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?"
7LEMON is a C++ library, so you can use it if you want to write C++
8programs. What kind of tasks does the library LEMON help to solve?
9It helps to write programs that solve optimization problems that arise
10frequently when <b>designing and testing certain networks</b>, for example
11in telecommunication, computer networks, and other areas that I cannot
12think of now. A very natural way of modelling these networks is by means
13of a <b> graph</b> (we will always mean a directed graph by that and say
14<b> undirected graph </b> otherwise).
15So if you want to write a program that works with
16graphs then you might find it useful to use our library LEMON. LEMON
17defines various graph concepts depending on what you want to do with the
18graph: a very good description can be found in the page
19about \ref graphs "graphs".
21You will also want to assign data to the edges or nodes of the graph, for
22example a length or capacity function defined on the edges. You can do this in
23LEMON 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".
25In 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.
26You 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".
28Have fun!
30<ul> <li> The first thing to discuss is the way one can create data structures
31like graphs and maps in a program using LEMON.
32//There are more graph types
33//implemented in LEMON and you can implement your own graph type just as well:
34//read more about this in the already mentioned page on \ref graphs "graphs".
36First we show how to add nodes and edges to a graph manually. We will also
37define a map on the edges of the graph. After this we show the way one can
38read a graph (and perhaps maps on it) from a stream (e.g. a file). Of course
39we also have routines that write a graph (and perhaps maps) to a stream
40(file): this will also be shown. LEMON supports the DIMACS file formats to
41read network optimization problems, but more importantly we also have our own
42file format that gives a more flexible way to store data related to network
45<ol> <li>The following code shows how to build a graph from scratch
46and iterate on its nodes and edges.  This example also shows how to
47give a map on the edges of the graph.  The type Listgraph is one of
48the LEMON graph types: the typedefs in the beginning are for
49convenience and we will assume them later as well.
53See the whole program in file \ref in the \c demo subdir of
54LEMON package.
56    If you want to read more on the LEMON graph structures and
57concepts, read the page about \ref graphs "graphs".
60<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
61short example file in this format: read the detailed description of the LEMON
62graph file format and input-output routines here: \ref graph-io-page.
64So here is a file describing a graph of 6 nodes (0 to 5), two nodemaps
65(called \c coordinates_x and \c coordinates_y), several edges, an edge map
66called \c capacity and two designated nodes (called \c source and \c target).
68\include sample.lgf
70Finally let us give a simple example that reads a graph from a file and writes
71it to the standard output.
75See the whole program in file \ref
77<li> The following code shows how to read a graph from a stream
78(e.g. a file) in the DIMACS file format (find the documentation of the
79DIMACS file formats on the web).
82Graph g;
83std::ifstream f("graph.dim");
84readDimacs(f, g);
87One can also store network (graph+capacity on the edges) instances and
88other things (minimum cost flow instances etc.) in DIMACS format and
89read these in LEMON: to see the details read the documentation of the
90\ref dimacs.h "Dimacs file format reader".
93<li> If you want to solve some transportation problems in a network then
94you will want to find shortest paths between nodes of a graph. This is
95usually solved using Dijkstra's algorithm. A utility
96that solves this is  the \ref lemon::Dijkstra "LEMON Dijkstra class".
97The following code is a simple program using the
98\ref lemon::Dijkstra "LEMON Dijkstra class": it calculates the shortest path between node \c s and \c t in a graph \c g.
99We omit the part reading the graph  \c g and the length map \c len.
102\skip ListGraph
103\until Graph g
105\skip Dijkstra algorithm
106\until std::cout <<
108See the whole program in \ref
110Some explanation: after instantiating a member of the Dijkstra class
111we run the Dijkstra algorithm from node \c s. After this we read some
112of the results.  You can do much more with the Dijkstra class, for
113example you can run it step by step and gain full control of the
114execution. For a detailed description, see the documentation of the
115\ref lemon::Dijkstra "LEMON Dijkstra class".
118<li> If you want to design a network and want to minimize the total length
119of wires then you might be looking for a <b>minimum spanning tree</b> in
120an undirected graph. This can be found using the Kruskal algorithm: the
121function \ref lemon::kruskal "LEMON Kruskal ..." does this job for you.
122The following code fragment shows an example:
124Ide Zsuzska fog irni!
126<li>Many problems in network optimization can be formalized by means
127of a linear programming problem (LP problem, for short). In our
128library we decided not to write an LP solver, since such packages are
129available in the commercial world just as well as in the open source
130world, and it is also a difficult task to compete these. Instead we
131decided to develop an interface that makes it easier to use these
132solvers together with LEMON. The advantage of this approach is
133twofold. Firstly our C++ interface is more comfortable than the
134solvers' native interface. Secondly, changing the underlying solver in
135a certain software using LEMON's LP interface needs zero effort. So,
136for example, one may try his idea using a free solver, demonstrate its
137usability for a customer and if it works well, but the performance
138should be improved, then one may decide to purchase and use a better
139commercial solver.
141So far we have an
142interface for the commercial LP solver software \b CPLEX (developed by ILOG)
143and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming
146We will show two examples, the first one shows how simple it is to formalize
147and solve an LP problem in LEMON, while the second one shows how LEMON
148facilitates solving network optimization problems using LP solvers.
151<li>The following code shows how to solve an LP problem using the LEMON lp
152interface. The code together with the comments is self-explanatory.
155\skip A default solver is taken
156\until End of LEMON style code
158See the whole code in \ref
160<li>The second example shows how easy it is to formalize a max-flow
161problem as an LP problem using the LEMON LP interface: we are looking
162for a real valued function defined on the edges of the digraph
163satisfying the nonnegativity-, the capacity constraints and the
164flow-conservation constraints and giving the largest flow value
165between to designated nodes.
167In the following code we suppose that we already have the graph \c g,
168the capacity map \c cap, the source node \c s and the target node \c t
169in the memory. We will also omit the typedefs.
172\skip Define a map on the edges for the variables of the LP problem
173\until lp.max();
174\skip Solve with the underlying solver
175\until lp.solve();
178The complete program can be found in file \ref After compiling run it in the form:
180<tt>./lp_maxflow_demo < sample.lgf</tt>
182where 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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