doc/min_cost_flow.dox
changeset 869 1b89e29c9fc7
parent 802 134852d7fb0a
parent 833 e20173729589
child 956 141f9c0db4a3
     1.1 --- a/doc/min_cost_flow.dox	Thu Dec 10 17:05:35 2009 +0100
     1.2 +++ b/doc/min_cost_flow.dox	Thu Dec 10 17:18:25 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