Hmmm...
3 \page quicktour Quick Tour to LEMON
5 Let us first answer the question <b>"What do I want to use LEMON for?"
7 LEMON is a C++ library, so you can use it if you want to write C++
8 programs. What kind of tasks does the library LEMON help to solve?
9 It helps to write programs that solve optimization problems that arise
10 frequently when <b>designing and testing certain networks</b>, for example
11 in telecommunication, computer networks, and other areas that I cannot
12 think of now. A very natural way of modelling these networks is by means
13 of a <b> graph</b> (we will always mean a directed graph by that and say
14 <b> undirected graph </b> otherwise).
15 So if you want to write a program that works with
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
18 graph: a very good description can be found in the page
19 about \ref graphs "graphs".
21 You will also want to assign data to the edges or nodes of the graph, for
22 example a length or capacity function defined on the edges. You can do this in
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".
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):
27 <ul> <li> The first thing to discuss is the way one can create data structures
28 like graphs and maps in a program using LEMON.
29 //There are more graph types
30 //implemented in LEMON and you can implement your own graph type just as well:
31 //read more about this in the already mentioned page on \ref graphs "graphs".
33 First we show how to add nodes and edges to a graph manually. We will also
34 define a map on the edges of the graph. After this we show the way one can
35 read a graph (and perhaps maps on it) from a stream (e.g. a file). Of course
36 we also have routines that write a graph (and perhaps maps) to a stream
37 (file): this will also be shown. LEMON supports the DIMACS file formats to
38 store network optimization problems, but more importantly we also have our own
39 file format that gives a more flexible way to store data related to network
42 <ol> <li>The following code fragment shows how to fill a graph with
43 data. It creates a complete graph on 4 nodes. The type Listgraph is one of the
44 LEMON graph types: the typedefs in the beginning are for convenience and we
45 will suppose them later as well.
49 typedef ListGraph Graph;
50 typedef Graph::NodeIt NodeIt;
54 for (int i = 0; i < 3; i++)
57 for (NodeIt i(g); i!=INVALID; ++i)
58 for (NodeIt j(g); j!=INVALID; ++j)
59 if (i != j) g.addEdge(i, j);
63 See the whole program in file \ref helloworld.cc.
65 If you want to read more on the LEMON graph structures and concepts, read the page about \ref graphs "graphs".
67 <li> The following code shows how to read a graph from a stream (e.g. a file)
68 in the DIMACS file format (find the documentation of the DIMACS file formats on the web).
72 std::ifstream f("graph.dim");
76 One can also store network (graph+capacity on the edges) instances and other
77 things (minimum cost flow instances etc.) in DIMACS format and use these in LEMON: to see the details read the
78 documentation of the \ref dimacs.h "Dimacs file format reader". There you will
79 also find the details about the output routines into files of the DIMACS
82 <li>We needed much greater flexibility than the DIMACS formats could give us,
83 so we worked out our own file format. Instead of any explanation let us give a
84 short example file in this format: read the detailed description of the LEMON
85 graph file format and input-output routines \ref graph-io-page here.
87 So here is a file describing a graph of 10 nodes (0 to 9), two nodemaps
88 (called \c coordinates_x and \c coordinates_y), several edges, an edge map
89 called \c length and two designated nodes (called \c source and \c target).
91 \todo Maybe another example would be better here.
95 id coordinates_x coordinates_y
137 Finally let us give a simple example that reads a graph from a file and writes
140 \todo This is to be done!
143 <li> If you want to solve some transportation problems in a network then
144 you will want to find shortest paths between nodes of a graph. This is
145 usually solved using Dijkstra's algorithm. A utility
146 that solves this is the \ref lemon::Dijkstra "LEMON Dijkstra class".
147 The following code is a simple program using the
148 \ref lemon::Dijkstra "LEMON Dijkstra class" and it also shows how to define a map on the edges (the length
153 typedef ListGraph Graph;
154 typedef Graph::Node Node;
155 typedef Graph::Edge Edge;
156 typedef Graph::EdgeMap<int> LengthMap;
160 //An example from Ahuja's book
169 Edge s_v2=g.addEdge(s, v2);
170 Edge s_v3=g.addEdge(s, v3);
171 Edge v2_v4=g.addEdge(v2, v4);
172 Edge v2_v5=g.addEdge(v2, v5);
173 Edge v3_v5=g.addEdge(v3, v5);
174 Edge v4_t=g.addEdge(v4, t);
175 Edge v5_t=g.addEdge(v5, t);
187 std::cout << "The id of s is " << g.id(s)<< std::endl;
188 std::cout <<"The id of t is " << g.id(t)<<"."<<std::endl;
190 std::cout << "Dijkstra algorithm test..." << std::endl;
192 Dijkstra<Graph, LengthMap> dijkstra_test(g,len);
194 dijkstra_test.run(s);
197 std::cout << "The distance of node t from node s: " << dijkstra_test.dist(t)<<std::endl;
199 std::cout << "The shortest path from s to t goes through the following nodes" <<std::endl;
200 std::cout << " (the first one is t, the last one is s): "<<std::endl;
202 for (Node v=t;v != s; v=dijkstra_test.predNode(v)){
203 std::cout << g.id(v) << "<-";
205 std::cout << g.id(s) << std::endl;
208 See the whole program in \ref dijkstra_demo.cc.
210 The first part of the code is self-explanatory: we build the graph and set the
211 length values of the edges. Then we instantiate a member of the Dijkstra class
212 and run the Dijkstra algorithm from node \c s. After this we read some of the
214 You can do much more with the Dijkstra class, for example you can run it step
215 by step and gain full control of the execution. For a detailed description, see the documentation of the \ref lemon::Dijkstra "LEMON Dijkstra class".
218 <li> If you want to design a network and want to minimize the total length
219 of wires then you might be looking for a <b>minimum spanning tree</b> in
220 an undirected graph. This can be found using the Kruskal algorithm: the
221 class \ref lemon::Kruskal "LEMON Kruskal class" does this job for you.
222 The following code fragment shows an example:
224 Ide Zsuzska fog irni!
226 <li>Many problems in network optimization can be formalized by means
227 of a linear programming problem (LP problem, for short). In our
228 library we decided not to write an LP solver, since such packages are
229 available in the commercial world just as well as in the open source
230 world, and it is also a difficult task to compete these. Instead we
231 decided to develop an interface that makes it easier to use these
232 solvers together with LEMON. The advantage of this approach is
233 twofold. Firstly our C++ interface is more comfortable than the
234 solvers' native interface. Secondly, changing the underlying solver in
235 a certain software using LEMON's LP interface needs zero effort. So,
236 for example, one may try his idea using a free solver, demonstrate its
237 usability for a customer and if it works well, but the performance
238 should be improved, then one may decide to purchase and use a better
242 interface for the commercial LP solver software \b CLPLEX (developed by ILOG)
243 and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming
246 We will show two examples, the first one shows how simple it is to formalize
247 and solve an LP problem in LEMON, while the second one shows how LEMON
248 facilitates solving network optimization problems using LP solvers.
251 <li>The following code shows how to solve an LP problem using the LEMON lp
252 interface. The code together with the comments is self-explanatory.
256 //A default solver is taken
258 typedef LpDefault::Row Row;
259 typedef LpDefault::Col Col;
262 //This will be a maximization
265 //We add coloumns (variables) to our problem
266 Col x1 = lp.addCol();
267 Col x2 = lp.addCol();
268 Col x3 = lp.addCol();
271 lp.addRow(x1+x2+x3 <=100);
272 lp.addRow(10*x1+4*x2+5*x3<=600);
273 lp.addRow(2*x1+2*x2+6*x3<=300);
274 //Nonnegativity of the variables
275 lp.colLowerBound(x1, 0);
276 lp.colLowerBound(x2, 0);
277 lp.colLowerBound(x3, 0);
279 lp.setObj(10*x1+6*x2+4*x3);
281 //Call the routine of the underlying LP solver
285 if (lp.primalStatus()==LpSolverBase::OPTIMAL){
286 printf("Z = %g; x1 = %g; x2 = %g; x3 = %g\n",
288 lp.primal(x1), lp.primal(x2), lp.primal(x3));
291 std::cout<<"Optimal solution not found!"<<std::endl;
297 See the whole code in \ref lp_demo.cc.
299 <li>The second example shows how easy it is to formalize a max-flow
300 problem as an LP problem using the LEMON LP interface: we are looking
301 for a real valued function defined on the edges of the digraph
302 satisfying the nonnegativity-, the capacity constraints and the
303 flow-conservation constraints and giving the largest flow value
304 between to designated nodes.
306 In the following code we suppose that we already have the graph \c g,
307 the capacity map \c cap, the source node \c s and the target node \c t
308 in the memory. We will also omit the typedefs.
311 //Define a map on the edges for the variables of the LP problem
312 typename G::template EdgeMap<LpDefault::Col> x(g);
315 //Nonnegativity and capacity constraints
316 for(EdgeIt e(g);e!=INVALID;++e) {
317 lp.colUpperBound(x[e],cap[e]);
318 lp.colLowerBound(x[e],0);
322 //Flow conservation constraints for the nodes (except for 's' and 't')
323 for(NodeIt n(g);n!=INVALID;++n) if(n!=s&&n!=t) {
325 for(InEdgeIt e(g,n);e!=INVALID;++e) ex+=x[e];
326 for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e];
330 //Objective function: the flow value entering 't'
333 for(InEdgeIt e(g,t);e!=INVALID;++e) ex+=x[e];
334 for(OutEdgeIt e(g,t);e!=INVALID;++e) ex-=x[e];
341 //Solve with the underlying solver
346 The complete program can be found in file \ref lp_maxflow_demo.cc. After compiling run it in the form:
348 <tt>./lp_maxflow_demo < ?????????.lgf</tt>
350 where ?????????.lgf is a file in the lemon format containing a maxflow instance (designated "source", "target" nodes and "capacity" map on the edges).