doc/min_cost_flow.dox
 branch 1.1 changeset 1081 f1398882a928 parent 710 8b0df68370a4
     1.1 --- a/doc/min_cost_flow.dox	Fri Aug 05 09:33:42 2011 +0200
1.2 +++ b/doc/min_cost_flow.dox	Mon Aug 08 12:36:16 2011 +0200
1.3 @@ -2,7 +2,7 @@
1.4   *
1.5   * This file is a part of LEMON, a generic C++ optimization library.
1.6   *
1.7 - * Copyright (C) 2003-2009
1.8 + * Copyright (C) 2003-2011
1.9   * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.10   * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.11   *
1.12 @@ -81,7 +81,7 @@
1.13     - \f$\pi(u)<=0\f$;
1.14     - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$,
1.15       then \f$\pi(u)=0\f$.
1.16 -
1.17 +
1.18  Here \f$cost^\pi(uv)\f$ denotes the \e reduced \e cost of the arc
1.19  \f$uv\in A\f$ with respect to the potential function \f$\pi\f$, i.e.
1.20  \f[ cost^\pi(uv) = cost(uv) + \pi(u) - \pi(v).\f]
1.21 @@ -119,7 +119,7 @@
1.22      sup(u) \quad \forall u\in V \f]
1.23  \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f]
1.24
1.25 -It means that the total demand must be less or equal to the
1.26 +It means that the total demand must be less or equal to the
1.27  total supply (i.e. \f$\sum_{u\in V} sup(u)\f$ must be zero or
1.28  positive) and all the demands have to be satisfied, but there
1.29  could be supplies that are not carried out from the supply