16 graphs then you might find it useful to use our library LEMON. LEMON |
16 graphs then you might find it useful to use our library LEMON. LEMON |
17 defines various graph concepts depending on what you want to do with the |
17 defines various graph concepts depending on what you want to do with the |
18 graph: a very good description can be found in the page |
18 graph: a very good description can be found in the page |
19 about \ref graphs "graphs". |
19 about \ref graphs "graphs". |
20 |
20 |
21 You will also want to assign data to the edges or nodes of the graph, for example a length or capacity function defined on the edges. You can do this in LEMON using so called \ref maps "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". |
21 You will also want to assign data to the edges or nodes of the graph, for |
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22 example a length or capacity function defined on the edges. You can do this in |
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23 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". |
22 |
24 |
23 Some examples are the following (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 getsart How to start using LEMON): |
25 Some examples are the following (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 getsart How to start using LEMON): |
24 |
26 |
25 - First we give two examples that show how to instantiate a graph. The |
27 <ul> |
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28 <li> First we give two examples that show how to instantiate a graph. The |
26 first one shows the methods that add nodes and edges, but one will |
29 first one shows the methods that add nodes and edges, but one will |
27 usually use the second way which reads a graph from a stream (file). |
30 usually use the second way which reads a graph from a stream (file). |
28 -# The following code fragment shows how to fill a graph with data. It creates a complete graph on 4 nodes. The type Listgraph is one of the LEMON graph types: the typedefs in the beginning are for convenience and we will suppose them later as well. |
31 <ol> |
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32 <li>The following code fragment shows how to fill a graph with data. It creates a complete graph on 4 nodes. The type Listgraph is one of the LEMON graph types: the typedefs in the beginning are for convenience and we will suppose them later as well. |
29 \code |
33 \code |
30 typedef ListGraph Graph; |
34 typedef ListGraph Graph; |
31 typedef Graph::NodeIt NodeIt; |
35 typedef Graph::NodeIt NodeIt; |
32 |
36 |
33 Graph g; |
37 Graph g; |
40 if (i != j) g.addEdge(i, j); |
44 if (i != j) g.addEdge(i, j); |
41 \endcode |
45 \endcode |
42 |
46 |
43 See the whole program in file \ref helloworld.cc. |
47 See the whole program in file \ref helloworld.cc. |
44 |
48 |
45 If you want to read more on the LEMON graph structures and concepts, read the page about \ref graphs "graphs". |
49 If you want to read more on the LEMON graph structures and concepts, read the page about \ref graphs "graphs". |
46 |
50 |
47 -# The following code shows how to read a graph from a stream (e.g. a file). LEMON supports the DIMACS file format: it can read a graph instance from a file |
51 <li> The following code shows how to read a graph from a stream (e.g. a file). LEMON supports the DIMACS file format: it can read a graph instance from a file |
48 in that format (find the documentation of the DIMACS file format on the web). |
52 in that format (find the documentation of the DIMACS file format on the web). |
49 \code |
53 \code |
50 Graph g; |
54 Graph g; |
51 std::ifstream f("graph.dim"); |
55 std::ifstream f("graph.dim"); |
52 readDimacs(f, g); |
56 readDimacs(f, g); |
53 \endcode |
57 \endcode |
54 One can also store network (graph+capacity on the edges) instances and other things in DIMACS format and use these in LEMON: to see the details read the documentation of the \ref dimacs.h "Dimacs file format reader". |
58 One can also store network (graph+capacity on the edges) instances and other things in DIMACS format and use these in LEMON: to see the details read the documentation of the \ref dimacs.h "Dimacs file format reader". |
55 |
59 |
56 |
60 </ol> |
57 - If you want to solve some transportation problems in a network then |
61 <li> If you want to solve some transportation problems in a network then |
58 you will want to find shortest paths between nodes of a graph. This is |
62 you will want to find shortest paths between nodes of a graph. This is |
59 usually solved using Dijkstra's algorithm. A utility |
63 usually solved using Dijkstra's algorithm. A utility |
60 that solves this is the \ref lemon::Dijkstra "LEMON Dijkstra class". |
64 that solves this is the \ref lemon::Dijkstra "LEMON Dijkstra class". |
61 The following code is a simple program using the \ref lemon::Dijkstra "LEMON |
65 The following code is a simple program using the \ref lemon::Dijkstra "LEMON |
62 Dijkstra class" and it also shows how to define a map on the edges (the length |
66 Dijkstra class" and it also shows how to define a map on the edges (the length |
127 results. |
131 results. |
128 You can do much more with the Dijkstra class, for example you can run it step |
132 You can do much more with the Dijkstra class, for example you can run it step |
129 by step and gain full control of the execution. For a detailed description, see the documentation of the \ref lemon::Dijkstra "LEMON Dijkstra class". |
133 by step and gain full control of the execution. For a detailed description, see the documentation of the \ref lemon::Dijkstra "LEMON Dijkstra class". |
130 |
134 |
131 |
135 |
132 - If you want to design a network and want to minimize the total length |
136 <li> If you want to design a network and want to minimize the total length |
133 of wires then you might be looking for a <b>minimum spanning tree</b> in |
137 of wires then you might be looking for a <b>minimum spanning tree</b> in |
134 an undirected graph. This can be found using the Kruskal algorithm: the |
138 an undirected graph. This can be found using the Kruskal algorithm: the |
135 class \ref lemon::Kruskal "LEMON Kruskal class" does this job for you. |
139 class \ref lemon::Kruskal "LEMON Kruskal class" does this job for you. |
136 The following code fragment shows an example: |
140 The following code fragment shows an example: |
137 |
141 |
138 Ide Zsuzska fog irni! |
142 Ide Zsuzska fog irni! |
139 |
143 |
140 - |
144 <li>Many problems in network optimization can be formalized by means of a |
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145 linear programming problem (LP problem, for short). In our library we decided |
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146 not to write an LP solver, since such packages are available in the commercial |
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147 world just as well as in the open source world, and it is also a difficult |
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148 task to compete these. Instead we decided to develop an interface that makes |
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149 it easier to use these solvers together with LEMON. So far we have an |
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150 interface for the commercial LP solver software \b CLPLEX (developed by ILOG) |
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151 and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming |
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152 Toolkit). |
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153 |
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154 We will show two examples, the first one shows how simple it is to formalize |
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155 and solve an LP problem in LEMON, while the second one shows how LEMON |
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156 facilitates solving network optimization problems using LP solvers. |
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157 |
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158 <ol> |
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159 <li>The following code shows how to solve an LP problem using the LEMON lp |
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160 interface. |
141 |
161 |
142 \code |
162 \code |
143 |
163 |
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164 //A default solver is taken |
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165 LpDefault lp; |
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166 typedef LpDefault::Row Row; |
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167 typedef LpDefault::Col Col; |
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168 |
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169 |
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170 //This will be a maximization |
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171 lp.max(); |
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172 |
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173 //We add coloumns (variables) to our problem |
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174 Col x1 = lp.addCol(); |
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175 Col x2 = lp.addCol(); |
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176 Col x3 = lp.addCol(); |
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177 |
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178 //Constraints |
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179 lp.addRow(x1+x2+x3 <=100); |
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180 lp.addRow(10*x1+4*x2+5*x3<=600); |
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181 lp.addRow(2*x1+2*x2+6*x3<=300); |
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182 //Nonnegativity of the variables |
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183 lp.colLowerBound(x1, 0); |
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184 lp.colLowerBound(x2, 0); |
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185 lp.colLowerBound(x3, 0); |
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186 //Objective function |
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187 lp.setObj(10*x1+6*x2+4*x3); |
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188 |
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189 //Call the routine of the underlying LP solver |
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190 lp.solve(); |
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191 |
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192 //Print results |
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193 if (lp.primalStatus()==LpSolverBase::OPTIMAL){ |
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194 printf("Z = %g; x1 = %g; x2 = %g; x3 = %g\n", |
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195 lp.primalValue(), |
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196 lp.primal(x1), lp.primal(x2), lp.primal(x3)); |
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197 } |
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198 else{ |
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199 std::cout<<"Optimal solution not found!"<<std::endl; |
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200 } |
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201 |
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202 |
144 \endcode |
203 \endcode |
145 |
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 network |
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208 optimization problem as an LP problem using the LEMON LP interface. |
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209 |
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210 </ol> |
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211 </ul> |
146 |
212 |
147 */ |
213 */ |