3 \page quicktour Quick Tour to LEMON
5 Let us first answer the question <b>"What do I want to use LEMON for?"</b>.
6 LEMON is a C++ library, so you can use it if you want to write C++
7 programs. What kind of tasks does the library LEMON help to solve?
8 It helps to write programs that solve optimization problems that arise
9 frequently when <b>designing and testing certain networks</b>, for example
10 in telecommunication, computer networks, and other areas that I cannot
11 think of now. A very natural way of modelling these networks is by means
12 of a <b> graph</b> (we will always mean a directed graph by that and say
13 <b> undirected graph </b> otherwise).
14 So if you want to write a program that works with
15 graphs then you might find it useful to use our library LEMON. LEMON
16 defines various graph concepts depending on what you want to do with the
17 graph: a very good description can be found in the page
18 about \ref graphs "graphs".
20 You will also want to assign data to the edges or nodes of the graph, for
21 example a length or capacity function defined on the edges. You can do this in
22 LEMON 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".
24 In 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.
25 You 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".
29 <ul> <li> The first thing to discuss is the way one can create data structures
30 like 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".
35 First we show how to add nodes and edges to a graph manually. We will also
36 define a map on the edges of the graph. After this we show the way one can
37 read a graph (and perhaps maps on it) from a stream (e.g. a file). Of course
38 we 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
40 read network optimization problems, but more importantly we also have our own
41 file 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
45 and iterate on its nodes and edges. This example also shows how to
46 give a map on the edges of the graph. The type Listgraph is one of
47 the LEMON graph types: the typedefs in the beginning are for
48 convenience and we will assume them later as well.
50 \include hello_lemon.cc
52 See the whole program in file \ref hello_lemon.cc in the \c demo subdir of
55 If you want to read more on the LEMON graph structures and
56 concepts, 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
60 short example file in this format: read the detailed description of the LEMON
61 graph file format and input-output routines here: \ref graph-io-page.
63 So 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
65 called \c capacity and two designated nodes (called \c source and \c target).
69 id coordinates_x coordinates_y
85 #This is a comment here
91 author "Attila BERNATH"
95 Finally let us give a simple example that reads a graph from a file and writes
96 it to the standard output.
98 \include reader_writer_demo.cc
100 See the whole program in file \ref reader_writer_demo.cc.
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
104 DIMACS file formats on the web).
108 std::ifstream f("graph.dim");
112 One can also store network (graph+capacity on the edges) instances and
113 other things (minimum cost flow instances etc.) in DIMACS format and
114 read 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
119 you will want to find shortest paths between nodes of a graph. This is
120 usually solved using Dijkstra's algorithm. A utility
121 that solves this is the \ref lemon::Dijkstra "LEMON Dijkstra class".
122 The 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.
124 We omit the part reading the graph \c g and the length map \c len.
126 \dontinclude dijkstra_demo.cc
130 \skip Dijkstra algorithm
131 \until std::cout << g.id(s)
133 See the whole program in \ref dijkstra_demo.cc.
135 Some explanation: after instantiating a member of the Dijkstra class
136 we run the Dijkstra algorithm from node \c s. After this we read some
137 of the results. You can do much more with the Dijkstra class, for
138 example you can run it step by step and gain full control of the
139 execution. 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
144 length of wires then you might be looking for a <b>minimum spanning
145 tree</b> in an undirected graph. This can be found using the Kruskal
146 algorithm: the function \ref lemon::kruskal "LEMON Kruskal " does
147 this job for you. After we had a graph \c g and a cost map \c
148 edge_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):
150 \dontinclude kruskal_demo.cc
154 In the variable \c tree_map the function gives back an edge bool map, which contains the edges of the found tree.
156 If the costs are non-uniform, for example the cost is given by \c
157 edge_cost_map_2 , or the edges of the tree have to be given in a
158 vector, then we can give to the kruskal a vector \c tree_edge_vec , instead of
161 \skip edge_cost_map_2
162 \until edge_cost_map_2, std::back_inserter
164 And finally the next fragment shows how to use the functions \c makeKruskalMapInput and \c makeKruskalSequenceOutPut:
166 \skip makeKruskalSequenceOutput
169 See the whole program in \ref kruskal_demo.cc.
173 <li>Many problems in network optimization can be formalized by means
174 of a linear programming problem (LP problem, for short). In our
175 library we decided not to write an LP solver, since such packages are
176 available in the commercial world just as well as in the open source
177 world, and it is also a difficult task to compete these. Instead we
178 decided to develop an interface that makes it easier to use these
179 solvers together with LEMON. The advantage of this approach is
180 twofold. Firstly our C++ interface is more comfortable than the
181 solvers' native interface. Secondly, changing the underlying solver in
182 a certain software using LEMON's LP interface needs zero effort. So,
183 for example, one may try his idea using a free solver, demonstrate its
184 usability for a customer and if it works well, but the performance
185 should be improved, then one may decide to purchase and use a better
189 interface for the commercial LP solver software \b CPLEX (developed by ILOG)
190 and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming
193 We will show two examples, the first one shows how simple it is to formalize
194 and solve an LP problem in LEMON, while the second one shows how LEMON
195 facilitates solving network optimization problems using LP solvers.
198 <li>The following code shows how to solve an LP problem using the LEMON lp
199 interface. The code together with the comments is self-explanatory.
201 \dontinclude lp_demo.cc
202 \skip A default solver is taken
203 \until End of LEMON style code
205 See the whole code in \ref lp_demo.cc.
207 <li>The second example shows how easy it is to formalize a max-flow
208 problem as an LP problem using the LEMON LP interface: we are looking
209 for a real valued function defined on the edges of the digraph
210 satisfying the nonnegativity-, the capacity constraints and the
211 flow-conservation constraints and giving the largest flow value
212 between to designated nodes.
214 In the following code we suppose that we already have the graph \c g,
215 the capacity map \c cap, the source node \c s and the target node \c t
216 in the memory. We will also omit the typedefs.
218 \dontinclude lp_maxflow_demo.cc
219 \skip Define a map on the edges for the variables of the LP problem
221 \skip Solve with the underlying solver
225 The complete program can be found in file \ref lp_maxflow_demo.cc. After compiling run it in the form:
227 <tt>./lp_maxflow_demo < sample.lgf</tt>
229 where sample.lgf is a file in the lemon format containing a maxflow instance (designated "source", "target" nodes and "capacity" map on the edges).