diff --git a/lemon/circulation.h b/lemon/circulation.h --- a/lemon/circulation.h +++ b/lemon/circulation.h @@ -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). * @@ -59,8 +59,8 @@ /// \brief The type of supply map. /// - /// The type of the map that stores the signed supply values of the - /// nodes. + /// The type of the map that stores the signed supply values of the + /// nodes. /// It must conform to the \ref concepts::ReadMap "ReadMap" concept. typedef SM SupplyMap; @@ -134,7 +134,7 @@ \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \geq sup(u) \quad \forall u\in V, \f] \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A. \f] - + The sum of the supply values, i.e. \f$\sum_{u\in V} sup(u)\f$ must be zero or negative in order to have a feasible solution (since the sum of the expressions on the left-hand side of the inequalities is zero). @@ -144,7 +144,7 @@ If \f$\sum_{u\in V} sup(u)\f$ is zero, then all the supply/demand constraints have to be satisfied with equality, i.e. all demands have to be satisfied and all supplies have to be used. - + If you need the opposite inequalities in the supply/demand constraints (i.e. the total demand is less than the total supply and all the demands have to be satisfied while there could be supplies that are not used), @@ -325,7 +325,7 @@ /// /// \param graph The digraph the algorithm runs on. /// \param lower The lower bounds for the flow values on the arcs. - /// \param upper The upper bounds (capacities) for the flow values + /// \param upper The upper bounds (capacities) for the flow values /// on the arcs. /// \param supply The signed supply values of the nodes. Circulation(const Digraph &graph, const LowerMap &lower,