COIN-OR::LEMON - Graph Library

source: lemon-0.x/doc/quicktour.dox @ 1640:9c7834ac5e64

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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.
51\skip include
52\until }
54See the whole program in file \ref in the \c demo subdir of
55LEMON package.
57    If you want to read more on the LEMON graph structures and
58concepts, read the page about \ref graphs "graphs".
61<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
62short example file in this format: read the detailed description of the LEMON
63graph file format and input-output routines here: \ref graph-io-page.
65So here is a file describing a graph of 6 nodes (0 to 5), two nodemaps
66(called \c coordinates_x and \c coordinates_y), several edges, an edge map
67called \c capacity and two designated nodes (called \c source and \c target).
71id      coordinates_x   coordinates_y
725       796.398 208.035
734       573.002 63.002
743       568.549 401.748
752       277.889 68.476
761       288.248 397.327
770       102.239 257.532
79                id      capacity
804       5       6       8
813       5       5       8
822       4       4       5
831       4       3       8
841       3       2       5
850       2       1       10
860       1       0       10
87#This is a comment here
89source 0
90target 5
93author "Attila BERNATH"
97Finally let us give a simple example that reads a graph from a file and writes
98it to the standard output.
101\skip include
102\until return
103\until }
105See the whole program in file \ref
107<li> The following code shows how to read a graph from a stream
108(e.g. a file) in the DIMACS file format (find the documentation of the
109DIMACS file formats on the web).
112Graph g;
113std::ifstream f("graph.dim");
114readDimacs(f, g);
117One can also store network (graph+capacity on the edges) instances and
118other things (minimum cost flow instances etc.) in DIMACS format and
119read these in LEMON: to see the details read the documentation of the
120\ref dimacs.h "Dimacs file format reader".
123<li> If you want to solve some transportation problems in a network then
124you will want to find shortest paths between nodes of a graph. This is
125usually solved using Dijkstra's algorithm. A utility
126that solves this is  the \ref lemon::Dijkstra "LEMON Dijkstra class".
127The following code is a simple program using the
128\ref lemon::Dijkstra "LEMON Dijkstra class": it calculates the shortest path between node \c s and \c t in a graph \c g.
129We omit the part reading the graph  \c g and the length map \c len.
132\skip ListGraph
133\until Graph g
135\skip Dijkstra algorithm
136\until std::cout <<
138See the whole program in \ref
140Some explanation: after instantiating a member of the Dijkstra class
141we run the Dijkstra algorithm from node \c s. After this we read some
142of the results.  You can do much more with the Dijkstra class, for
143example you can run it step by step and gain full control of the
144execution. For a detailed description, see the documentation of the
145\ref lemon::Dijkstra "LEMON Dijkstra class".
148<li> If you want to design a network and want to minimize the total
149length of wires then you might be looking for a <b>minimum spanning
150tree</b> in an undirected graph. This can be found using the Kruskal
151algorithm: the function \ref lemon::kruskal "LEMON Kruskal " does this
152job for you. 
154First make a graph \c g and a cost map \c
155edge_cost_map, then make a bool edgemap \c tree_map or a vector \c
156tree_edge_vec for the algorithm output. After calling the function it
157gives back the weight of the minimum spanning tree and the \c tree_map or
158the \c tree_edge_vec contains the edges of the tree.
160If you want to store the edges in a bool edgemap, then use the
161function as follows:
164\skip Kruskal with boolmap;
165\until  std::endl
167And if you rather use a vector instead of a bool map:
169\skip Kruskal with vector;
170\until std::endl
172See the whole program in \ref
176<li>Many problems in network optimization can be formalized by means
177of a linear programming problem (LP problem, for short). In our
178library we decided not to write an LP solver, since such packages are
179available in the commercial world just as well as in the open source
180world, and it is also a difficult task to compete these. Instead we
181decided to develop an interface that makes it easier to use these
182solvers together with LEMON. The advantage of this approach is
183twofold. Firstly our C++ interface is more comfortable than the
184solvers' native interface. Secondly, changing the underlying solver in
185a certain software using LEMON's LP interface needs zero effort. So,
186for example, one may try his idea using a free solver, demonstrate its
187usability for a customer and if it works well, but the performance
188should be improved, then one may decide to purchase and use a better
189commercial solver.
191So far we have an
192interface for the commercial LP solver software \b CPLEX (developed by ILOG)
193and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming
196We will show two examples, the first one shows how simple it is to formalize
197and solve an LP problem in LEMON, while the second one shows how LEMON
198facilitates solving network optimization problems using LP solvers.
201<li>The following code shows how to solve an LP problem using the LEMON lp
202interface. The code together with the comments is self-explanatory.
205\skip A default solver is taken
206\until End of LEMON style code
208See the whole code in \ref
210<li>The second example shows how easy it is to formalize a max-flow
211problem as an LP problem using the LEMON LP interface: we are looking
212for a real valued function defined on the edges of the digraph
213satisfying the nonnegativity-, the capacity constraints and the
214flow-conservation constraints and giving the largest flow value
215between to designated nodes.
217In the following code we suppose that we already have the graph \c g,
218the capacity map \c cap, the source node \c s and the target node \c t
219in the memory. We will also omit the typedefs.
222\skip Define a map on the edges for the variables of the LP problem
223\until lp.max();
224\skip Solve with the underlying solver
225\until lp.solve();
228The complete program can be found in file \ref After compiling run it in the form:
230<tt>./lp_maxflow_demo < sample.lgf</tt>
232where 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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