COIN-OR::LEMON - Graph Library

source: lemon-0.x/doc/quicktour.dox @ 1580:a9e4208cf4e3

Last change on this file since 1580:a9e4208cf4e3 was 1580:a9e4208cf4e3, checked in by athos, 18 years ago

Some changes to kruskal stuff.

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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
147this job for you.  After we had a graph \c g and a cost map \c
148edge_cost_map , the following code fragment shows an example how to get weight of the minmum spanning tree (in this first example the costs are uniform; this is of course not the case in real life applications):
151\skip std::cout
152\until kruskal
154In the variable \c tree_map the function gives back an edge bool map, which contains the edges of the found tree.
156If the costs are non-uniform, for example  the cost is given by \c
157edge_cost_map_2 , or the edges of the tree  have to be given in a
158vector, then we can give to the kruskal a vector \c tree_edge_vec , instead of
159an edge bool map:
161\skip edge_cost_map_2
162\until edge_cost_map_2, std::back_inserter
164And finally the next fragment shows how to use the functions \c makeKruskalMapInput and \c makeKruskalSequenceOutPut:
166\skip makeKruskalSequenceOutput
167\until tree_edge_vec
169See the whole program in \ref
173<li>Many problems in network optimization can be formalized by means
174of a linear programming problem (LP problem, for short). In our
175library we decided not to write an LP solver, since such packages are
176available in the commercial world just as well as in the open source
177world, and it is also a difficult task to compete these. Instead we
178decided to develop an interface that makes it easier to use these
179solvers together with LEMON. The advantage of this approach is
180twofold. Firstly our C++ interface is more comfortable than the
181solvers' native interface. Secondly, changing the underlying solver in
182a certain software using LEMON's LP interface needs zero effort. So,
183for example, one may try his idea using a free solver, demonstrate its
184usability for a customer and if it works well, but the performance
185should be improved, then one may decide to purchase and use a better
186commercial solver.
188So far we have an
189interface for the commercial LP solver software \b CPLEX (developed by ILOG)
190and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming
193We will show two examples, the first one shows how simple it is to formalize
194and solve an LP problem in LEMON, while the second one shows how LEMON
195facilitates solving network optimization problems using LP solvers.
198<li>The following code shows how to solve an LP problem using the LEMON lp
199interface. The code together with the comments is self-explanatory.
202\skip A default solver is taken
203\until End of LEMON style code
205See the whole code in \ref
207<li>The second example shows how easy it is to formalize a max-flow
208problem as an LP problem using the LEMON LP interface: we are looking
209for a real valued function defined on the edges of the digraph
210satisfying the nonnegativity-, the capacity constraints and the
211flow-conservation constraints and giving the largest flow value
212between to designated nodes.
214In the following code we suppose that we already have the graph \c g,
215the capacity map \c cap, the source node \c s and the target node \c t
216in the memory. We will also omit the typedefs.
219\skip Define a map on the edges for the variables of the LP problem
220\until lp.max();
221\skip Solve with the underlying solver
222\until lp.solve();
225The complete program can be found in file \ref After compiling run it in the form:
227<tt>./lp_maxflow_demo < sample.lgf</tt>
229where 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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