COIN-OR::LEMON - Graph Library

source: lemon-0.x/doc/quicktour.dox @ 1528:1aa71600000c

Last change on this file since 1528:1aa71600000c was 1528:1aa71600000c, checked in by athos, 14 years ago

Graph input-output demo, some documentation.

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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
25In 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.
26You 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".
27
28Have fun!
29
30<ul> <li> The first thing to discuss is the way one can create data structures
31like graphs and maps in a program using LEMON.
32//There are more graph types
33//implemented in LEMON and you can implement your own graph type just as well:
34//read more about this in the already mentioned page on \ref graphs "graphs".
35
36First we show how to add nodes and edges to a graph manually. We will also
37define a map on the edges of the graph. After this we show the way one can
38read a graph (and perhaps maps on it) from a stream (e.g. a file). Of course
39we also have routines that write a graph (and perhaps maps) to a stream
40(file): this will also be shown. LEMON supports the DIMACS file formats to
41store network optimization problems, but more importantly we also have our own
42file format that gives a more flexible way to store data related to network
43optimization.
44
45<ol> <li>The following code fragment shows how to fill a graph with
46data. It creates a complete graph on 4 nodes. The type Listgraph is one of the
47LEMON graph types: the typedefs in the beginning are for convenience and we
48will suppose them later as well. 
49
50\dontinclude hello_lemon.cc
51\skip ListGraph
52\until addEdge
53
54See the whole program in file \ref hello_lemon.cc in \c demo subdir of
55LEMON package.
56
57    If you want to read more on the LEMON graph structures and
58concepts, read the page about \ref graphs "graphs".
59
60<li> The following code shows how to read a graph from a stream
61(e.g. a file) in the DIMACS file format (find the documentation of the
62DIMACS file formats on the web).
63
64\code
65Graph g;
66std::ifstream f("graph.dim");
67readDimacs(f, g);
68\endcode
69
70One can also store network (graph+capacity on the edges) instances and
71other things (minimum cost flow instances etc.) in DIMACS format and
72use these in LEMON: to see the details read the documentation of the
73\ref dimacs.h "Dimacs file format reader". There you will also find
74the details about the output routines into files of the DIMACS format.
75
76<li>DIMACS formats could not give us the flexibility we needed,
77so we worked out our own file format. Instead of any explanation let us give a
78short example file in this format: read the detailed description of the LEMON
79graph file format and input-output routines \ref graph-io-page here.
80
81So here is a file describing a graph of 10 nodes (0 to 9), two nodemaps
82(called \c coordinates_x and \c coordinates_y), several edges, an edge map
83called \c length and two designated nodes (called \c source and \c target).
84
85\todo Maybe a shorter example would be better here.
86
87\include route.lgf
88
89Finally let us give a simple example that reads a graph from a file and writes
90it to the standard output.
91
92\include reader_writer_demo.cc
93
94See the whole program in file \ref reader_writer_demo.cc.
95
96\todo This is still under construction!
97
98</ol>
99<li> If you want to solve some transportation problems in a network then
100you will want to find shortest paths between nodes of a graph. This is
101usually solved using Dijkstra's algorithm. A utility
102that solves this is  the \ref lemon::Dijkstra "LEMON Dijkstra class".
103The following code is a simple program using the
104\ref lemon::Dijkstra "LEMON Dijkstra class" and it also shows how to define a map on the edges (the length
105function):
106
107\dontinclude dijkstra_demo.cc
108\skip ListGraph
109\until std::cout << g.id(s)
110
111See the whole program in \ref dijkstra_demo.cc.
112
113The first part of the code is self-explanatory: we build the graph and set the
114length values of the edges. Then we instantiate a member of the Dijkstra class
115and run the Dijkstra algorithm from node \c s. After this we read some of the
116results.
117You can do much more with the Dijkstra class, for example you can run it step
118by step and gain full control of the execution. For a detailed description, see the documentation of the \ref lemon::Dijkstra "LEMON Dijkstra class".
119
120
121<li> If you want to design a network and want to minimize the total length
122of wires then you might be looking for a <b>minimum spanning tree</b> in
123an undirected graph. This can be found using the Kruskal algorithm: the
124function \ref lemon::kruskal "LEMON Kruskal ..." does this job for you.
125The following code fragment shows an example:
126
127Ide Zsuzska fog irni!
128
129<li>Many problems in network optimization can be formalized by means
130of a linear programming problem (LP problem, for short). In our
131library we decided not to write an LP solver, since such packages are
132available in the commercial world just as well as in the open source
133world, and it is also a difficult task to compete these. Instead we
134decided to develop an interface that makes it easier to use these
135solvers together with LEMON. The advantage of this approach is
136twofold. Firstly our C++ interface is more comfortable than the
137solvers' native interface. Secondly, changing the underlying solver in
138a certain software using LEMON's LP interface needs zero effort. So,
139for example, one may try his idea using a free solver, demonstrate its
140usability for a customer and if it works well, but the performance
141should be improved, then one may decide to purchase and use a better
142commercial solver.
143
144So far we have an
145interface for the commercial LP solver software \b CPLEX (developed by ILOG)
146and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming
147Toolkit).
148
149We will show two examples, the first one shows how simple it is to formalize
150and solve an LP problem in LEMON, while the second one shows how LEMON
151facilitates solving network optimization problems using LP solvers.
152
153<ol>
154<li>The following code shows how to solve an LP problem using the LEMON lp
155interface. The code together with the comments is self-explanatory.
156
157\code
158
159  //A default solver is taken
160  LpDefault lp;
161  typedef LpDefault::Row Row;
162  typedef LpDefault::Col Col;
163 
164
165  //This will be a maximization
166  lp.max();
167
168  //We add coloumns (variables) to our problem
169  Col x1 = lp.addCol();
170  Col x2 = lp.addCol();
171  Col x3 = lp.addCol();
172
173  //Constraints
174  lp.addRow(x1+x2+x3 <=100); 
175  lp.addRow(10*x1+4*x2+5*x3<=600); 
176  lp.addRow(2*x1+2*x2+6*x3<=300); 
177  //Nonnegativity of the variables
178  lp.colLowerBound(x1, 0);
179  lp.colLowerBound(x2, 0);
180  lp.colLowerBound(x3, 0);
181  //Objective function
182  lp.setObj(10*x1+6*x2+4*x3);
183 
184  //Call the routine of the underlying LP solver
185  lp.solve();
186
187  //Print results
188  if (lp.primalStatus()==LpSolverBase::OPTIMAL){
189    printf("Z = %g; x1 = %g; x2 = %g; x3 = %g\n",
190           lp.primalValue(),
191           lp.primal(x1), lp.primal(x2), lp.primal(x3));
192  }
193  else{
194    std::cout<<"Optimal solution not found!"<<std::endl;
195  }
196
197
198\endcode
199
200See the whole code in \ref lp_demo.cc.
201
202<li>The second example shows how easy it is to formalize a max-flow
203problem as an LP problem using the LEMON LP interface: we are looking
204for a real valued function defined on the edges of the digraph
205satisfying the nonnegativity-, the capacity constraints and the
206flow-conservation constraints and giving the largest flow value
207between to designated nodes.
208
209In the following code we suppose that we already have the graph \c g,
210the capacity map \c cap, the source node \c s and the target node \c t
211in the memory. We will also omit the typedefs.
212
213\code
214  //Define a map on the edges for the variables of the LP problem
215  typename G::template EdgeMap<LpDefault::Col> x(g);
216  lp.addColSet(x);
217 
218  //Nonnegativity and capacity constraints
219  for(EdgeIt e(g);e!=INVALID;++e) {
220    lp.colUpperBound(x[e],cap[e]);
221    lp.colLowerBound(x[e],0);
222  }
223
224
225  //Flow conservation constraints for the nodes (except for 's' and 't')
226  for(NodeIt n(g);n!=INVALID;++n) if(n!=s&&n!=t) {
227    LpDefault::Expr ex;
228    for(InEdgeIt  e(g,n);e!=INVALID;++e) ex+=x[e];
229    for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e];
230    lp.addRow(ex==0);
231  }
232 
233  //Objective function: the flow value entering 't'
234  {
235    LpDefault::Expr ex;
236    for(InEdgeIt  e(g,t);e!=INVALID;++e) ex+=x[e];
237    for(OutEdgeIt e(g,t);e!=INVALID;++e) ex-=x[e];
238    lp.setObj(ex);
239  }
240
241  //Maximization
242  lp.max();
243
244  //Solve with the underlying solver
245  lp.solve();
246
247\endcode
248
249The complete program can be found in file \ref lp_maxflow_demo.cc. After compiling run it in the form:
250
251<tt>./lp_maxflow_demo < sample.lgf</tt>
252
253where sample.lgf is a file in the lemon format containing a maxflow instance (designated "source", "target" nodes and "capacity" map on the edges).
254
255
256
257</ol>
258</ul>
259
260*/
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