COIN-OR::LEMON - Graph Library

source: lemon-0.x/doc/quicktour.dox

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1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2008
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
21\page quicktour Quick Tour to LEMON
23Let us first answer the question <b>"What do I want to use LEMON for?"</b>.
24LEMON is a C++ library, so you can use it if you want to write C++
25programs. What kind of tasks does the library LEMON help to solve?
26It helps to write programs that solve optimization problems that arise
27frequently when <b>designing and testing certain networks</b>, for example
28in telecommunication, computer networks, and other areas that I cannot
29think of now. A very natural way of modelling these networks is by means
30of a <b> graph</b> (we will always mean a directed graph by that and say
31<b> undirected graph </b> otherwise).
32So if you want to write a program that works with
33graphs then you might find it useful to use our library LEMON. LEMON
34defines various graph concepts depending on what you want to do with the
35graph: a very good description can be found in the page
36about \ref graphs "graphs".
38You will also want to assign data to the edges or nodes of the graph, for
39example a length or capacity function defined on the edges. You can do this in
40LEMON 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".
42In 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.
43You 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".
45Have fun!
47<ul> <li> The first thing to discuss is the way one can create data structures
48like graphs and maps in a program using LEMON.
49//There are more graph types
50//implemented in LEMON and you can implement your own graph type just as well:
51//read more about this in the already mentioned page on \ref graphs "graphs".
53First we show how to add nodes and edges to a graph manually. We will also
54define a map on the edges of the graph. After this we show the way one can
55read a graph (and perhaps maps on it) from a stream (e.g. a file). Of course
56we also have routines that write a graph (and perhaps maps) to a stream
57(file): this will also be shown. LEMON supports the DIMACS file formats to
58read network optimization problems, but more importantly we also have our own
59file format that gives a more flexible way to store data related to network
62<ol> <li>The following code shows how to build a graph from scratch
63and iterate on its nodes and edges.  This example also shows how to
64give a map on the edges of the graph.  The type Listgraph is one of
65the LEMON graph types: the typedefs in the beginning are for
66convenience and we will assume them later as well.
69\skip include
70\until }
72See the whole program in file \ref in the \c demo subdir of
73LEMON package.
75    If you want to read more on the LEMON graph structures and
76concepts, read the page about \ref graphs "graphs".
79<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
80short example file in this format: read the detailed description of the LEMON
81graph file format and input-output routines here: \ref graph-io-page.
83So here is a file describing a graph of 6 nodes (0 to 5), two nodemaps
84(called \c coordinates_x and \c coordinates_y), several edges, an edge map
85called \c capacity and two designated nodes (called \c source and \c target).
89id      coordinates_x   coordinates_y
905       796.398 208.035
914       573.002 63.002
923       568.549 401.748
932       277.889 68.476
941       288.248 397.327
950       102.239 257.532
97                id      capacity
984       5       6       8
993       5       5       8
1002       4       4       5
1011       4       3       8
1021       3       2       5
1030       2       1       10
1040       1       0       10
105#This is a comment here
107source 0
108target 5
111author "Attila BERNATH"
115Finally let us give a simple example that reads a graph from a file and writes
116it to the standard output.
119\skip include
120\until return
121\until }
123See the whole program in file \ref
125<li> The following code shows how to read a graph from a stream
126(e.g. a file) in the DIMACS file format (find the documentation of the
127DIMACS file formats on the web).
130Graph g;
131std::ifstream f("graph.dim");
132readDimacs(f, g);
135One can also store network (graph+capacity on the edges) instances and
136other things (minimum cost flow instances etc.) in DIMACS format and
137read these in LEMON: to see the details read the documentation of the
138\ref dimacs.h "Dimacs file format reader".
141<li> If you want to solve some transportation problems in a network then
142you will want to find shortest paths between nodes of a graph. This is
143usually solved using Dijkstra's algorithm. A utility
144that solves this is  the \ref lemon::Dijkstra "LEMON Dijkstra class".
145The following code is a simple program using the
146\ref lemon::Dijkstra "LEMON Dijkstra class": it calculates the shortest path between node \c s and \c t in a graph \c g.
147We omit the part reading the graph  \c g and the length map \c len.
150\skip ListGraph
151\until Graph g
153\skip Dijkstra algorithm
154\until std::cout <<
156See the whole program in \ref
158Some explanation: after instantiating a member of the Dijkstra class
159we run the Dijkstra algorithm from node \c s. After this we read some
160of the results.  You can do much more with the Dijkstra class, for
161example you can run it step by step and gain full control of the
162execution. For a detailed description, see the documentation of the
163\ref lemon::Dijkstra "LEMON Dijkstra class".
166<li> If you want to design a network and want to minimize the total
167length of wires then you might be looking for a <b>minimum spanning
168tree</b> in an undirected graph. This can be found using the Kruskal
169algorithm: the function \ref lemon::kruskal "LEMON Kruskal " does this
170job for you. 
172First make a graph \c g and a cost map \c
173edge_cost_map, then make a bool edgemap \c tree_map or a vector \c
174tree_edge_vec for the algorithm output. After calling the function it
175gives back the weight of the minimum spanning tree and the \c tree_map or
176the \c tree_edge_vec contains the edges of the tree.
178If you want to store the edges in a bool edgemap, then use the
179function as follows:
182\skip Kruskal with boolmap;
183\until  std::endl
185And if you rather use a vector instead of a bool map:
187\skip Kruskal with vector;
188\until std::endl
190See the whole program in \ref
194<li>Many problems in network optimization can be formalized by means
195of a linear programming problem (LP problem, for short). In our
196library we decided not to write an LP solver, since such packages are
197available in the commercial world just as well as in the open source
198world, and it is also a difficult task to compete these. Instead we
199decided to develop an interface that makes it easier to use these
200solvers together with LEMON. The advantage of this approach is
201twofold. Firstly our C++ interface is more comfortable than the
202solvers' native interface. Secondly, changing the underlying solver in
203a certain software using LEMON's LP interface needs zero effort. So,
204for example, one may try his idea using a free solver, demonstrate its
205usability for a customer and if it works well, but the performance
206should be improved, then one may decide to purchase and use a better
207commercial solver.
209So far we have an
210interface for the commercial LP solver software \b CPLEX (developed by ILOG)
211and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming
214We will show two examples, the first one shows how simple it is to formalize
215and solve an LP problem in LEMON, while the second one shows how LEMON
216facilitates solving network optimization problems using LP solvers.
219<li>The following code shows how to solve an LP problem using the LEMON lp
220interface. The code together with the comments is self-explanatory.
223\skip A default solver is taken
224\until End of LEMON style code
226See the whole code in \ref
228<li>The second example shows how easy it is to formalize a max-flow
229problem as an LP problem using the LEMON LP interface: we are looking
230for a real valued function defined on the edges of the digraph
231satisfying the nonnegativity-, the capacity constraints and the
232flow-conservation constraints and giving the largest flow value
233between to designated nodes.
235In the following code we suppose that we already have the graph \c g,
236the capacity map \c cap, the source node \c s and the target node \c t
237in the memory. We will also omit the typedefs.
240\skip Define a map on the edges for the variables of the LP problem
241\until lp.max();
242\skip Solve with the underlying solver
243\until lp.solve();
246The complete program can be found in file \ref After compiling run it in the form:
248<tt>./lp_maxflow_demo < sample.lgf</tt>
250where 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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