constructor. Then, the following block will read these data from the file, or exit if the file is missing or corrupt. \skip try \until } \until } The algorithm needs a "level" integer value assigned to each node. In the beginning, the nodes are on level 0. \skipline level The deficiency (\c def) of a node is the in-degree requirement minus the actual in-degree. \skip def \until subMap A node is \e active if its deficiency is positive (i.e. if it doesn't meet the degree requirement). \skip active \until def We also store in a bool map which edges are reverted. Actually this is only used to draw these edges with different color in the output picture. The algorithm will update this map called \c rev, but will not use it otherwise. \skip rev \until reversed The variable \c nodeNum will refer to the number of nodes. \skipline nodeNum Here comes the algorithms itself. In each iteration we choose an active node (\c act will store it). If there is no such a node, then the orientation is feasible so we are done. \skip act \until while Then we check if there exists an edge leaving this node that steps down exactly one level. \skip OutEdge \until while If there exists, we decrease the "activity" of the node \c act by reverting this egde. Fortunately, \ref lemon::ListGraph "ListGraph" has a special function \ref lemon::ListGraph::reverseEdge() "reverseEdge()" that makes this easy. We also have to update the maps \c def and \c rev. \skipline if \skip if \until } Otherwise (i.e. if there is no edge stepping down one level). We lift up the current active node \c act. If it reaches level \c nodeNum, then there exists no appropriate orientation so we stop. \skipline else \skipline if \skipline return \until } \until } \until } Believe it or not, this algorithm works and runs fast. Finally, we print the obtained orientation. Note, how the different \c bool values of \c rev are transformed into different \ref lemon::Color "RGB color"s using the class \ref lemon::ColorSet "ColorSet" and the \ref map_adaptors "map adaptor" called \ref lemon::ComposeMap "composeMap". \skip graphToEps \until run \until end of main Finally here are again the list of the used include files (because I can't turn this section off.) */ }