diff --git a/doc/min_cost_flow.dox b/doc/min_cost_flow.dox --- a/doc/min_cost_flow.dox +++ b/doc/min_cost_flow.dox @@ -2,7 +2,7 @@ * * This file is a part of LEMON, a generic C++ optimization library. * - * Copyright (C) 2003-2009 + * Copyright (C) 2003-2011 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport * (Egervary Research Group on Combinatorial Optimization, EGRES). * @@ -81,7 +81,7 @@ - \f$\pi(u)<=0\f$; - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$, then \f$\pi(u)=0\f$. - + Here \f$cost^\pi(uv)\f$ denotes the \e reduced \e cost of the arc \f$uv\in A\f$ with respect to the potential function \f$\pi\f$, i.e. \f[ cost^\pi(uv) = cost(uv) + \pi(u) - \pi(v).\f] @@ -119,7 +119,7 @@ sup(u) \quad \forall u\in V \f] \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f] -It means that the total demand must be less or equal to the +It means that the total demand must be less or equal to the total supply (i.e. \f$\sum_{u\in V} sup(u)\f$ must be zero or positive) and all the demands have to be satisfied, but there could be supplies that are not carried out from the supply