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@1511: 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):
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@1522: \code 
athos@1522: 
athos@1522:   typedef ListGraph Graph; 
athos@1175:   typedef Graph::NodeIt NodeIt;
athos@1175: 
athos@1175:   Graph g;
athos@1175:   
athos@1175:   for (int i = 0; i < 3; i++)
athos@1175:     g.addNode();
athos@1175:   
athos@1175:   for (NodeIt i(g); i!=INVALID; ++i)
athos@1175:     for (NodeIt j(g); j!=INVALID; ++j)
athos@1175:       if (i != j) g.addEdge(i, j);
athos@1522: 
athos@1522: \endcode 
athos@1175: 
athos@1511: See the whole program in file \ref helloworld.cc.
athos@1511: 
athos@1514:     If you want to read more on the LEMON graph structures and concepts, read the page about \ref graphs "graphs". 
athos@1181: 
athos@1522: <li> The following code shows how to read a graph from a stream (e.g. a file)
athos@1522: in the DIMACS file format (find the documentation of the 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@1522: One can also store network (graph+capacity on the edges) instances and other
athos@1522: things (minimum cost flow instances etc.) in DIMACS format and use these in LEMON: to see the details read the
athos@1522: documentation of the \ref dimacs.h "Dimacs file format reader". There you will
athos@1522: also find the details about the output routines into files of the DIMACS
athos@1522: format. 
athos@1522: 
athos@1522: <li>We needed much greater flexibility than the DIMACS formats could give us,
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@1522: \todo Maybe another example would be better here.
athos@1522: 
athos@1522: \code
athos@1522: @nodeset
athos@1522: id	coordinates_x	coordinates_y	
athos@1522: 9	447.907	578.328	
athos@1522: 8	79.2573	909.464	
athos@1522: 7	878.677	960.04	
athos@1522: 6	11.5504	938.413	
athos@1522: 5	327.398	815.035	
athos@1522: 4	427.002	954.002	
athos@1522: 3	148.549	753.748	
athos@1522: 2	903.889	326.476	
athos@1522: 1	408.248	577.327	
athos@1522: 0	189.239	92.5316	
athos@1522: @edgeset
athos@1522: 		length	
athos@1522: 2	3	901.074	
athos@1522: 8	5	270.85	
athos@1522: 6	9	601.553	
athos@1522: 5	9	285.022	
athos@1522: 9	4	408.091	
athos@1522: 3	0	719.712	
athos@1522: 7	5	612.836	
athos@1522: 0	4	933.353	
athos@1522: 5	0	778.871	
athos@1522: 5	5	0	
athos@1522: 7	1	664.049	
athos@1522: 5	5	0	
athos@1522: 0	9	560.464	
athos@1522: 4	8	352.36	
athos@1522: 4	9	399.625	
athos@1522: 4	1	402.171	
athos@1522: 1	2	591.688	
athos@1522: 3	8	182.376	
athos@1522: 4	5	180.254	
athos@1522: 3	1	345.283	
athos@1522: 5	4	184.511	
athos@1522: 6	2	1112.45	
athos@1522: 0	1	556.624	
athos@1522: @nodes
athos@1522: source	1	
athos@1522: target	8	
athos@1522: @end
athos@1522: \endcode
athos@1522: 
athos@1522: Finally let us give a simple example that reads a graph from a file and writes
athos@1522: it to another.
athos@1522: 
athos@1522: \todo This is to be done!
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@1175: \code
athos@1183: 
athos@1183:     typedef ListGraph Graph;
athos@1183:     typedef Graph::Node Node;
athos@1183:     typedef Graph::Edge Edge;
athos@1183:     typedef Graph::EdgeMap<int> LengthMap;
athos@1183: 
athos@1183:     Graph g;
athos@1183: 
athos@1183:     //An example from Ahuja's book
athos@1183: 
athos@1183:     Node s=g.addNode();
athos@1183:     Node v2=g.addNode();
athos@1183:     Node v3=g.addNode();
athos@1183:     Node v4=g.addNode();
athos@1183:     Node v5=g.addNode();
athos@1183:     Node t=g.addNode();
athos@1183: 
athos@1183:     Edge s_v2=g.addEdge(s, v2);
athos@1183:     Edge s_v3=g.addEdge(s, v3);
athos@1183:     Edge v2_v4=g.addEdge(v2, v4);
athos@1183:     Edge v2_v5=g.addEdge(v2, v5);
athos@1183:     Edge v3_v5=g.addEdge(v3, v5);
athos@1183:     Edge v4_t=g.addEdge(v4, t);
athos@1183:     Edge v5_t=g.addEdge(v5, t);
athos@1183:   
athos@1183:     LengthMap len(g);
athos@1183: 
athos@1183:     len.set(s_v2, 10);
athos@1183:     len.set(s_v3, 10);
athos@1183:     len.set(v2_v4, 5);
athos@1183:     len.set(v2_v5, 8);
athos@1183:     len.set(v3_v5, 5);
athos@1183:     len.set(v4_t, 8);
athos@1183:     len.set(v5_t, 8);
athos@1183: 
athos@1511:     std::cout << "The id of s is " << g.id(s)<< std::endl;
athos@1511:     std::cout <<"The id of t is " << g.id(t)<<"."<<std::endl;
athos@1183: 
athos@1183:     std::cout << "Dijkstra algorithm test..." << std::endl;
athos@1183: 
athos@1183:     Dijkstra<Graph, LengthMap> dijkstra_test(g,len);
athos@1183:     
athos@1183:     dijkstra_test.run(s);
athos@1183: 
athos@1183:     
athos@1183:     std::cout << "The distance of node t from node s: " << dijkstra_test.dist(t)<<std::endl;
athos@1183: 
athos@1511:     std::cout << "The shortest path from s to t goes through the following nodes" <<std::endl;
athos@1511:  std::cout << " (the first one is t, the last one is s): "<<std::endl;
athos@1183: 
athos@1183:     for (Node v=t;v != s; v=dijkstra_test.predNode(v)){
athos@1183: 	std::cout << g.id(v) << "<-";
athos@1183:     }
athos@1183:     std::cout << g.id(s) << std::endl;	
athos@1175: \endcode
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@1175: class \ref lemon::Kruskal "LEMON Kruskal class" 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@1514: interface for the commercial LP solver software \b CLPLEX (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@1517: <tt>./lp_maxflow_demo < ?????????.lgf</tt>
athos@1517: 
athos@1521: where ?????????.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: */