lemon/circulation.h
branch1.1
changeset 761 f1398882a928
parent 690 1f08e846df29
child 793 8d2e55fac752
     1.1 --- a/lemon/circulation.h	Fri Aug 05 09:33:42 2011 +0200
     1.2 +++ b/lemon/circulation.h	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 @@ -59,8 +59,8 @@
    1.13  
    1.14      /// \brief The type of supply map.
    1.15      ///
    1.16 -    /// The type of the map that stores the signed supply values of the 
    1.17 -    /// nodes. 
    1.18 +    /// The type of the map that stores the signed supply values of the
    1.19 +    /// nodes.
    1.20      /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
    1.21      typedef SM SupplyMap;
    1.22  
    1.23 @@ -134,7 +134,7 @@
    1.24       \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu)
    1.25       \geq sup(u) \quad \forall u\in V, \f]
    1.26       \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A. \f]
    1.27 -     
    1.28 +
    1.29       The sum of the supply values, i.e. \f$\sum_{u\in V} sup(u)\f$ must be
    1.30       zero or negative in order to have a feasible solution (since the sum
    1.31       of the expressions on the left-hand side of the inequalities is zero).
    1.32 @@ -144,7 +144,7 @@
    1.33       If \f$\sum_{u\in V} sup(u)\f$ is zero, then all the supply/demand
    1.34       constraints have to be satisfied with equality, i.e. all demands
    1.35       have to be satisfied and all supplies have to be used.
    1.36 -     
    1.37 +
    1.38       If you need the opposite inequalities in the supply/demand constraints
    1.39       (i.e. the total demand is less than the total supply and all the demands
    1.40       have to be satisfied while there could be supplies that are not used),
    1.41 @@ -325,7 +325,7 @@
    1.42      ///
    1.43      /// \param graph The digraph the algorithm runs on.
    1.44      /// \param lower The lower bounds for the flow values on the arcs.
    1.45 -    /// \param upper The upper bounds (capacities) for the flow values 
    1.46 +    /// \param upper The upper bounds (capacities) for the flow values
    1.47      /// on the arcs.
    1.48      /// \param supply The signed supply values of the nodes.
    1.49      Circulation(const Digraph &graph, const LowerMap &lower,