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76 - For all \f$uv\in A\f$ arcs: |
76 - For all \f$uv\in A\f$ arcs: |
77 - if \f$cost^\pi(uv)>0\f$, then \f$f(uv)=lower(uv)\f$; |
77 - if \f$cost^\pi(uv)>0\f$, then \f$f(uv)=lower(uv)\f$; |
78 - if \f$lower(uv)<f(uv)<upper(uv)\f$, then \f$cost^\pi(uv)=0\f$; |
78 - if \f$lower(uv)<f(uv)<upper(uv)\f$, then \f$cost^\pi(uv)=0\f$; |
79 - if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$. |
79 - if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$. |
80 - For all \f$u\in V\f$ nodes: |
80 - For all \f$u\in V\f$ nodes: |
81 - \f$\pi(u)<=0\f$; |
81 - \f$\pi(u)\leq 0\f$; |
82 - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$, |
82 - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$, |
83 then \f$\pi(u)=0\f$. |
83 then \f$\pi(u)=0\f$. |
84 |
84 |
85 Here \f$cost^\pi(uv)\f$ denotes the \e reduced \e cost of the arc |
85 Here \f$cost^\pi(uv)\f$ denotes the \e reduced \e cost of the arc |
86 \f$uv\in A\f$ with respect to the potential function \f$\pi\f$, i.e. |
86 \f$uv\in A\f$ with respect to the potential function \f$\pi\f$, i.e. |
143 - For all \f$uv\in A\f$ arcs: |
143 - For all \f$uv\in A\f$ arcs: |
144 - if \f$cost^\pi(uv)>0\f$, then \f$f(uv)=lower(uv)\f$; |
144 - if \f$cost^\pi(uv)>0\f$, then \f$f(uv)=lower(uv)\f$; |
145 - if \f$lower(uv)<f(uv)<upper(uv)\f$, then \f$cost^\pi(uv)=0\f$; |
145 - if \f$lower(uv)<f(uv)<upper(uv)\f$, then \f$cost^\pi(uv)=0\f$; |
146 - if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$. |
146 - if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$. |
147 - For all \f$u\in V\f$ nodes: |
147 - For all \f$u\in V\f$ nodes: |
148 - \f$\pi(u)>=0\f$; |
148 - \f$\pi(u)\geq 0\f$; |
149 - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$, |
149 - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$, |
150 then \f$\pi(u)=0\f$. |
150 then \f$\pi(u)=0\f$. |
151 |
151 |
152 */ |
152 */ |
153 } |
153 } |