COIN-OR::LEMON - Graph Library

Changeset 1952:6150d1cf0825 in lemon-0.x for lemon/graph_adaptor.h


Ignore:
Timestamp:
02/03/06 15:22:45 (14 years ago)
Author:
Mihaly Barasz
Branch:
default
Phase:
public
Convert:
svn:c9d7d8f5-90d6-0310-b91f-818b3a526b0e/lemon/trunk@2527
Message:

graph_adaptor.h: spacing corrections in doc

File:
1 edited

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  • lemon/graph_adaptor.h

    r1951 r1952  
    440440  /// edge-set. If the \c checked parameter is true then it filters the edgeset
    441441  /// to do not get invalid edges without source or target.
    442   /// Let  \f$  G=(V, A)  \f$ be a directed graph
     442  /// Let \f$ G=(V, A) \f$ be a directed graph
    443443  /// and suppose that the graph instance \c g of type ListGraph
    444   /// implements  \f$  G  \f$ .
    445   /// Let moreover  \f$  b_V  \f$  and  \f$  b_A  \f$ be bool-valued functions resp.
     444  /// implements \f$ G \f$.
     445  /// Let moreover \f$ b_V \f$ and \f$ b_A \f$ be bool-valued functions resp.
    446446  /// on the node-set and edge-set.
    447447  /// SubGraphAdaptor<...>::NodeIt iterates
    448   /// on the node-set  \f$ \{v\in V : b_V(v)=true\} \f$ and
     448  /// on the node-set \f$ \{v\in V : b_V(v)=true\} \f$ and
    449449  /// SubGraphAdaptor<...>::EdgeIt iterates
    450   /// on the edge-set  \f$ \{e\in A : b_A(e)=true\} \f$ . Similarly,
     450  /// on the edge-set \f$ \{e\in A : b_A(e)=true\} \f$. Similarly,
    451451  /// SubGraphAdaptor<...>::OutEdgeIt and
    452452  /// SubGraphAdaptor<...>::InEdgeIt iterates
     
    10501050  ///parts of the lib. Use them at you own risk.
    10511051  ///
    1052   /// Let  \f$  G=(V, A)  \f$ be a directed graph and for each directed edge
    1053   ///  \f$  e\in A  \f$ , let  \f$  \bar e  \f$ denote the edge obtained by
     1052  /// Let \f$ G=(V, A) \f$ be a directed graph and for each directed edge
     1053  ///\f$ e\in A \f$, let \f$ \bar e \f$ denote the edge obtained by
    10541054  /// reversing its orientation. We are given moreover two bool valued
    10551055  /// maps on the edge-set,
    1056   ///  \f$  forward\_filter  \f$ , and  \f$  backward\_filter  \f$ .
     1056  ///\f$ forward\_filter \f$, and \f$ backward\_filter \f$.
    10571057  /// SubBidirGraphAdaptor implements the graph structure with node-set
    1058   ///  \f$  V  \f$ and edge-set
    1059   ///  \f$  \{e : e\in A \mbox{ and } forward\_filter(e) \mbox{ is true}\}+\{\bar e : e\in A \mbox{ and } backward\_filter(e) \mbox{ is true}\}  \f$ .
     1058  ///\f$ V \f$ and edge-set
     1059  ///\f$ \{e : e\in A \mbox{ and } forward\_filter(e) \mbox{ is true}\}+\{\bar e : e\in A \mbox{ and } backward\_filter(e) \mbox{ is true}\} \f$.
    10601060  /// The purpose of writing + instead of union is because parallel
    10611061  /// edges can arise. (Similarly, antiparallel edges also can arise).
     
    11861186  ///An adaptor for composing the residual graph for
    11871187  ///directed flow and circulation problems.
    1188   ///Let  \f$ G=(V, A) \f$  be a directed graph and let  \f$ F \f$ be a
     1188  ///Let \f$ G=(V, A) \f$ be a directed graph and let \f$ F \f$ be a
    11891189  ///number type. Let moreover
    1190   /// \f$ f,c:A\to F \f$ , be functions on the edge-set.
    1191   ///In the appications of ResGraphAdaptor,  \f$ f \f$ usually stands for a flow
    1192   ///and  \f$ c \f$ for a capacity function.   
     1190  ///\f$ f,c:A\to F \f$, be functions on the edge-set.
     1191  ///In the appications of ResGraphAdaptor, \f$ f \f$ usually stands for a flow
     1192  ///and \f$ c \f$ for a capacity function.   
    11931193  ///Suppose that a graph instange \c g of type
    1194   ///\c ListGraph implements  \f$ G \f$  .
     1194  ///\c ListGraph implements \f$ G \f$.
    11951195  ///\code
    11961196  ///  ListGraph g;
    11971197  ///\endcode
    11981198  ///Then RevGraphAdaptor implements the graph structure with node-set
    1199   /// \f$ V \f$  and edge-set  \f$ A_{forward}\cup A_{backward} \f$ , where
    1200   /// \f$ A_{forward}=\{uv : uv\in A, f(uv)<c(uv)\} \f$ and
    1201   /// \f$ A_{backward}=\{vu : uv\in A, f(uv)>0\} \f$ ,
     1199  ///\f$ V \f$ and edge-set \f$ A_{forward}\cup A_{backward} \f$, where
     1200  ///\f$ A_{forward}=\{uv : uv\in A, f(uv)<c(uv)\} \f$ and
     1201  ///\f$ A_{backward}=\{vu : uv\in A, f(uv)>0\} \f$,
    12021202  ///i.e. the so called residual graph.
    1203   ///When we take the union  \f$ A_{forward}\cup A_{backward} \f$ ,
     1203  ///When we take the union \f$ A_{forward}\cup A_{backward} \f$,
    12041204  ///multilicities are counted, i.e. if an edge is in both
    1205   /// \f$ A_{forward} \f$  and  \f$ A_{backward} \f$ , then in the adaptor it
     1205  ///\f$ A_{forward} \f$ and \f$ A_{backward} \f$, then in the adaptor it
    12061206  ///appears twice.
    12071207  ///The following code shows how
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