Changeset 1952:6150d1cf0825 in lemon0.x
 Timestamp:
 02/03/06 15:22:45 (15 years ago)
 Branch:
 default
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 public
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 svn:c9d7d8f590d60310b91f818b3a526b0e/lemon/trunk@2527
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 1 edited
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lemon/graph_adaptor.h
r1951 r1952 440 440 /// edgeset. If the \c checked parameter is true then it filters the edgeset 441 441 /// to do not get invalid edges without source or target. 442 /// Let \f$ G=(V, A) \f$be a directed graph442 /// Let \f$ G=(V, A) \f$ be a directed graph 443 443 /// 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$be boolvalued functions resp.444 /// implements \f$ G \f$. 445 /// Let moreover \f$ b_V \f$ and \f$ b_A \f$ be boolvalued functions resp. 446 446 /// on the nodeset and edgeset. 447 447 /// SubGraphAdaptor<...>::NodeIt iterates 448 /// on the nodeset \f$ \{v\in V : b_V(v)=true\} \f$and448 /// on the nodeset \f$ \{v\in V : b_V(v)=true\} \f$ and 449 449 /// SubGraphAdaptor<...>::EdgeIt iterates 450 /// on the edgeset \f$ \{e\in A : b_A(e)=true\} \f$. Similarly,450 /// on the edgeset \f$ \{e\in A : b_A(e)=true\} \f$. Similarly, 451 451 /// SubGraphAdaptor<...>::OutEdgeIt and 452 452 /// SubGraphAdaptor<...>::InEdgeIt iterates … … 1050 1050 ///parts of the lib. Use them at you own risk. 1051 1051 /// 1052 /// Let \f$ G=(V, A) \f$be a directed graph and for each directed edge1053 /// \f$ e\in A \f$ , let \f$ \bar e \f$denote the edge obtained by1052 /// Let \f$ 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 1054 1054 /// reversing its orientation. We are given moreover two bool valued 1055 1055 /// maps on the edgeset, 1056 /// \f$ forward\_filter \f$ , and \f$ backward\_filter \f$.1056 ///\f$ forward\_filter \f$, and \f$ backward\_filter \f$. 1057 1057 /// SubBidirGraphAdaptor implements the graph structure with nodeset 1058 /// \f$ V \f$and edgeset1059 /// \f$ \{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 edgeset 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$. 1060 1060 /// The purpose of writing + instead of union is because parallel 1061 1061 /// edges can arise. (Similarly, antiparallel edges also can arise). … … 1186 1186 ///An adaptor for composing the residual graph for 1187 1187 ///directed flow and circulation problems. 1188 ///Let \f$ G=(V, A) \f$ be a directed graph and let \f$ F \f$be a1188 ///Let \f$ G=(V, A) \f$ be a directed graph and let \f$ F \f$ be a 1189 1189 ///number type. Let moreover 1190 /// \f$ f,c:A\to F \f$, be functions on the edgeset.1191 ///In the appications of ResGraphAdaptor, \f$ f \f$usually stands for a flow1192 ///and \f$ c \f$for a capacity function.1190 ///\f$ f,c:A\to F \f$, be functions on the edgeset. 1191 ///In the appications of ResGraphAdaptor, \f$ f \f$ usually stands for a flow 1192 ///and \f$ c \f$ for a capacity function. 1193 1193 ///Suppose that a graph instange \c g of type 1194 ///\c ListGraph implements \f$ G \f$.1194 ///\c ListGraph implements \f$ G \f$. 1195 1195 ///\code 1196 1196 /// ListGraph g; 1197 1197 ///\endcode 1198 1198 ///Then RevGraphAdaptor implements the graph structure with nodeset 1199 /// \f$ V \f$ and edgeset \f$ A_{forward}\cup A_{backward} \f$, where1200 /// \f$ A_{forward}=\{uv : uv\in A, f(uv)<c(uv)\} \f$and1201 /// \f$ A_{backward}=\{vu : uv\in A, f(uv)>0\} \f$,1199 ///\f$ V \f$ and edgeset \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$, 1202 1202 ///i.e. the so called residual graph. 1203 ///When we take the union \f$ A_{forward}\cup A_{backward} \f$,1203 ///When we take the union \f$ A_{forward}\cup A_{backward} \f$, 1204 1204 ///multilicities are counted, i.e. if an edge is in both 1205 /// \f$ A_{forward} \f$ and \f$ A_{backward} \f$, then in the adaptor it1205 ///\f$ A_{forward} \f$ and \f$ A_{backward} \f$, then in the adaptor it 1206 1206 ///appears twice. 1207 1207 ///The following code shows how
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