COIN-OR::LEMON - Graph Library

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3\page quicktour Quick Tour to LEMON
5Let us first answer the question <b>"What do I want to use LEMON for?"</b>.
6LEMON is a C++ library, so you can use it if you want to write C++
7programs. What kind of tasks does the library LEMON help to solve?
8It helps to write programs that solve optimization problems that arise
9frequently when <b>designing and testing certain networks</b>, for example
10in telecommunication, computer networks, and other areas that I cannot
11think of now. A very natural way of modelling these networks is by means
12of a <b> graph</b> (we will always mean a directed graph by that and say
13<b> undirected graph </b> otherwise).
14So if you want to write a program that works with
15graphs then you might find it useful to use our library LEMON. LEMON
16defines various graph concepts depending on what you want to do with the
17graph: a very good description can be found in the page
18about \ref graphs "graphs".
20You will also want to assign data to the edges or nodes of the graph, for
21example a length or capacity function defined on the edges. You can do this in
22LEMON 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".
24In 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.
25You 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".
27Have fun!
29<ul> <li> The first thing to discuss is the way one can create data structures
30like graphs and maps in a program using LEMON.
31//There are more graph types
32//implemented in LEMON and you can implement your own graph type just as well:
33//read more about this in the already mentioned page on \ref graphs "graphs".
35First we show how to add nodes and edges to a graph manually. We will also
36define a map on the edges of the graph. After this we show the way one can
37read a graph (and perhaps maps on it) from a stream (e.g. a file). Of course
38we also have routines that write a graph (and perhaps maps) to a stream
39(file): this will also be shown. LEMON supports the DIMACS file formats to
40read network optimization problems, but more importantly we also have our own
41file format that gives a more flexible way to store data related to network
44<ol> <li>The following code shows how to build a graph from scratch
45and iterate on its nodes and edges.  This example also shows how to
46give a map on the edges of the graph.  The type Listgraph is one of
47the LEMON graph types: the typedefs in the beginning are for
48convenience and we will assume them later as well.
52See the whole program in file \ref in the \c demo subdir of
53LEMON package.
55    If you want to read more on the LEMON graph structures and
56concepts, read the page about \ref graphs "graphs".
59<li>LEMON has an own file format for storing graphs, maps on edges/nodes and some other things. Instead of any explanation let us give a
60short example file in this format: read the detailed description of the LEMON
61graph file format and input-output routines here: \ref graph-io-page.
63So here is a file describing a graph of 6 nodes (0 to 5), two nodemaps
64(called \c coordinates_x and \c coordinates_y), several edges, an edge map
65called \c capacity and two designated nodes (called \c source and \c target).
69id      coordinates_x   coordinates_y
705       796.398 208.035
714       573.002 63.002
723       568.549 401.748
732       277.889 68.476
741       288.248 397.327
750       102.239 257.532
77                id      capacity
784       5       6       8
793       5       5       8
802       4       4       5
811       4       3       8
821       3       2       5
830       2       1       10
840       1       0       10
85#This is a comment here
87source 0
88target 5
91author "Attila BERNATH"
95Finally let us give a simple example that reads a graph from a file and writes
96it to the standard output.
100See the whole program in file \ref
102<li> The following code shows how to read a graph from a stream
103(e.g. a file) in the DIMACS file format (find the documentation of the
104DIMACS file formats on the web).
107Graph g;
108std::ifstream f("graph.dim");
109readDimacs(f, g);
112One can also store network (graph+capacity on the edges) instances and
113other things (minimum cost flow instances etc.) in DIMACS format and
114read these in LEMON: to see the details read the documentation of the
115\ref dimacs.h "Dimacs file format reader".
118<li> If you want to solve some transportation problems in a network then
119you will want to find shortest paths between nodes of a graph. This is
120usually solved using Dijkstra's algorithm. A utility
121that solves this is  the \ref lemon::Dijkstra "LEMON Dijkstra class".
122The following code is a simple program using the
123\ref lemon::Dijkstra "LEMON Dijkstra class": it calculates the shortest path between node \c s and \c t in a graph \c g.
124We omit the part reading the graph  \c g and the length map \c len.
127\skip ListGraph
128\until Graph g
130\skip Dijkstra algorithm
131\until std::cout <<
133See the whole program in \ref
135Some explanation: after instantiating a member of the Dijkstra class
136we run the Dijkstra algorithm from node \c s. After this we read some
137of the results.  You can do much more with the Dijkstra class, for
138example you can run it step by step and gain full control of the
139execution. For a detailed description, see the documentation of the
140\ref lemon::Dijkstra "LEMON Dijkstra class".
143<li> If you want to design a network and want to minimize the total
144length of wires then you might be looking for a <b>minimum spanning
145tree</b> in an undirected graph. This can be found using the Kruskal
146algorithm: the function \ref lemon::kruskal "LEMON Kruskal " does this
147job for you. 
149First make a graph \c g and a cost map \c
150edge_cost_map, then make a bool edgemap \c tree_map or a vector \c
151tree_edge_vec for the algorithm output. After calling the function it
152gives back the weight of the minimum spanning tree and the \c tree_map or
153the \c tree_edge_vec contains the edges of the tree.
155If you want to store the edges in a bool edgemap, then use the
156function as follows:
159\skip Kruskal with boolmap;
160\until  std::endl
162And if you rather use a vector instead of a bool map:
164\skip Kruskal with vector;
165\until std::endl
167See the whole program in \ref
171<li>Many problems in network optimization can be formalized by means
172of a linear programming problem (LP problem, for short). In our
173library we decided not to write an LP solver, since such packages are
174available in the commercial world just as well as in the open source
175world, and it is also a difficult task to compete these. Instead we
176decided to develop an interface that makes it easier to use these
177solvers together with LEMON. The advantage of this approach is
178twofold. Firstly our C++ interface is more comfortable than the
179solvers' native interface. Secondly, changing the underlying solver in
180a certain software using LEMON's LP interface needs zero effort. So,
181for example, one may try his idea using a free solver, demonstrate its
182usability for a customer and if it works well, but the performance
183should be improved, then one may decide to purchase and use a better
184commercial solver.
186So far we have an
187interface for the commercial LP solver software \b CPLEX (developed by ILOG)
188and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming
191We will show two examples, the first one shows how simple it is to formalize
192and solve an LP problem in LEMON, while the second one shows how LEMON
193facilitates solving network optimization problems using LP solvers.
196<li>The following code shows how to solve an LP problem using the LEMON lp
197interface. The code together with the comments is self-explanatory.
200\skip A default solver is taken
201\until End of LEMON style code
203See the whole code in \ref
205<li>The second example shows how easy it is to formalize a max-flow
206problem as an LP problem using the LEMON LP interface: we are looking
207for a real valued function defined on the edges of the digraph
208satisfying the nonnegativity-, the capacity constraints and the
209flow-conservation constraints and giving the largest flow value
210between to designated nodes.
212In the following code we suppose that we already have the graph \c g,
213the capacity map \c cap, the source node \c s and the target node \c t
214in the memory. We will also omit the typedefs.
217\skip Define a map on the edges for the variables of the LP problem
218\until lp.max();
219\skip Solve with the underlying solver
220\until lp.solve();
223The complete program can be found in file \ref After compiling run it in the form:
225<tt>./lp_maxflow_demo < sample.lgf</tt>
227where sample.lgf is a file in the lemon format containing a maxflow instance (designated "source", "target" nodes and "capacity" map on the edges).
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