[1560] | 1 | /* -*- C++ -*- |
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| 2 | * demo/lp_maxflow_demo.cc - Part of LEMON, a generic C++ optimization library |
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| 3 | * |
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| 4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 6 | * |
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| 7 | * Permission to use, modify and distribute this software is granted |
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| 8 | * provided that this copyright notice appears in all copies. For |
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| 9 | * precise terms see the accompanying LICENSE file. |
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| 10 | * |
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| 11 | * This software is provided "AS IS" with no warranty of any kind, |
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| 12 | * express or implied, and with no claim as to its suitability for any |
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| 13 | * purpose. |
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| 14 | * |
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| 15 | */ |
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| 16 | |
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| 17 | ///\ingroup demos |
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| 18 | ///\file |
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| 19 | ///\brief Max flow problem solved with an LP solver (demo). |
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| 20 | /// |
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[1583] | 21 | /// This demo program shows how to solve a maximum (or maximal) flow |
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| 22 | /// problem using the LEMON LP solver interface. We would like to lay |
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| 23 | /// the emphasis on the simplicity of the way one can formulate LP |
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| 24 | /// constraints that arise in graph theory in our library LEMON . |
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[1641] | 25 | /// |
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| 26 | /// \include lp_maxflow_demo.cc |
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[1560] | 27 | |
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[1361] | 28 | #include<lemon/graph_reader.h> |
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| 29 | #include<lemon/list_graph.h> |
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[1610] | 30 | #include <lemon/lp.h> |
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[1361] | 31 | |
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[1560] | 32 | #include <fstream> |
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| 33 | #include <iostream> |
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| 34 | |
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[1381] | 35 | |
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| 36 | |
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[1361] | 37 | using namespace lemon; |
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| 38 | |
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| 39 | template<class G,class C> |
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| 40 | double maxFlow(const G &g,const C &cap,typename G::Node s,typename G::Node t) |
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| 41 | { |
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[1610] | 42 | Lp lp; |
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[1361] | 43 | |
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| 44 | typedef G Graph; |
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| 45 | typedef typename G::Node Node; |
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| 46 | typedef typename G::NodeIt NodeIt; |
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| 47 | typedef typename G::Edge Edge; |
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| 48 | typedef typename G::EdgeIt EdgeIt; |
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| 49 | typedef typename G::OutEdgeIt OutEdgeIt; |
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| 50 | typedef typename G::InEdgeIt InEdgeIt; |
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| 51 | |
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[1518] | 52 | //Define a map on the edges for the variables of the LP problem |
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[1610] | 53 | typename G::template EdgeMap<Lp::Col> x(g); |
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[1361] | 54 | lp.addColSet(x); |
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| 55 | |
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[1518] | 56 | //Nonnegativity and capacity constraints |
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[1361] | 57 | for(EdgeIt e(g);e!=INVALID;++e) { |
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| 58 | lp.colUpperBound(x[e],cap[e]); |
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| 59 | lp.colLowerBound(x[e],0); |
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| 60 | } |
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| 61 | |
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[1518] | 62 | |
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| 63 | //Flow conservation constraints for the nodes (except for 's' and 't') |
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[1361] | 64 | for(NodeIt n(g);n!=INVALID;++n) if(n!=s&&n!=t) { |
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[1610] | 65 | Lp::Expr ex; |
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[1361] | 66 | for(InEdgeIt e(g,n);e!=INVALID;++e) ex+=x[e]; |
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| 67 | for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e]; |
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| 68 | lp.addRow(ex==0); |
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| 69 | } |
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[1518] | 70 | |
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| 71 | //Objective function: the flow value entering 't' |
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[1610] | 72 | Lp::Expr obj; |
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[1571] | 73 | for(InEdgeIt e(g,t);e!=INVALID;++e) obj+=x[e]; |
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| 74 | for(OutEdgeIt e(g,t);e!=INVALID;++e) obj-=x[e]; |
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| 75 | lp.setObj(obj); |
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| 76 | |
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[1518] | 77 | |
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| 78 | //Maximization |
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[1361] | 79 | lp.max(); |
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| 80 | |
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[1610] | 81 | #if DEFAULT_LP==GLPK |
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[1361] | 82 | lp.presolver(true); |
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| 83 | lp.messageLevel(3); |
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[1381] | 84 | #endif |
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[1361] | 85 | |
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[1577] | 86 | std::cout<<"Solver used: "<<default_solver_name<<std::endl; |
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| 87 | |
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[1518] | 88 | //Solve with the underlying solver |
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[1361] | 89 | lp.solve(); |
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| 90 | |
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| 91 | return lp.primalValue(); |
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| 92 | } |
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| 93 | |
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[1560] | 94 | int main(int argc, char *argv[]) |
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[1361] | 95 | { |
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[1560] | 96 | if(argc<2) |
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| 97 | { |
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[1577] | 98 | std::cerr << " USAGE: lp_maxflow_demo input_file.lgf" << std::endl; |
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[1561] | 99 | std::cerr << " The file 'input_file.lgf' has to contain a max " |
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| 100 | << "flow instance in\n" |
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| 101 | << " LEMON format (e.g. sample.lgf is such a file)." |
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| 102 | << std::endl; |
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[1560] | 103 | return 0; |
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| 104 | } |
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| 105 | |
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| 106 | |
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| 107 | //input stream to read the graph from |
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| 108 | std::ifstream is(argv[1]); |
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| 109 | |
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| 110 | |
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[1361] | 111 | ListGraph g; |
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| 112 | ListGraph::Node s; |
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| 113 | ListGraph::Node t; |
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| 114 | |
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| 115 | ListGraph::EdgeMap<double> cap(g); |
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| 116 | |
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[1560] | 117 | GraphReader<ListGraph> reader(is,g); |
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[1394] | 118 | reader.readNode("source",s).readNode("target",t) |
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| 119 | .readEdgeMap("capacity",cap).run(); |
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[1361] | 120 | |
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| 121 | std::cout << "Max flow value = " << maxFlow(g,cap,s,t) << std::endl; |
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| 122 | |
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| 123 | } |
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