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 In 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.
26 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 getstart "How to start using LEMON".
30 <ul> <li> The first thing to discuss is the way one can create data structures
31 like 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".
36 First we show how to add nodes and edges to a graph manually. We will also
37 define a map on the edges of the graph. After this we show the way one can
38 read a graph (and perhaps maps on it) from a stream (e.g. a file). Of course
39 we 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
41 store network optimization problems, but more importantly we also have our own
42 file format that gives a more flexible way to store data related to network
45 <ol> <li>The following code fragment shows how to fill a graph with
46 data. It creates a complete graph on 4 nodes. The type Listgraph is one of the
47 LEMON graph types: the typedefs in the beginning are for convenience and we
48 will suppose them later as well.
50 \dontinclude hello_lemon.cc
54 See the whole program in file \ref hello_lemon.cc in \c demo subdir of
57 If you want to read more on the LEMON graph structures and
58 concepts, read the page about \ref graphs "graphs".
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
62 DIMACS file formats on the web).
66 std::ifstream f("graph.dim");
70 One can also store network (graph+capacity on the edges) instances and
71 other things (minimum cost flow instances etc.) in DIMACS format and
72 use 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
74 the details about the output routines into files of the DIMACS format.
76 <li>DIMACS formats could not give us the flexibility we needed,
77 so we worked out our own file format. Instead of any explanation let us give a
78 short example file in this format: read the detailed description of the LEMON
79 graph file format and input-output routines \ref graph-io-page here.
81 So 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
83 called \c length and two designated nodes (called \c source and \c target).
85 \todo Maybe a shorter example would be better here.
89 Finally let us give a simple example that reads a graph from a file and writes
90 it to the standard output.
92 \include reader_writer_demo.cc
94 See the whole program in file \ref reader_writer_demo.cc.
96 \todo This is still under construction!
99 <li> If you want to solve some transportation problems in a network then
100 you will want to find shortest paths between nodes of a graph. This is
101 usually solved using Dijkstra's algorithm. A utility
102 that solves this is the \ref lemon::Dijkstra "LEMON Dijkstra class".
103 The 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
107 \dontinclude dijkstra_demo.cc
109 \until std::cout << g.id(s)
111 See the whole program in \ref dijkstra_demo.cc.
113 The first part of the code is self-explanatory: we build the graph and set the
114 length values of the edges. Then we instantiate a member of the Dijkstra class
115 and run the Dijkstra algorithm from node \c s. After this we read some of the
117 You can do much more with the Dijkstra class, for example you can run it step
118 by step and gain full control of the execution. For a detailed description, see the documentation of the \ref lemon::Dijkstra "LEMON Dijkstra class".
121 <li> If you want to design a network and want to minimize the total length
122 of wires then you might be looking for a <b>minimum spanning tree</b> in
123 an undirected graph. This can be found using the Kruskal algorithm: the
124 function \ref lemon::kruskal "LEMON Kruskal ..." does this job for you.
125 The following code fragment shows an example:
127 Ide Zsuzska fog irni!
129 <li>Many problems in network optimization can be formalized by means
130 of a linear programming problem (LP problem, for short). In our
131 library we decided not to write an LP solver, since such packages are
132 available in the commercial world just as well as in the open source
133 world, and it is also a difficult task to compete these. Instead we
134 decided to develop an interface that makes it easier to use these
135 solvers together with LEMON. The advantage of this approach is
136 twofold. Firstly our C++ interface is more comfortable than the
137 solvers' native interface. Secondly, changing the underlying solver in
138 a certain software using LEMON's LP interface needs zero effort. So,
139 for example, one may try his idea using a free solver, demonstrate its
140 usability for a customer and if it works well, but the performance
141 should be improved, then one may decide to purchase and use a better
145 interface for the commercial LP solver software \b CPLEX (developed by ILOG)
146 and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming
149 We will show two examples, the first one shows how simple it is to formalize
150 and solve an LP problem in LEMON, while the second one shows how LEMON
151 facilitates solving network optimization problems using LP solvers.
154 <li>The following code shows how to solve an LP problem using the LEMON lp
155 interface. The code together with the comments is self-explanatory.
159 //A default solver is taken
161 typedef LpDefault::Row Row;
162 typedef LpDefault::Col Col;
165 //This will be a maximization
168 //We add coloumns (variables) to our problem
169 Col x1 = lp.addCol();
170 Col x2 = lp.addCol();
171 Col x3 = lp.addCol();
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);
182 lp.setObj(10*x1+6*x2+4*x3);
184 //Call the routine of the underlying LP solver
188 if (lp.primalStatus()==LpSolverBase::OPTIMAL){
189 printf("Z = %g; x1 = %g; x2 = %g; x3 = %g\n",
191 lp.primal(x1), lp.primal(x2), lp.primal(x3));
194 std::cout<<"Optimal solution not found!"<<std::endl;
200 See the whole code in \ref lp_demo.cc.
202 <li>The second example shows how easy it is to formalize a max-flow
203 problem as an LP problem using the LEMON LP interface: we are looking
204 for a real valued function defined on the edges of the digraph
205 satisfying the nonnegativity-, the capacity constraints and the
206 flow-conservation constraints and giving the largest flow value
207 between to designated nodes.
209 In the following code we suppose that we already have the graph \c g,
210 the capacity map \c cap, the source node \c s and the target node \c t
211 in the memory. We will also omit the typedefs.
214 //Define a map on the edges for the variables of the LP problem
215 typename G::template EdgeMap<LpDefault::Col> x(g);
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);
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) {
228 for(InEdgeIt e(g,n);e!=INVALID;++e) ex+=x[e];
229 for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e];
233 //Objective function: the flow value entering 't'
236 for(InEdgeIt e(g,t);e!=INVALID;++e) ex+=x[e];
237 for(OutEdgeIt e(g,t);e!=INVALID;++e) ex-=x[e];
244 //Solve with the underlying solver
249 The complete program can be found in file \ref lp_maxflow_demo.cc. After compiling run it in the form:
251 <tt>./lp_maxflow_demo < sample.lgf</tt>
253 where sample.lgf is a file in the lemon format containing a maxflow instance (designated "source", "target" nodes and "capacity" map on the edges).