COIN-OR::LEMON - Graph Library

source: lemon-0.x/doc/quicktour.dox @ 1521:5815b382421b

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1/**
2
3\page quicktour Quick Tour to LEMON
4
5Let us first answer the question <b>"What do I want to use LEMON for?"
6</b>.
7LEMON is a C++ library, so you can use it if you want to write C++
8programs. What kind of tasks does the library LEMON help to solve?
9It helps to write programs that solve optimization problems that arise
10frequently when <b>designing and testing certain networks</b>, for example
11in telecommunication, computer networks, and other areas that I cannot
12think of now. A very natural way of modelling these networks is by means
13of a <b> graph</b> (we will always mean a directed graph by that and say
14<b> undirected graph </b> otherwise).
15So if you want to write a program that works with
16graphs then you might find it useful to use our library LEMON. LEMON
17defines various graph concepts depending on what you want to do with the
18graph: a very good description can be found in the page
19about \ref graphs "graphs".
20
21You will also want to assign data to the edges or nodes of the graph, for
22example a length or capacity function defined on the edges. You can do this in
23LEMON 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".
24
25Some 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):
26
27<ul>
28<li> First we give two examples that show how to instantiate a graph. The
29first one shows the methods that add nodes and edges, but one will
30usually use the second way which reads a graph from a stream (file).
31<ol>
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.
33 \code
34  typedef ListGraph Graph;
35  typedef Graph::NodeIt NodeIt;
36
37  Graph g;
38 
39  for (int i = 0; i < 3; i++)
40    g.addNode();
41 
42  for (NodeIt i(g); i!=INVALID; ++i)
43    for (NodeIt j(g); j!=INVALID; ++j)
44      if (i != j) g.addEdge(i, j);
45 \endcode
46
47See the whole program in file \ref helloworld.cc.
48
49    If you want to read more on the LEMON graph structures and concepts, read the page about \ref graphs "graphs".
50
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
52in that format (find the documentation of the DIMACS file format on the web).
53\code
54Graph g;
55std::ifstream f("graph.dim");
56readDimacs(f, g);
57\endcode
58One 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".
59
60</ol>
61<li> If you want to solve some transportation problems in a network then
62you will want to find shortest paths between nodes of a graph. This is
63usually solved using Dijkstra's algorithm. A utility
64that solves this is  the \ref lemon::Dijkstra "LEMON Dijkstra class".
65The following code is a simple program using the \ref lemon::Dijkstra "LEMON
66Dijkstra class" and it also shows how to define a map on the edges (the length
67function):
68
69\code
70
71    typedef ListGraph Graph;
72    typedef Graph::Node Node;
73    typedef Graph::Edge Edge;
74    typedef Graph::EdgeMap<int> LengthMap;
75
76    Graph g;
77
78    //An example from Ahuja's book
79
80    Node s=g.addNode();
81    Node v2=g.addNode();
82    Node v3=g.addNode();
83    Node v4=g.addNode();
84    Node v5=g.addNode();
85    Node t=g.addNode();
86
87    Edge s_v2=g.addEdge(s, v2);
88    Edge s_v3=g.addEdge(s, v3);
89    Edge v2_v4=g.addEdge(v2, v4);
90    Edge v2_v5=g.addEdge(v2, v5);
91    Edge v3_v5=g.addEdge(v3, v5);
92    Edge v4_t=g.addEdge(v4, t);
93    Edge v5_t=g.addEdge(v5, t);
94 
95    LengthMap len(g);
96
97    len.set(s_v2, 10);
98    len.set(s_v3, 10);
99    len.set(v2_v4, 5);
100    len.set(v2_v5, 8);
101    len.set(v3_v5, 5);
102    len.set(v4_t, 8);
103    len.set(v5_t, 8);
104
105    std::cout << "The id of s is " << g.id(s)<< std::endl;
106    std::cout <<"The id of t is " << g.id(t)<<"."<<std::endl;
107
108    std::cout << "Dijkstra algorithm test..." << std::endl;
109
110    Dijkstra<Graph, LengthMap> dijkstra_test(g,len);
111   
112    dijkstra_test.run(s);
113
114   
115    std::cout << "The distance of node t from node s: " << dijkstra_test.dist(t)<<std::endl;
116
117    std::cout << "The shortest path from s to t goes through the following nodes" <<std::endl;
118 std::cout << " (the first one is t, the last one is s): "<<std::endl;
119
120    for (Node v=t;v != s; v=dijkstra_test.predNode(v)){
121        std::cout << g.id(v) << "<-";
122    }
123    std::cout << g.id(s) << std::endl; 
124\endcode
125
126See the whole program in \ref dijkstra_demo.cc.
127
128The first part of the code is self-explanatory: we build the graph and set the
129length values of the edges. Then we instantiate a member of the Dijkstra class
130and run the Dijkstra algorithm from node \c s. After this we read some of the
131results.
132You can do much more with the Dijkstra class, for example you can run it step
133by step and gain full control of the execution. For a detailed description, see the documentation of the \ref lemon::Dijkstra "LEMON Dijkstra class".
134
135
136<li> If you want to design a network and want to minimize the total length
137of wires then you might be looking for a <b>minimum spanning tree</b> in
138an undirected graph. This can be found using the Kruskal algorithm: the
139class \ref lemon::Kruskal "LEMON Kruskal class" does this job for you.
140The following code fragment shows an example:
141
142Ide Zsuzska fog irni!
143
144<li>Many problems in network optimization can be formalized by means
145of a linear programming problem (LP problem, for short). In our
146library we decided not to write an LP solver, since such packages are
147available in the commercial world just as well as in the open source
148world, and it is also a difficult task to compete these. Instead we
149decided to develop an interface that makes it easier to use these
150solvers together with LEMON. The advantage of this approach is
151twofold. Firstly our C++ interface is more comfortable than the
152solvers' native interface. Secondly, changing the underlying solver in
153a certain software using LEMON's LP interface needs zero effort. So,
154for example, one may try his idea using a free solver, demonstrate its
155usability for a customer and if it works well, but the performance
156should be improved, then one may decide to purchase and use a better
157commercial solver.
158
159So far we have an
160interface for the commercial LP solver software \b CLPLEX (developed by ILOG)
161and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming
162Toolkit).
163
164We will show two examples, the first one shows how simple it is to formalize
165and solve an LP problem in LEMON, while the second one shows how LEMON
166facilitates solving network optimization problems using LP solvers.
167
168<ol>
169<li>The following code shows how to solve an LP problem using the LEMON lp
170interface. The code together with the comments is self-explanatory.
171
172\code
173
174  //A default solver is taken
175  LpDefault lp;
176  typedef LpDefault::Row Row;
177  typedef LpDefault::Col Col;
178 
179
180  //This will be a maximization
181  lp.max();
182
183  //We add coloumns (variables) to our problem
184  Col x1 = lp.addCol();
185  Col x2 = lp.addCol();
186  Col x3 = lp.addCol();
187
188  //Constraints
189  lp.addRow(x1+x2+x3 <=100); 
190  lp.addRow(10*x1+4*x2+5*x3<=600); 
191  lp.addRow(2*x1+2*x2+6*x3<=300); 
192  //Nonnegativity of the variables
193  lp.colLowerBound(x1, 0);
194  lp.colLowerBound(x2, 0);
195  lp.colLowerBound(x3, 0);
196  //Objective function
197  lp.setObj(10*x1+6*x2+4*x3);
198 
199  //Call the routine of the underlying LP solver
200  lp.solve();
201
202  //Print results
203  if (lp.primalStatus()==LpSolverBase::OPTIMAL){
204    printf("Z = %g; x1 = %g; x2 = %g; x3 = %g\n",
205           lp.primalValue(),
206           lp.primal(x1), lp.primal(x2), lp.primal(x3));
207  }
208  else{
209    std::cout<<"Optimal solution not found!"<<std::endl;
210  }
211
212
213\endcode
214
215See the whole code in \ref lp_demo.cc.
216
217<li>The second example shows how easy it is to formalize a max-flow
218problem as an LP problem using the LEMON LP interface: we are looking
219for a real valued function defined on the edges of the digraph
220satisfying the nonnegativity-, the capacity constraints and the
221flow-conservation constraints and giving the largest flow value
222between to designated nodes.
223
224In the following code we suppose that we already have the graph \c g,
225the capacity map \c cap, the source node \c s and the target node \c t
226in the memory. We will also omit the typedefs.
227
228\code
229  //Define a map on the edges for the variables of the LP problem
230  typename G::template EdgeMap<LpDefault::Col> x(g);
231  lp.addColSet(x);
232 
233  //Nonnegativity and capacity constraints
234  for(EdgeIt e(g);e!=INVALID;++e) {
235    lp.colUpperBound(x[e],cap[e]);
236    lp.colLowerBound(x[e],0);
237  }
238
239
240  //Flow conservation constraints for the nodes (except for 's' and 't')
241  for(NodeIt n(g);n!=INVALID;++n) if(n!=s&&n!=t) {
242    LpDefault::Expr ex;
243    for(InEdgeIt  e(g,n);e!=INVALID;++e) ex+=x[e];
244    for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e];
245    lp.addRow(ex==0);
246  }
247 
248  //Objective function: the flow value entering 't'
249  {
250    LpDefault::Expr ex;
251    for(InEdgeIt  e(g,t);e!=INVALID;++e) ex+=x[e];
252    for(OutEdgeIt e(g,t);e!=INVALID;++e) ex-=x[e];
253    lp.setObj(ex);
254  }
255
256  //Maximization
257  lp.max();
258
259  //Solve with the underlying solver
260  lp.solve();
261
262\endcode
263
264The complete program can be found in file \ref lp_maxflow_demo.cc. After compiling run it in the form:
265
266<tt>./lp_maxflow_demo < ?????????.lgf</tt>
267
268where ?????????.lgf is a file in the lemon format containing a maxflow instance (designated "source", "target" nodes and "capacity" map on the edges).
269
270
271
272</ol>
273</ul>
274
275*/
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