1.1 --- a/doc/min_cost_flow.dox Sun Oct 04 10:15:32 2009 +0200
1.2 +++ b/doc/min_cost_flow.dox Wed Dec 09 11:14:06 2009 +0100
1.3 @@ -26,7 +26,7 @@
1.4 The \e minimum \e cost \e flow \e problem is to find a feasible flow of
1.5 minimum total cost from a set of supply nodes to a set of demand nodes
1.6 in a network with capacity constraints (lower and upper bounds)
1.7 -and arc costs.
1.8 +and arc costs \ref amo93networkflows.
1.9
1.10 Formally, let \f$G=(V,A)\f$ be a digraph, \f$lower: A\rightarrow\mathbf{R}\f$,
1.11 \f$upper: A\rightarrow\mathbf{R}\cup\{+\infty\}\f$ denote the lower and
1.12 @@ -78,7 +78,7 @@
1.13 - if \f$lower(uv)<f(uv)<upper(uv)\f$, then \f$cost^\pi(uv)=0\f$;
1.14 - if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$.
1.15 - For all \f$u\in V\f$ nodes:
1.16 - - \f$\pi(u)<=0\f$;
1.17 + - \f$\pi(u)\leq 0\f$;
1.18 - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$,
1.19 then \f$\pi(u)=0\f$.
1.20
1.21 @@ -145,7 +145,7 @@
1.22 - if \f$lower(uv)<f(uv)<upper(uv)\f$, then \f$cost^\pi(uv)=0\f$;
1.23 - if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$.
1.24 - For all \f$u\in V\f$ nodes:
1.25 - - \f$\pi(u)>=0\f$;
1.26 + - \f$\pi(u)\geq 0\f$;
1.27 - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$,
1.28 then \f$\pi(u)=0\f$.
1.29