Changes in doc/min_cost_flow.dox [663:8b0df68370a4:877:141f9c0db4a3] in lemon1.2
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doc/min_cost_flow.dox
r663 r877 3 3 * This file is a part of LEMON, a generic C++ optimization library. 4 4 * 5 * Copyright (C) 200320 095 * Copyright (C) 20032010 6 6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport 7 7 * (Egervary Research Group on Combinatorial Optimization, EGRES). … … 27 27 minimum total cost from a set of supply nodes to a set of demand nodes 28 28 in a network with capacity constraints (lower and upper bounds) 29 and arc costs .29 and arc costs \ref amo93networkflows. 30 30 31 31 Formally, let \f$G=(V,A)\f$ be a digraph, \f$lower: A\rightarrow\mathbf{R}\f$, … … 79 79  if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$. 80 80  For all \f$u\in V\f$ nodes: 81  \f$\pi(u) <=0\f$;81  \f$\pi(u)\leq 0\f$; 82 82  if \f$\sum_{uv\in A} f(uv)  \sum_{vu\in A} f(vu) \neq sup(u)\f$, 83 83 then \f$\pi(u)=0\f$. 84 84 85 85 Here \f$cost^\pi(uv)\f$ denotes the \e reduced \e cost of the arc 86 86 \f$uv\in A\f$ with respect to the potential function \f$\pi\f$, i.e. … … 120 120 \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f] 121 121 122 It means that the total demand must be less or equal to the 122 It means that the total demand must be less or equal to the 123 123 total supply (i.e. \f$\sum_{u\in V} sup(u)\f$ must be zero or 124 124 positive) and all the demands have to be satisfied, but there … … 146 146  if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$. 147 147  For all \f$u\in V\f$ nodes: 148  \f$\pi(u) >=0\f$;148  \f$\pi(u)\geq 0\f$; 149 149  if \f$\sum_{uv\in A} f(uv)  \sum_{vu\in A} f(vu) \neq sup(u)\f$, 150 150 then \f$\pi(u)=0\f$.
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