1 | /** |
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2 | |
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3 | \page quicktour Quick Tour to LEMON |
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4 | |
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5 | Let us first answer the question <b>"What do I want to use LEMON for?"</b>. |
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6 | LEMON is a C++ library, so you can use it if you want to write C++ |
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7 | programs. What kind of tasks does the library LEMON help to solve? |
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8 | It helps to write programs that solve optimization problems that arise |
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9 | frequently when <b>designing and testing certain networks</b>, for example |
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10 | in telecommunication, computer networks, and other areas that I cannot |
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11 | think of now. A very natural way of modelling these networks is by means |
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12 | of a <b> graph</b> (we will always mean a directed graph by that and say |
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13 | <b> undirected graph </b> otherwise). |
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14 | So if you want to write a program that works with |
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15 | graphs then you might find it useful to use our library LEMON. LEMON |
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16 | defines various graph concepts depending on what you want to do with the |
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17 | graph: a very good description can be found in the page |
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18 | about \ref graphs "graphs". |
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19 | |
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20 | You will also want to assign data to the edges or nodes of the graph, for |
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21 | example a length or capacity function defined on the edges. You can do this in |
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22 | LEMON using so called \b maps. You can define a map on the nodes or on the edges of the graph and the value of the map (the range of the function) can be practically almost of any type. Read more about maps \ref maps-page "here". |
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23 | |
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24 | In this quick tour we want to show you some facilities LEMON library can provide through examples (simple demo programs). The examples will only show part of the functionality, but links will always be given to reach complete details. |
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25 | You will find links next to the code fragments that help to download full demo programs: save them on your computer and compile them according to the description in the page about \ref getstart "How to start using LEMON". |
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26 | |
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27 | Have fun! |
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28 | |
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29 | <ul> <li> The first thing to discuss is the way one can create data structures |
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30 | like graphs and maps in a program using LEMON. |
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31 | //There are more graph types |
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32 | //implemented in LEMON and you can implement your own graph type just as well: |
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33 | //read more about this in the already mentioned page on \ref graphs "graphs". |
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34 | |
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35 | First we show how to add nodes and edges to a graph manually. We will also |
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36 | define a map on the edges of the graph. After this we show the way one can |
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37 | read a graph (and perhaps maps on it) from a stream (e.g. a file). Of course |
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38 | we also have routines that write a graph (and perhaps maps) to a stream |
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39 | (file): this will also be shown. LEMON supports the DIMACS file formats to |
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40 | read network optimization problems, but more importantly we also have our own |
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41 | file format that gives a more flexible way to store data related to network |
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42 | optimization. |
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43 | |
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44 | <ol> <li>The following code shows how to build a graph from scratch |
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45 | and iterate on its nodes and edges. This example also shows how to |
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46 | give a map on the edges of the graph. The type Listgraph is one of |
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47 | the LEMON graph types: the typedefs in the beginning are for |
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48 | convenience and we will assume them later as well. |
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49 | |
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50 | \include hello_lemon.cc |
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51 | |
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52 | See the whole program in file \ref hello_lemon.cc in the \c demo subdir of |
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53 | LEMON package. |
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54 | |
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55 | If you want to read more on the LEMON graph structures and |
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56 | concepts, read the page about \ref graphs "graphs". |
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57 | |
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58 | |
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59 | <li>LEMON has an own file format for storing graphs, maps on edges/nodes and some other things. Instead of any explanation let us give a |
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60 | short example file in this format: read the detailed description of the LEMON |
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61 | graph file format and input-output routines here: \ref graph-io-page. |
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62 | |
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63 | So here is a file describing a graph of 6 nodes (0 to 5), two nodemaps |
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64 | (called \c coordinates_x and \c coordinates_y), several edges, an edge map |
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65 | called \c capacity and two designated nodes (called \c source and \c target). |
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66 | |
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67 | \verbatim |
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68 | @nodeset |
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69 | id coordinates_x coordinates_y |
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70 | 5 796.398 208.035 |
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71 | 4 573.002 63.002 |
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72 | 3 568.549 401.748 |
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73 | 2 277.889 68.476 |
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74 | 1 288.248 397.327 |
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75 | 0 102.239 257.532 |
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76 | @edgeset |
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77 | id capacity |
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78 | 4 5 6 8 |
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79 | 3 5 5 8 |
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80 | 2 4 4 5 |
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81 | 1 4 3 8 |
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82 | 1 3 2 5 |
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83 | 0 2 1 10 |
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84 | 0 1 0 10 |
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85 | #This is a comment here |
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86 | @nodes |
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87 | source 0 |
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88 | target 5 |
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89 | @edges |
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90 | @attributes |
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91 | author "Attila BERNATH" |
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92 | @end |
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93 | \endverbatim |
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94 | |
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95 | Finally let us give a simple example that reads a graph from a file and writes |
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96 | it to the standard output. |
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97 | |
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98 | \include reader_writer_demo.cc |
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99 | |
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100 | See the whole program in file \ref reader_writer_demo.cc. |
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101 | |
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102 | <li> The following code shows how to read a graph from a stream |
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103 | (e.g. a file) in the DIMACS file format (find the documentation of the |
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104 | DIMACS file formats on the web). |
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105 | |
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106 | \code |
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107 | Graph g; |
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108 | std::ifstream f("graph.dim"); |
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109 | readDimacs(f, g); |
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110 | \endcode |
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111 | |
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112 | One can also store network (graph+capacity on the edges) instances and |
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113 | other things (minimum cost flow instances etc.) in DIMACS format and |
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114 | read these in LEMON: to see the details read the documentation of the |
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115 | \ref dimacs.h "Dimacs file format reader". |
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116 | |
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117 | </ol> |
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118 | <li> If you want to solve some transportation problems in a network then |
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119 | you will want to find shortest paths between nodes of a graph. This is |
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120 | usually solved using Dijkstra's algorithm. A utility |
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121 | that solves this is the \ref lemon::Dijkstra "LEMON Dijkstra class". |
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122 | The following code is a simple program using the |
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123 | \ref lemon::Dijkstra "LEMON Dijkstra class": it calculates the shortest path between node \c s and \c t in a graph \c g. |
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124 | We omit the part reading the graph \c g and the length map \c len. |
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125 | |
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126 | \dontinclude dijkstra_demo.cc |
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127 | \skip ListGraph |
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128 | \until Graph g |
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129 | ... |
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130 | \skip Dijkstra algorithm |
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131 | \until std::cout << g.id(s) |
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132 | |
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133 | See the whole program in \ref dijkstra_demo.cc. |
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134 | |
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135 | Some explanation: after instantiating a member of the Dijkstra class |
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136 | we run the Dijkstra algorithm from node \c s. After this we read some |
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137 | of the results. You can do much more with the Dijkstra class, for |
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138 | example you can run it step by step and gain full control of the |
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139 | execution. For a detailed description, see the documentation of the |
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140 | \ref lemon::Dijkstra "LEMON Dijkstra class". |
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141 | |
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142 | |
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143 | <li> If you want to design a network and want to minimize the total |
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144 | length of wires then you might be looking for a <b>minimum spanning |
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145 | tree</b> in an undirected graph. This can be found using the Kruskal |
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146 | algorithm: the function \ref lemon::kruskal "LEMON Kruskal " does |
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147 | this job for you. After we had a graph \c g and a cost map \c |
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148 | edge_cost_map , the following code fragment shows an example how to get weight of the minmum spanning tree (in this first example the costs are uniform; this is of course not the case in real life applications): |
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149 | |
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150 | \dontinclude kruskal_demo.cc |
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151 | \skip std::cout |
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152 | \until kruskal |
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153 | |
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154 | In the variable \c tree_map the function gives back an edge bool map, which contains the edges of the found tree. |
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155 | |
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156 | If the costs are non-uniform, for example the cost is given by \c |
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157 | edge_cost_map_2 , or the edges of the tree have to be given in a |
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158 | vector, then we can give to the kruskal a vector \c tree_edge_vec , instead of |
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159 | an edge bool map: |
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160 | |
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161 | \skip edge_cost_map_2 |
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162 | \until edge_cost_map_2, std::back_inserter |
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163 | |
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164 | And finally the next fragment shows how to use the functions \c makeKruskalMapInput and \c makeKruskalSequenceOutPut: |
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165 | |
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166 | \skip makeKruskalSequenceOutput |
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167 | \until tree_edge_vec |
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168 | |
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169 | See the whole program in \ref kruskal_demo.cc. |
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170 | |
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171 | |
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172 | |
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173 | <li>Many problems in network optimization can be formalized by means |
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174 | of a linear programming problem (LP problem, for short). In our |
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175 | library we decided not to write an LP solver, since such packages are |
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176 | available in the commercial world just as well as in the open source |
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177 | world, and it is also a difficult task to compete these. Instead we |
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178 | decided to develop an interface that makes it easier to use these |
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179 | solvers together with LEMON. The advantage of this approach is |
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180 | twofold. Firstly our C++ interface is more comfortable than the |
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181 | solvers' native interface. Secondly, changing the underlying solver in |
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182 | a certain software using LEMON's LP interface needs zero effort. So, |
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183 | for example, one may try his idea using a free solver, demonstrate its |
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184 | usability for a customer and if it works well, but the performance |
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185 | should be improved, then one may decide to purchase and use a better |
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186 | commercial solver. |
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187 | |
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188 | So far we have an |
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189 | interface for the commercial LP solver software \b CPLEX (developed by ILOG) |
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190 | and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming |
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191 | Toolkit). |
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192 | |
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193 | We will show two examples, the first one shows how simple it is to formalize |
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194 | and solve an LP problem in LEMON, while the second one shows how LEMON |
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195 | facilitates solving network optimization problems using LP solvers. |
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196 | |
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197 | <ol> |
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198 | <li>The following code shows how to solve an LP problem using the LEMON lp |
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199 | interface. The code together with the comments is self-explanatory. |
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200 | |
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201 | \dontinclude lp_demo.cc |
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202 | \skip A default solver is taken |
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203 | \until End of LEMON style code |
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204 | |
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205 | See the whole code in \ref lp_demo.cc. |
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206 | |
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207 | <li>The second example shows how easy it is to formalize a max-flow |
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208 | problem as an LP problem using the LEMON LP interface: we are looking |
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209 | for a real valued function defined on the edges of the digraph |
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210 | satisfying the nonnegativity-, the capacity constraints and the |
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211 | flow-conservation constraints and giving the largest flow value |
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212 | between to designated nodes. |
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213 | |
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214 | In the following code we suppose that we already have the graph \c g, |
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215 | the capacity map \c cap, the source node \c s and the target node \c t |
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216 | in the memory. We will also omit the typedefs. |
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217 | |
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218 | \dontinclude lp_maxflow_demo.cc |
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219 | \skip Define a map on the edges for the variables of the LP problem |
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220 | \until lp.max(); |
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221 | \skip Solve with the underlying solver |
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222 | \until lp.solve(); |
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223 | |
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224 | |
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225 | The complete program can be found in file \ref lp_maxflow_demo.cc. After compiling run it in the form: |
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226 | |
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227 | <tt>./lp_maxflow_demo < sample.lgf</tt> |
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228 | |
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229 | where sample.lgf is a file in the lemon format containing a maxflow instance (designated "source", "target" nodes and "capacity" map on the edges). |
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230 | |
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231 | |
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232 | |
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233 | </ol> |
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234 | </ul> |
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235 | |
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236 | */ |
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