doc/graph_orientation.dox
author deba
Mon, 27 Mar 2006 08:01:10 +0000
changeset 2016 ecb067198349
parent 1715 e71778873dd0
child 2158 0b620ff10e7c
permissions -rw-r--r--
Doc rearrangement
Section readers moved to own group
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namespace lemon {
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/**
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\ingroup demos
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\file graph_orientation.cc
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\brief Graph orientation with lower bound requirement on the
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in-degree of the nodes.
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This demo shows an adaptation of the well-known "preflow push" algorithm to
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a simple graph orientation problem.
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The input of the problem is a(n undirected) graph and an integer value
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<i>f(n)</i> assigned to each node \e n. The task is to find an orientation
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of the edges for which the number of edge arriving to each node \e n is at
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least least <i>f(n)</i>.
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In fact, the algorithm reads a directed graph and computes a set of edges to
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be reversed in order to achieve the in-degree requirement.
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This input is given using 
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\ref graph-io-page ".lgf (Lemon Graph Format)" file. It should contain
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three node maps. The one called "f" contains the in-degree requirements, while
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"coordinate_x" and "coordinate_y" indicate the position of the nodes. These
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latter ones are used to generate the output, which is a <tt>.eps</tt> file.
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\section go-alg-dec The C++ source file
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Here you find how to solve the problem above using lemon.
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\subsection go-alg-head Headers and convenience typedefs
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First we include some important headers.
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The first one defines \ref lemon::ListGraph "ListGraph",
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the "Swiss army knife" graph implementation.
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\dontinclude graph_orientation.cc
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\skipline list_graph
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The next is  to read a \ref graph-io-page ".lgf" (Lemon Graph Format) file.
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\skipline reader
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This provides us with some special purpose graph \ref maps "maps".
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\skipline iterable
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The following header defines a simple data structure to store and manipulate
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planar coordinates. It will be used to draw the result.
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\skipline xy
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And finally, this header contains a simple graph drawing utility.
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\skipline eps
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As we don't want to type in \ref lemon "lemon::" million times, the
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following line seems to be useful.
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\skipline namespace
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The following <tt>typedef</tt>s will also save a lot of typing.
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\skip typedef
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\until InEdgeIt
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\subsection go-alg-main The main() function
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Well, we are ready to start <tt>main()</tt>.
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\skip main
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\until {
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First we check whether the program is called with exactly one parameter.
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If it isn't, we print a short help message end exit.
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The vast majority of people would probably skip this block.
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\skip if
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\until }
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Now, we read a graph \c g, and a map \c f containing
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the in-deg requirements from a \ref graph-io-page ".lgf (Lemon Graph Format)"
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file. To generate the output picture, we also read the node titles (\c label)
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and
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coordinates (\c coords).
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So, first we create the graph
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\skipline ListGraph
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and the corresponding NodeMaps.
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\skipline NodeMap
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\until coords
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\note The graph must be given to the maps' constructor.
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Then, the following block will read these data from the file, or exit if
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the file is missing or corrupt.
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\skip try
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\until }
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\until }
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The algorithm needs an integer value assigned to each node. We call this "level" and the nodes are on level 0 at the
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beginning of the execution.
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\skipline level
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The deficiency (\c def) of a node is the in-degree requirement minus the 
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actual in-degree.
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\skip def
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\until subMap
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A node is \e active if its deficiency is positive (i.e. if it doesn't meet
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the degree requirement).
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\skip active
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\until def
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We also store in a bool map indicating which edges are reverted.
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Actually this map called \c rev is only
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used to draw these edges with different color in the output picture. The
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algorithm updates this map, but will not use it otherwise.
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\skip rev
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\until reversed
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The variable \c nodeNum will refer to the number of nodes.
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\skipline nodeNum
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Here comes the algorithms itself. 
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In each iteration we choose an active node (\c act will do it for us).
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If there is
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no such a node, then the orientation is feasible so we are done.
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\skip act
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\until while
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Then we check if there exists an edge leaving this node that steps down exactly
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one level.
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\skip OutEdge
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\until while
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If there exists, we decrease the "activity" of the node \c act by reverting
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this egde.
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Fortunately, \ref lemon::ListGraph "ListGraph"
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has a special function \ref lemon::ListGraph::reverseEdge() "reverseEdge()"
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that makes this easy.
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We also have to update the maps \c def and
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\c rev.
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\skipline if
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\skip if
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\until }
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Otherwise (i.e. if there is no edge stepping down one level). We lift up the
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current active node \c act. If it reaches level \c nodeNum, then there
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exists no appropriate orientation so we stop.
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\skipline else
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\skipline if
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\skipline return
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\until }
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\until }
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\until }
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Believe it or not, this algorithm works and runs fast.
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Finally, we print the obtained orientation. Note, how the different
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\c bool values of
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\c rev are transformed into different \ref lemon::Color "RGB color"s
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using the class
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\ref lemon::ColorSet "ColorSet"
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and the \ref map_adaptors "map adaptor" called
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\ref lemon::ComposeMap "composeMap".
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\skip graphToEps
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\until run
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\until end of main
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Finally here are again the list of the used include files (because I can't turn
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this section off.)
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*/
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}