athos@1169: /**
athos@1169: 
alpar@1170: \page quicktour Quick Tour to LEMON
alpar@1170: 
athos@1175: Let us first answer the question <b>"What do I want to use LEMON for?"
athos@1175: </b>. 
athos@1175: LEMON is a C++ library, so you can use it if you want to write C++ 
athos@1175: programs. What kind of tasks does the library LEMON help to solve? 
athos@1175: It helps to write programs that solve optimization problems that arise
athos@1175: frequently when <b>designing and testing certain networks</b>, for example
athos@1175: in telecommunication, computer networks, and other areas that I cannot
athos@1175: think of now. A very natural way of modelling these networks is by means
athos@1183: of a <b> graph</b> (we will always mean a directed graph by that and say
athos@1183: <b> undirected graph </b> otherwise). 
athos@1175: So if you want to write a program that works with 
athos@1183: graphs then you might find it useful to use our library LEMON. LEMON 
athos@1183: defines various graph concepts depending on what you want to do with the 
athos@1183: graph: a very good description can be found in the page
athos@1183: about \ref graphs "graphs".
athos@1175: 
athos@1514: You will also want to assign data to the edges or nodes of the graph, for
athos@1514: example a length or capacity function defined on the edges. You can do this in
athos@1514: 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".
athos@1175: 
athos@1528: 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. 
athos@1528: 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". 
athos@1528: 
athos@1528: Have fun!
athos@1175: 
athos@1522: <ul> <li> The first thing to discuss is the way one can create data structures
athos@1522: like graphs and maps in a program using LEMON. 
athos@1522: //There are more graph types
athos@1522: //implemented in LEMON and you can implement your own graph type just as well:
athos@1522: //read more about this in the already mentioned page on \ref graphs "graphs".
athos@1522: 
athos@1522: First we show how to add nodes and edges to a graph manually. We will also
athos@1522: define a map on the edges of the graph. After this we show the way one can
athos@1522: read a graph (and perhaps maps on it) from a stream (e.g. a file). Of course
athos@1522: we also have routines that write a graph (and perhaps maps) to a stream
athos@1522: (file): this will also be shown. LEMON supports the DIMACS file formats to
athos@1522: store network optimization problems, but more importantly we also have our own
athos@1522: file format that gives a more flexible way to store data related to network
athos@1522: optimization.
athos@1522: 
athos@1522: <ol> <li>The following code fragment shows how to fill a graph with
athos@1522: data. It creates a complete graph on 4 nodes. The type Listgraph is one of the
athos@1522: LEMON graph types: the typedefs in the beginning are for convenience and we
athos@1522: will suppose them later as well.  
athos@1522: 
athos@1526: \dontinclude hello_lemon.cc
athos@1526: \skip ListGraph
athos@1526: \until addEdge
athos@1522: 
athos@1526: See the whole program in file \ref hello_lemon.cc in \c demo subdir of
athos@1526: LEMON package.
athos@1175: 
athos@1526:     If you want to read more on the LEMON graph structures and
athos@1526: concepts, read the page about \ref graphs "graphs".
athos@1522: 
athos@1526: <li> The following code shows how to read a graph from a stream
athos@1526: (e.g. a file) in the DIMACS file format (find the documentation of the
athos@1526: DIMACS file formats on the web).
athos@1522: 
athos@1181: \code
athos@1181: Graph g;
athos@1181: std::ifstream f("graph.dim");
athos@1181: readDimacs(f, g);
athos@1181: \endcode
athos@1522: 
athos@1526: One can also store network (graph+capacity on the edges) instances and
athos@1526: other things (minimum cost flow instances etc.) in DIMACS format and
athos@1526: use these in LEMON: to see the details read the documentation of the
athos@1526: \ref dimacs.h "Dimacs file format reader". There you will also find
athos@1526: the details about the output routines into files of the DIMACS format.
athos@1522: 
athos@1526: <li>DIMACS formats could not give us the flexibility we needed,
athos@1522: so we worked out our own file format. Instead of any explanation let us give a
athos@1522: short example file in this format: read the detailed description of the LEMON
athos@1522: graph file format and input-output routines \ref graph-io-page here.
athos@1522: 
athos@1522: So here is a file describing a graph of 10 nodes (0 to 9), two nodemaps
athos@1522: (called \c coordinates_x and \c coordinates_y), several edges, an edge map
athos@1522: called \c length and two designated nodes (called \c source and \c target).
athos@1522: 
athos@1528: \todo Maybe a shorter example would be better here.
athos@1522: 
athos@1528: \include route.lgf
athos@1522: 
athos@1522: Finally let us give a simple example that reads a graph from a file and writes
athos@1528: it to the standard output.
athos@1522: 
athos@1528: \include reader_writer_demo.cc
athos@1528: 
athos@1528: See the whole program in file \ref reader_writer_demo.cc.
athos@1528: 
athos@1528: \todo This is still under construction!
athos@1181: 
athos@1514: </ol>
athos@1514: <li> If you want to solve some transportation problems in a network then 
athos@1175: you will want to find shortest paths between nodes of a graph. This is 
athos@1175: usually solved using Dijkstra's algorithm. A utility
athos@1175: that solves this is  the \ref lemon::Dijkstra "LEMON Dijkstra class".
athos@1522: The following code is a simple program using the 
athos@1522: \ref lemon::Dijkstra "LEMON Dijkstra class" and it also shows how to define a map on the edges (the length
athos@1183: function):
athos@1175: 
athos@1528: \dontinclude dijkstra_demo.cc
athos@1528: \skip ListGraph
athos@1528: \until std::cout << g.id(s)
athos@1175: 
alpar@1287: See the whole program in \ref dijkstra_demo.cc.
athos@1183: 
athos@1183: The first part of the code is self-explanatory: we build the graph and set the
athos@1183: length values of the edges. Then we instantiate a member of the Dijkstra class
athos@1183: and run the Dijkstra algorithm from node \c s. After this we read some of the
athos@1183: results. 
athos@1183: You can do much more with the Dijkstra class, for example you can run it step
athos@1183: by step and gain full control of the execution. For a detailed description, see the documentation of the \ref lemon::Dijkstra "LEMON Dijkstra class".
athos@1183: 
athos@1183: 
athos@1514: <li> If you want to design a network and want to minimize the total length
athos@1175: of wires then you might be looking for a <b>minimum spanning tree</b> in
athos@1175: an undirected graph. This can be found using the Kruskal algorithm: the 
athos@1528: function \ref lemon::kruskal "LEMON Kruskal ..." does this job for you.
athos@1175: The following code fragment shows an example:
athos@1175: 
athos@1511: Ide Zsuzska fog irni!
athos@1511: 
athos@1517: <li>Many problems in network optimization can be formalized by means
athos@1517: of a linear programming problem (LP problem, for short). In our
athos@1517: library we decided not to write an LP solver, since such packages are
athos@1517: available in the commercial world just as well as in the open source
athos@1517: world, and it is also a difficult task to compete these. Instead we
athos@1517: decided to develop an interface that makes it easier to use these
athos@1517: solvers together with LEMON. The advantage of this approach is
athos@1517: twofold. Firstly our C++ interface is more comfortable than the
athos@1517: solvers' native interface. Secondly, changing the underlying solver in
athos@1517: a certain software using LEMON's LP interface needs zero effort. So,
athos@1517: for example, one may try his idea using a free solver, demonstrate its
athos@1517: usability for a customer and if it works well, but the performance
athos@1517: should be improved, then one may decide to purchase and use a better
athos@1517: commercial solver.
athos@1517: 
athos@1517: So far we have an
athos@1526: interface for the commercial LP solver software \b CPLEX (developed by ILOG)
athos@1514: and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming
athos@1517: Toolkit).
athos@1514: 
athos@1514: We will show two examples, the first one shows how simple it is to formalize
athos@1514: and solve an LP problem in LEMON, while the second one shows how LEMON
athos@1514: facilitates solving network optimization problems using LP solvers.
athos@1514: 
athos@1514: <ol>
athos@1514: <li>The following code shows how to solve an LP problem using the LEMON lp
athos@1517: interface. The code together with the comments is self-explanatory.
athos@1511: 
athos@1175: \code
athos@1175: 
athos@1514:   //A default solver is taken
athos@1514:   LpDefault lp;
athos@1514:   typedef LpDefault::Row Row;
athos@1514:   typedef LpDefault::Col Col;
athos@1514:   
athos@1514: 
athos@1514:   //This will be a maximization
athos@1514:   lp.max();
athos@1514: 
athos@1514:   //We add coloumns (variables) to our problem
athos@1514:   Col x1 = lp.addCol();
athos@1514:   Col x2 = lp.addCol();
athos@1514:   Col x3 = lp.addCol();
athos@1514: 
athos@1514:   //Constraints
athos@1514:   lp.addRow(x1+x2+x3 <=100);  
athos@1514:   lp.addRow(10*x1+4*x2+5*x3<=600);  
athos@1514:   lp.addRow(2*x1+2*x2+6*x3<=300);  
athos@1514:   //Nonnegativity of the variables
athos@1514:   lp.colLowerBound(x1, 0);
athos@1514:   lp.colLowerBound(x2, 0);
athos@1514:   lp.colLowerBound(x3, 0);
athos@1514:   //Objective function
athos@1514:   lp.setObj(10*x1+6*x2+4*x3);
athos@1514:   
athos@1514:   //Call the routine of the underlying LP solver
athos@1514:   lp.solve();
athos@1514: 
athos@1514:   //Print results
athos@1514:   if (lp.primalStatus()==LpSolverBase::OPTIMAL){
athos@1514:     printf("Z = %g; x1 = %g; x2 = %g; x3 = %g\n", 
athos@1514: 	   lp.primalValue(), 
athos@1514: 	   lp.primal(x1), lp.primal(x2), lp.primal(x3));
athos@1514:   }
athos@1514:   else{
athos@1514:     std::cout<<"Optimal solution not found!"<<std::endl;
athos@1514:   }
athos@1514: 
athos@1514: 
athos@1175: \endcode
athos@1175: 
athos@1514: See the whole code in \ref lp_demo.cc.
athos@1514: 
athos@1517: <li>The second example shows how easy it is to formalize a max-flow
athos@1517: problem as an LP problem using the LEMON LP interface: we are looking
athos@1517: for a real valued function defined on the edges of the digraph
athos@1517: satisfying the nonnegativity-, the capacity constraints and the
athos@1517: flow-conservation constraints and giving the largest flow value
athos@1517: between to designated nodes.
athos@1517: 
athos@1517: In the following code we suppose that we already have the graph \c g,
athos@1517: the capacity map \c cap, the source node \c s and the target node \c t
athos@1517: in the memory. We will also omit the typedefs.
athos@1517: 
athos@1517: \code
athos@1517:   //Define a map on the edges for the variables of the LP problem
athos@1517:   typename G::template EdgeMap<LpDefault::Col> x(g);
athos@1517:   lp.addColSet(x);
athos@1517:   
athos@1517:   //Nonnegativity and capacity constraints
athos@1517:   for(EdgeIt e(g);e!=INVALID;++e) {
athos@1517:     lp.colUpperBound(x[e],cap[e]);
athos@1517:     lp.colLowerBound(x[e],0);
athos@1517:   }
athos@1517: 
athos@1517: 
athos@1517:   //Flow conservation constraints for the nodes (except for 's' and 't')
athos@1517:   for(NodeIt n(g);n!=INVALID;++n) if(n!=s&&n!=t) {
athos@1517:     LpDefault::Expr ex;
athos@1517:     for(InEdgeIt  e(g,n);e!=INVALID;++e) ex+=x[e];
athos@1517:     for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e];
athos@1517:     lp.addRow(ex==0);
athos@1517:   }
athos@1517:   
athos@1517:   //Objective function: the flow value entering 't'
athos@1517:   {
athos@1517:     LpDefault::Expr ex;
athos@1517:     for(InEdgeIt  e(g,t);e!=INVALID;++e) ex+=x[e];
athos@1517:     for(OutEdgeIt e(g,t);e!=INVALID;++e) ex-=x[e];
athos@1517:     lp.setObj(ex);
athos@1517:   }
athos@1517: 
athos@1517:   //Maximization
athos@1517:   lp.max();
athos@1517: 
athos@1517:   //Solve with the underlying solver
athos@1517:   lp.solve();
athos@1517: 
athos@1517: \endcode
athos@1517: 
athos@1517: The complete program can be found in file \ref lp_maxflow_demo.cc. After compiling run it in the form:
athos@1517: 
athos@1528: <tt>./lp_maxflow_demo < sample.lgf</tt>
athos@1517: 
athos@1528: where sample.lgf is a file in the lemon format containing a maxflow instance (designated "source", "target" nodes and "capacity" map on the edges).
athos@1517: 
athos@1517: 
athos@1514: 
athos@1514: </ol>
athos@1514: </ul>
athos@1175: 
athos@1175: */