1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2006 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | ///\ingroup demos |
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20 | ///\file |
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21 | ///\brief Max flow problem solved with an LP solver (demo). |
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22 | /// |
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23 | /// This demo program shows how to solve a maximum (or maximal) flow |
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24 | /// problem using the LEMON LP solver interface. We would like to lay |
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25 | /// the emphasis on the simplicity of the way one can formulate LP |
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26 | /// constraints that arise in graph theory in our library LEMON . |
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27 | /// |
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28 | /// \include lp_maxflow_demo.cc |
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29 | |
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30 | #include<lemon/graph_reader.h> |
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31 | #include<lemon/list_graph.h> |
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32 | #include <lemon/lp.h> |
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33 | |
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34 | #include <fstream> |
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35 | #include <iostream> |
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36 | |
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37 | |
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38 | |
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39 | using namespace lemon; |
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40 | |
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41 | template<class G,class C> |
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42 | double maxFlow(const G &g,const C &cap,typename G::Node s,typename G::Node t) |
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43 | { |
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44 | Lp lp; |
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45 | |
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46 | typedef G Graph; |
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47 | typedef typename G::Node Node; |
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48 | typedef typename G::NodeIt NodeIt; |
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49 | typedef typename G::Edge Edge; |
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50 | typedef typename G::EdgeIt EdgeIt; |
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51 | typedef typename G::OutEdgeIt OutEdgeIt; |
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52 | typedef typename G::InEdgeIt InEdgeIt; |
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53 | |
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54 | //Define a map on the edges for the variables of the LP problem |
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55 | typename G::template EdgeMap<Lp::Col> x(g); |
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56 | lp.addColSet(x); |
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57 | |
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58 | //Nonnegativity and capacity constraints |
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59 | for(EdgeIt e(g);e!=INVALID;++e) { |
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60 | lp.colUpperBound(x[e],cap[e]); |
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61 | lp.colLowerBound(x[e],0); |
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62 | } |
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63 | |
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64 | |
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65 | //Flow conservation constraints for the nodes (except for 's' and 't') |
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66 | for(NodeIt n(g);n!=INVALID;++n) if(n!=s&&n!=t) { |
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67 | Lp::Expr ex; |
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68 | for(InEdgeIt e(g,n);e!=INVALID;++e) ex+=x[e]; |
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69 | for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e]; |
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70 | lp.addRow(ex==0); |
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71 | } |
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72 | |
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73 | //Objective function: the flow value entering 't' |
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74 | Lp::Expr obj; |
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75 | for(InEdgeIt e(g,t);e!=INVALID;++e) obj+=x[e]; |
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76 | for(OutEdgeIt e(g,t);e!=INVALID;++e) obj-=x[e]; |
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77 | lp.obj(obj); |
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78 | |
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79 | |
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80 | //Maximization |
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81 | lp.max(); |
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82 | |
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83 | #if DEFAULT_LP==GLPK |
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84 | lp.presolver(true); |
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85 | lp.messageLevel(3); |
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86 | #endif |
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87 | |
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88 | std::cout<<"Solver used: "<<default_solver_name<<std::endl; |
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89 | |
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90 | //Solve with the underlying solver |
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91 | lp.solve(); |
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92 | |
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93 | return lp.primalValue(); |
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94 | } |
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95 | |
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96 | int main(int argc, char *argv[]) |
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97 | { |
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98 | if(argc<2) |
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99 | { |
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100 | std::cerr << " USAGE: lp_maxflow_demo input_file.lgf" << std::endl; |
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101 | std::cerr << " The file 'input_file.lgf' has to contain a max " |
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102 | << "flow instance in\n" |
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103 | << " LEMON format (e.g. sample.lgf is such a file)." |
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104 | << std::endl; |
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105 | return 0; |
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106 | } |
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107 | |
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108 | |
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109 | //input stream to read the graph from |
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110 | std::ifstream is(argv[1]); |
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111 | |
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112 | |
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113 | ListGraph g; |
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114 | ListGraph::Node s; |
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115 | ListGraph::Node t; |
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116 | |
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117 | ListGraph::EdgeMap<double> cap(g); |
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118 | |
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119 | GraphReader<ListGraph> reader(is,g); |
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120 | reader.readNode("source",s).readNode("target",t) |
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121 | .readEdgeMap("capacity",cap).run(); |
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122 | |
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123 | std::cout << "Max flow value = " << maxFlow(g,cap,s,t) << std::endl; |
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124 | |
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125 | } |
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