source: lemon-0.x/doc/quicktour.dox @ 1526:8c14aa8f27a2

/**

\page quicktour Quick Tour to LEMON

Let us first answer the question <b>"What do I want to use LEMON for?"
</b>. 
LEMON is a C++ library, so you can use it if you want to write C++ 
programs. What kind of tasks does the library LEMON help to solve? 
It helps to write programs that solve optimization problems that arise
frequently when <b>designing and testing certain networks</b>, for example
in telecommunication, computer networks, and other areas that I cannot
think of now. A very natural way of modelling these networks is by means
of a <b> graph</b> (we will always mean a directed graph by that and say
<b> undirected graph </b> otherwise). 
So if you want to write a program that works with 
graphs then you might find it useful to use our library LEMON. LEMON 
defines various graph concepts depending on what you want to do with the 
graph: a very good description can be found in the page
about \ref graphs "graphs".

You will also want to assign data to the edges or nodes of the graph, for
example a length or capacity function defined on the edges. You can do this in
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".

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):

<ul> <li> The first thing to discuss is the way one can create data structures
like graphs and maps in a program using LEMON. 
//There are more graph types
//implemented in LEMON and you can implement your own graph type just as well:
//read more about this in the already mentioned page on \ref graphs "graphs".

First we show how to add nodes and edges to a graph manually. We will also
define a map on the edges of the graph. After this we show the way one can
read a graph (and perhaps maps on it) from a stream (e.g. a file). Of course
we also have routines that write a graph (and perhaps maps) to a stream
(file): this will also be shown. LEMON supports the DIMACS file formats to
store network optimization problems, but more importantly we also have our own
file format that gives a more flexible way to store data related to network
optimization.

<ol> <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.  

\dontinclude hello_lemon.cc
\skip ListGraph
\until addEdge

See the whole program in file \ref hello_lemon.cc in \c demo subdir of
LEMON package.

    If you want to read more on the LEMON graph structures and
concepts, read the page about \ref graphs "graphs".

<li> The following code shows how to read a graph from a stream
(e.g. a file) in the DIMACS file format (find the documentation of the
DIMACS file formats on the web).

\code
Graph g;
std::ifstream f("graph.dim");
readDimacs(f, g);
\endcode

One can also store network (graph+capacity on the edges) instances and
other things (minimum cost flow instances etc.) in DIMACS format and
use these in LEMON: to see the details read the documentation of the
\ref dimacs.h "Dimacs file format reader". There you will also find
the details about the output routines into files of the DIMACS format.

<li>DIMACS formats could not give us the flexibility we needed,
so we worked out our own file format. Instead of any explanation let us give a
short example file in this format: read the detailed description of the LEMON
graph file format and input-output routines \ref graph-io-page here.

So here is a file describing a graph of 10 nodes (0 to 9), two nodemaps
(called \c coordinates_x and \c coordinates_y), several edges, an edge map
called \c length and two designated nodes (called \c source and \c target).

\todo Maybe another example would be better here.

\code
@nodeset
id      coordinates_x   coordinates_y   
9       447.907 578.328 
8       79.2573 909.464 
7       878.677 960.04  
6       11.5504 938.413 
5       327.398 815.035 
4       427.002 954.002 
3       148.549 753.748 
2       903.889 326.476 
1       408.248 577.327 
0       189.239 92.5316 
@edgeset
                length  
2       3       901.074 
8       5       270.85  
6       9       601.553 
5       9       285.022 
9       4       408.091 
3       0       719.712 
7       5       612.836 
0       4       933.353 
5       0       778.871 
5       5       0       
7       1       664.049 
5       5       0       
0       9       560.464 
4       8       352.36  
4       9       399.625 
4       1       402.171 
1       2       591.688 
3       8       182.376 
4       5       180.254 
3       1       345.283 
5       4       184.511 
6       2       1112.45 
0       1       556.624 
@nodes
source  1       
target  8       
@end
\endcode

Finally let us give a simple example that reads a graph from a file and writes
it to another.

\todo This is to be done!

</ol>
<li> If you want to solve some transportation problems in a network then 
you will want to find shortest paths between nodes of a graph. This is 
usually solved using Dijkstra's algorithm. A utility
that solves this is  the \ref lemon::Dijkstra "LEMON Dijkstra class".
The following code is a simple program using the 
\ref lemon::Dijkstra "LEMON Dijkstra class" and it also shows how to define a map on the edges (the length
function):

\code

    typedef ListGraph Graph;
    typedef Graph::Node Node;
    typedef Graph::Edge Edge;
    typedef Graph::EdgeMap<int> LengthMap;

    Graph g;

    //An example from Ahuja's book

    Node s=g.addNode();
    Node v2=g.addNode();
    Node v3=g.addNode();
    Node v4=g.addNode();
    Node v5=g.addNode();
    Node t=g.addNode();

    Edge s_v2=g.addEdge(s, v2);
    Edge s_v3=g.addEdge(s, v3);
    Edge v2_v4=g.addEdge(v2, v4);
    Edge v2_v5=g.addEdge(v2, v5);
    Edge v3_v5=g.addEdge(v3, v5);
    Edge v4_t=g.addEdge(v4, t);
    Edge v5_t=g.addEdge(v5, t);
  
    LengthMap len(g);

    len.set(s_v2, 10);
    len.set(s_v3, 10);
    len.set(v2_v4, 5);
    len.set(v2_v5, 8);
    len.set(v3_v5, 5);
    len.set(v4_t, 8);
    len.set(v5_t, 8);

    std::cout << "The id of s is " << g.id(s)<< std::endl;
    std::cout <<"The id of t is " << g.id(t)<<"."<<std::endl;

    std::cout << "Dijkstra algorithm test..." << std::endl;

    Dijkstra<Graph, LengthMap> dijkstra_test(g,len);
    
    dijkstra_test.run(s);

    
    std::cout << "The distance of node t from node s: " << dijkstra_test.dist(t)<<std::endl;

    std::cout << "The shortest path from s to t goes through the following nodes" <<std::endl;
 std::cout << " (the first one is t, the last one is s): "<<std::endl;

    for (Node v=t;v != s; v=dijkstra_test.predNode(v)){
        std::cout << g.id(v) << "<-";
    }
    std::cout << g.id(s) << std::endl;  
\endcode

See the whole program in \ref dijkstra_demo.cc.

The first part of the code is self-explanatory: we build the graph and set the
length values of the edges. Then we instantiate a member of the Dijkstra class
and run the Dijkstra algorithm from node \c s. After this we read some of the
results. 
You can do much more with the Dijkstra class, for example you can run it step
by step and gain full control of the execution. For a detailed description, see the documentation of the \ref lemon::Dijkstra "LEMON Dijkstra class".


<li> If you want to design a network and want to minimize the total length
of wires then you might be looking for a <b>minimum spanning tree</b> in
an undirected graph. This can be found using the Kruskal algorithm: the 
class \ref lemon::Kruskal "LEMON Kruskal class" does this job for you.
The following code fragment shows an example:

Ide Zsuzska fog irni!

<li>Many problems in network optimization can be formalized by means
of a linear programming problem (LP problem, for short). In our
library we decided not to write an LP solver, since such packages are
available in the commercial world just as well as in the open source
world, and it is also a difficult task to compete these. Instead we
decided to develop an interface that makes it easier to use these
solvers together with LEMON. The advantage of this approach is
twofold. Firstly our C++ interface is more comfortable than the
solvers' native interface. Secondly, changing the underlying solver in
a certain software using LEMON's LP interface needs zero effort. So,
for example, one may try his idea using a free solver, demonstrate its
usability for a customer and if it works well, but the performance
should be improved, then one may decide to purchase and use a better
commercial solver.

So far we have an
interface for the commercial LP solver software \b CPLEX (developed by ILOG)
and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming
Toolkit).

We will show two examples, the first one shows how simple it is to formalize
and solve an LP problem in LEMON, while the second one shows how LEMON
facilitates solving network optimization problems using LP solvers.

<ol>
<li>The following code shows how to solve an LP problem using the LEMON lp
interface. The code together with the comments is self-explanatory.

\code

  //A default solver is taken
  LpDefault lp;
  typedef LpDefault::Row Row;
  typedef LpDefault::Col Col;
  

  //This will be a maximization
  lp.max();

  //We add coloumns (variables) to our problem
  Col x1 = lp.addCol();
  Col x2 = lp.addCol();
  Col x3 = lp.addCol();

  //Constraints
  lp.addRow(x1+x2+x3 <=100);  
  lp.addRow(10*x1+4*x2+5*x3<=600);  
  lp.addRow(2*x1+2*x2+6*x3<=300);  
  //Nonnegativity of the variables
  lp.colLowerBound(x1, 0);
  lp.colLowerBound(x2, 0);
  lp.colLowerBound(x3, 0);
  //Objective function
  lp.setObj(10*x1+6*x2+4*x3);
  
  //Call the routine of the underlying LP solver
  lp.solve();

  //Print results
  if (lp.primalStatus()==LpSolverBase::OPTIMAL){
    printf("Z = %g; x1 = %g; x2 = %g; x3 = %g\n", 
           lp.primalValue(), 
           lp.primal(x1), lp.primal(x2), lp.primal(x3));
  }
  else{
    std::cout<<"Optimal solution not found!"<<std::endl;
  }


\endcode

See the whole code in \ref lp_demo.cc.

<li>The second example shows how easy it is to formalize a max-flow
problem as an LP problem using the LEMON LP interface: we are looking
for a real valued function defined on the edges of the digraph
satisfying the nonnegativity-, the capacity constraints and the
flow-conservation constraints and giving the largest flow value
between to designated nodes.

In the following code we suppose that we already have the graph \c g,
the capacity map \c cap, the source node \c s and the target node \c t
in the memory. We will also omit the typedefs.

\code
  //Define a map on the edges for the variables of the LP problem
  typename G::template EdgeMap<LpDefault::Col> x(g);
  lp.addColSet(x);
  
  //Nonnegativity and capacity constraints
  for(EdgeIt e(g);e!=INVALID;++e) {
    lp.colUpperBound(x[e],cap[e]);
    lp.colLowerBound(x[e],0);
  }


  //Flow conservation constraints for the nodes (except for 's' and 't')
  for(NodeIt n(g);n!=INVALID;++n) if(n!=s&&n!=t) {
    LpDefault::Expr ex;
    for(InEdgeIt  e(g,n);e!=INVALID;++e) ex+=x[e];
    for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e];
    lp.addRow(ex==0);
  }
  
  //Objective function: the flow value entering 't'
  {
    LpDefault::Expr ex;
    for(InEdgeIt  e(g,t);e!=INVALID;++e) ex+=x[e];
    for(OutEdgeIt e(g,t);e!=INVALID;++e) ex-=x[e];
    lp.setObj(ex);
  }

  //Maximization
  lp.max();

  //Solve with the underlying solver
  lp.solve();

\endcode

The complete program can be found in file \ref lp_maxflow_demo.cc. After compiling run it in the form:

<tt>./lp_maxflow_demo < ?????????.lgf</tt>

where ?????????.lgf is a file in the lemon format containing a maxflow instance (designated "source", "target" nodes and "capacity" map on the edges).



</ol>
</ul>

*/