COIN-OR::LEMON - Graph Library

source: lemon-tutorial/algorithms.dox @ 50:72867897fcba

Last change on this file since 50:72867897fcba was 50:72867897fcba, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Minor improvements

File size: 8.3 KB
Line 
1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
5 * Copyright (C) 2003-2010
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 */
18
19namespace lemon {
20/**
21[PAGE]sec_algorithms[PAGE] Algorithms
22
23\todo This page is under construction.
24
25In addition to the graph structures, the most important parts of LEMON are
26the various algorithms related to graph theory and combinatorial optimization.
27The library probvides quite flexible and efficient implementations
28for well-known fundamental algorithms, such as breadth-first
29search (BFS), depth-first search (DFS), Dijkstra algorithm, Kruskal algorithm
30and methods for discovering graph properties like connectivity, bipartiteness
31or Euler property, as well as more complex optimization algorithms for finding
32maximum flows, minimum cuts, matchings, minimum cost flows and arc-disjoint
33paths.
34
35In this section, we present only some of the most fundamental algorithms.
36For a complete overview, see the \ref algs module of the reference manual.
37
38[SEC]sec_graph_search[SEC] Graph Search
39
40\todo The following contents are ported from the LEMON 0.x tutorial,
41thus they have to thouroughly revised, reorganized and reworked.
42
43See \ref Bfs, \ref Dfs and \ref graph_properties.
44
45Both \ref lemon::Bfs "Bfs" and \ref lemon::Dfs "Dfs" are highly adaptable and efficient
46implementations of the well known algorithms. The algorithms are placed most cases in
47separated files named after the algorithm itself but lower case as all other header file names.
48For example the next Bfs class is in the \c lemon/bfs.h.
49
50The algorithm is implemented in the \ref lemon::Bfs "Bfs" template class - rather than as function.
51The class has two template parameters: \b GR and \b TR.<br>
52GR is the digraph the algorithm runs on. It has \ref lemon::ListDigraph "ListDigraph" as default type.
53TR is a Traits class commonly used to easy the parametrization of templates. In most cases you
54wont need to modify the default type \ref lemon::BfsDefaultTraits "BfsDefaultTraits<GR>".
55
56To use the class, declare it!
57\code
58Bfs<ListGraph>  bfs(gr);
59\endcode
60Note the lack of second template argument because of the default parameter.
61
62It provides a simple but powerful interface to control the execution.
63\code
64int dist = bfs.run(s,t);
65\endcode
66It finds the shortest path from node \c s to node \c t and returns it, or zero
67if there is no path from \c s to \c t.<br>
68If you want the shortest path from a specified node to all other node, just write:
69\code
70bfs.run(s);
71\endcode
72Now the distances and path information are stored in maps which you can access with
73member functions like \ref lemon::Bfs::distMap "distMap()" or \ref lemon::Bfs::predMap "predMap()".<br>
74Or more directly with other member functions like \ref lemon::Bfs::predNode "predNode()". Once the algorithm
75is finished (or to be precise reached that node) \ref lemon::Bfs::dist "dist()" or \ref lemon::Bfs::predNode
76"predNode()" can be called.
77
78For an example let's say we want to print the shortest path of those nodes which
79are in a certain distance.
80\code
81bfs.run(s);
82
83for( ListGraph::NodeIt  n(gr); n != INVALID; ++n ) {
84  if( bfs.reached(n) && bfs.dist(n) <= max_dist ) {
85    std::cout << gr.id(n);
86
87    Node  prev = bfs.prevNode(n);
88    while( prev != INVALID ) {
89      std::cout << "<-" << gr.id(prev);
90      prev = bfs.prevNode(n);
91    }
92   
93    std::cout << std::endl;
94  }
95}
96\endcode
97
98In the previous code we only used \c run(). Now we introduce the way you can directly
99control the execution of the algorithm.
100
101First you have to initialize the variables with \ref lemon::Bfs::init "init()".
102\code
103  bfs.init();
104\endcode
105
106Then you add one or more source nodes to the queue. They will be processed, as they would
107be reached by the algorithm before. And yes - you can add more sources during the execution.
108\code
109  bfs.addSource(node_1);
110  bfs.addSource(node_2);
111  ...
112\endcode
113
114And finally you can start the process with \ref lemon::Bfs::start "start()", or
115you can write your own loop to process the nodes one-by-one.
116
117
118Since Dfs is very similar to Bfs with a few tiny differences we only see a bit more complex example
119to demonstrate Dfs's capabilities.
120
121We will see a program, which solves the problem of <b>topological ordering</b>.
122We need to know in which order we should put on our clothes. The program will do the following:
123<ol>
124<li>We run the dfs algorithm to all nodes.
125<li>Put every node into a list when processed completely.
126<li>Write out the list in reverse order.
127</ol>
128
129\dontinclude topological_ordering.cc
130First of all we will need an own \ref lemon::Dfs::ProcessedMap "ProcessedMap". The ordering
131will be done through it.
132\skip MyOrdererMap
133\until };
134The class meets the \ref concepts::WriteMap "WriteMap" concept. In it's \c set() method the only thing
135we need to do is insert the key - that is the node whose processing just finished - into the beginning
136of the list.<br>
137Although we implemented this needed helper class ourselves it was not necessary.
138The \ref lemon::FrontInserterBoolMap "FrontInserterBoolMap" class does exactly
139what we needed. To be correct it's more general - and it's all in \c LEMON. But
140we wanted to show you, how easy is to add additional functionality.
141
142First we declare the needed data structures: the digraph and a map to store the nodes' label.
143\skip ListDigraph
144\until label
145
146Now we build a digraph. But keep in mind that it must be DAG because cyclic digraphs has no topological
147ordering.
148\skip belt
149\until trousers
150We label them...
151\skip label
152\until trousers
153Then add arcs which represent the precedences between those items.
154\skip trousers, belt
155\until );
156
157See how easy is to access the internal information of this algorithm trough maps.
158We only need to set our own map as the class's \ref lemon::Dfs::ProcessedMap "ProcessedMap".
159\skip Dfs
160\until run
161
162And now comes the third part. Write out the list in reverse order. But the list was
163composed in reverse way (with \c push_front() instead of \c push_back() so we just iterate it.
164\skip std
165\until endl
166
167The program is to be found in the \ref demo directory: \ref topological_ordering.cc
168
169\todo Check the linking of the demo file, the code samples are missing.
170
171More algorithms are described in the \ref algorithms2 "second part".
172
173
174[SEC]sec_shortest_paths[SEC] Shortest Paths
175
176See \ref Dijkstra and \ref BellmanFord.
177
178
179If you want to solve some transportation problems in a network then you
180will want to find shortest paths between nodes of a graph. This is
181usually solved using Dijkstra's algorithm. A utility that solves this is
182the LEMON Dijkstra class. The following code is a simple program using
183the LEMON Dijkstra class: it calculates the shortest path between node s
184and t in a graph g. We omit the part reading the graph g and the length
185map len.
186
187<hr>
188 
189In LEMON, the algorithms are implemented basically as classes, but
190for some of them, function-type interfaces are also available
191for the sake of convenience.
192For instance, the Dijkstra algorithm is implemented in the \ref Dijkstra
193template class, but the \ref dijkstra() function is also defined,
194which can still be used quite flexibly due to named parameters.
195
196The original sample code could also use the class interface as follows.
197
198\code
199  Dijkstra<ListDigraph> dijkstra(g, length);
200  dijkstra.distMap(dist);
201  dijsktra.init();
202  dijkstra.addSource(u);
203  dijkstra.start();
204\endcode
205
206The previous code is obviously longer than the original, but the
207execution can be controlled to a higher extent. While using the function-type
208interface, only one source can be added to the algorithm, the class
209interface makes it possible to specify several root nodes.
210Moreover, the algorithm can also be executed step-by-step. For instance,
211the following code can be used instead of \ref dijkstra.start().
212
213\code
214  while (!dijkstra.emptyQueue()) {
215    ListDigraph::Node n = dijkstra.processNextNode();
216    cout << g.id(n) << ' ' << dijkstra.dist(g) << endl;
217  }
218\endcode
219
220
221[SEC]sec_max_flow[SEC] Maximum Flows
222
223See \ref Preflow.
224
225[TRAILER]
226*/
227}
Note: See TracBrowser for help on using the repository browser.