Only added comments.
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):
28 <li> First we give two examples that show how to instantiate a graph. The
29 first one shows the methods that add nodes and edges, but one will
30 usually use the second way which reads a graph from a stream (file).
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.
34 typedef ListGraph Graph;
35 typedef Graph::NodeIt NodeIt;
39 for (int i = 0; i < 3; i++)
42 for (NodeIt i(g); i!=INVALID; ++i)
43 for (NodeIt j(g); j!=INVALID; ++j)
44 if (i != j) g.addEdge(i, j);
47 See the whole program in file \ref helloworld.cc.
49 If you want to read more on the LEMON graph structures and concepts, read the page about \ref graphs "graphs".
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
52 in that format (find the documentation of the DIMACS file format on the web).
55 std::ifstream f("graph.dim");
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".
61 <li> If you want to solve some transportation problems in a network then
62 you will want to find shortest paths between nodes of a graph. This is
63 usually solved using Dijkstra's algorithm. A utility
64 that solves this is the \ref lemon::Dijkstra "LEMON Dijkstra class".
65 The following code is a simple program using the \ref lemon::Dijkstra "LEMON
66 Dijkstra class" and it also shows how to define a map on the edges (the length
71 typedef ListGraph Graph;
72 typedef Graph::Node Node;
73 typedef Graph::Edge Edge;
74 typedef Graph::EdgeMap<int> LengthMap;
78 //An example from Ahuja's book
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);
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;
108 std::cout << "Dijkstra algorithm test..." << std::endl;
110 Dijkstra<Graph, LengthMap> dijkstra_test(g,len);
112 dijkstra_test.run(s);
115 std::cout << "The distance of node t from node s: " << dijkstra_test.dist(t)<<std::endl;
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;
120 for (Node v=t;v != s; v=dijkstra_test.predNode(v)){
121 std::cout << g.id(v) << "<-";
123 std::cout << g.id(s) << std::endl;
126 See the whole program in \ref dijkstra_demo.cc.
128 The first part of the code is self-explanatory: we build the graph and set the
129 length values of the edges. Then we instantiate a member of the Dijkstra class
130 and run the Dijkstra algorithm from node \c s. After this we read some of the
132 You can do much more with the Dijkstra class, for example you can run it step
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".
136 <li> If you want to design a network and want to minimize the total length
137 of wires then you might be looking for a <b>minimum spanning tree</b> in
138 an undirected graph. This can be found using the Kruskal algorithm: the
139 class \ref lemon::Kruskal "LEMON Kruskal class" does this job for you.
140 The following code fragment shows an example:
142 Ide Zsuzska fog irni!
144 <li>Many problems in network optimization can be formalized by means
145 of a linear programming problem (LP problem, for short). In our
146 library we decided not to write an LP solver, since such packages are
147 available in the commercial world just as well as in the open source
148 world, and it is also a difficult task to compete these. Instead we
149 decided to develop an interface that makes it easier to use these
150 solvers together with LEMON. The advantage of this approach is
151 twofold. Firstly our C++ interface is more comfortable than the
152 solvers' native interface. Secondly, changing the underlying solver in
153 a certain software using LEMON's LP interface needs zero effort. So,
154 for example, one may try his idea using a free solver, demonstrate its
155 usability for a customer and if it works well, but the performance
156 should be improved, then one may decide to purchase and use a better
160 interface for the commercial LP solver software \b CLPLEX (developed by ILOG)
161 and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming
164 We will show two examples, the first one shows how simple it is to formalize
165 and solve an LP problem in LEMON, while the second one shows how LEMON
166 facilitates solving network optimization problems using LP solvers.
169 <li>The following code shows how to solve an LP problem using the LEMON lp
170 interface. The code together with the comments is self-explanatory.
174 //A default solver is taken
176 typedef LpDefault::Row Row;
177 typedef LpDefault::Col Col;
180 //This will be a maximization
183 //We add coloumns (variables) to our problem
184 Col x1 = lp.addCol();
185 Col x2 = lp.addCol();
186 Col x3 = lp.addCol();
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);
197 lp.setObj(10*x1+6*x2+4*x3);
199 //Call the routine of the underlying LP solver
203 if (lp.primalStatus()==LpSolverBase::OPTIMAL){
204 printf("Z = %g; x1 = %g; x2 = %g; x3 = %g\n",
206 lp.primal(x1), lp.primal(x2), lp.primal(x3));
209 std::cout<<"Optimal solution not found!"<<std::endl;
215 See the whole code in \ref lp_demo.cc.
217 <li>The second example shows how easy it is to formalize a max-flow
218 problem as an LP problem using the LEMON LP interface: we are looking
219 for a real valued function defined on the edges of the digraph
220 satisfying the nonnegativity-, the capacity constraints and the
221 flow-conservation constraints and giving the largest flow value
222 between to designated nodes.
224 In the following code we suppose that we already have the graph \c g,
225 the capacity map \c cap, the source node \c s and the target node \c t
226 in the memory. We will also omit the typedefs.
229 //Define a map on the edges for the variables of the LP problem
230 typename G::template EdgeMap<LpDefault::Col> x(g);
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);
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) {
243 for(InEdgeIt e(g,n);e!=INVALID;++e) ex+=x[e];
244 for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e];
248 //Objective function: the flow value entering 't'
251 for(InEdgeIt e(g,t);e!=INVALID;++e) ex+=x[e];
252 for(OutEdgeIt e(g,t);e!=INVALID;++e) ex-=x[e];
259 //Solve with the underlying solver
264 The complete program can be found in file \ref lp_maxflow_demo.cc. After compiling run it in the form:
266 <tt>./lp_maxflow_demo < ?????????.lgf</tt>
268 where ?????????.lgf is a file in the lemon format containing a maxflow instance (designated "source", "target" nodes and "capacity" map).
271 See the whole code in \ref lp_demo.cc.