COIN-OR::LEMON - Graph Library

source: lemon-0.x/doc/quicktour.dox @ 1514:c9b9bc63db4e

Last change on this file since 1514:c9b9bc63db4e was 1514:c9b9bc63db4e, checked in by athos, 14 years ago

Improved getsart.dox and quicktour.dox

File size: 7.6 KB
Line 
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 of a
145linear programming problem (LP problem, for short). In our library we decided
146not to write an LP solver, since such packages are available in the commercial
147world just as well as in the open source world, and it is also a difficult
148task to compete these. Instead we decided to develop an interface that makes
149it easier to use these solvers together with LEMON. So far we have an
150interface for the commercial LP solver software \b CLPLEX (developed by ILOG)
151and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming
152Toolkit).
153
154We will show two examples, the first one shows how simple it is to formalize
155and solve an LP problem in LEMON, while the second one shows how LEMON
156facilitates solving network optimization problems using LP solvers.
157
158<ol>
159<li>The following code shows how to solve an LP problem using the LEMON lp
160interface.
161
162\code
163
164  //A default solver is taken
165  LpDefault lp;
166  typedef LpDefault::Row Row;
167  typedef LpDefault::Col Col;
168 
169
170  //This will be a maximization
171  lp.max();
172
173  //We add coloumns (variables) to our problem
174  Col x1 = lp.addCol();
175  Col x2 = lp.addCol();
176  Col x3 = lp.addCol();
177
178  //Constraints
179  lp.addRow(x1+x2+x3 <=100); 
180  lp.addRow(10*x1+4*x2+5*x3<=600); 
181  lp.addRow(2*x1+2*x2+6*x3<=300); 
182  //Nonnegativity of the variables
183  lp.colLowerBound(x1, 0);
184  lp.colLowerBound(x2, 0);
185  lp.colLowerBound(x3, 0);
186  //Objective function
187  lp.setObj(10*x1+6*x2+4*x3);
188 
189  //Call the routine of the underlying LP solver
190  lp.solve();
191
192  //Print results
193  if (lp.primalStatus()==LpSolverBase::OPTIMAL){
194    printf("Z = %g; x1 = %g; x2 = %g; x3 = %g\n",
195           lp.primalValue(),
196           lp.primal(x1), lp.primal(x2), lp.primal(x3));
197  }
198  else{
199    std::cout<<"Optimal solution not found!"<<std::endl;
200  }
201
202
203\endcode
204
205See the whole code in \ref lp_demo.cc.
206
207<li>The second example shows how easy it is to formalize a network
208optimization problem as an LP problem using the LEMON LP interface.
209
210</ol>
211</ul>
212
213*/
Note: See TracBrowser for help on using the repository browser.