1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
3 * This file is a part of LEMON, a generic C++ optimization library.
5 * Copyright (C) 2003-2010
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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.
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
21 [PAGE]sec_algorithms[PAGE] Algorithms
23 \todo This page is under construction.
25 In addition to the graph structures, the most important parts of LEMON are
26 the various algorithms related to graph theory and combinatorial optimization.
27 The library probvides quite flexible and efficient implementations
28 for well-known fundamental algorithms, such as breadth-first
29 search (BFS), depth-first search (DFS), Dijkstra algorithm, Kruskal algorithm
30 and methods for discovering graph properties like connectivity, bipartiteness
31 or Euler property, as well as more complex optimization algorithms for finding
32 maximum flows, minimum cuts, matchings, minimum cost flows and arc-disjoint
35 In this section, we present only some of the most fundamental algorithms.
36 For a complete overview, see the \ref algs module of the reference manual.
38 [SEC]sec_graph_search[SEC] Graph Search
40 \todo The following contents are ported from the LEMON 0.x tutorial,
41 thus they have to thouroughly revised, reorganized and reworked.
43 See \ref Bfs, \ref Dfs and \ref graph_properties.
45 Both \ref lemon::Bfs "Bfs" and \ref lemon::Dfs "Dfs" are highly adaptable and efficient
46 implementations of the well known algorithms. The algorithms are placed most cases in
47 separated files named after the algorithm itself but lower case as all other header file names.
48 For example the next Bfs class is in the \c lemon/bfs.h.
50 The algorithm is implemented in the \ref lemon::Bfs "Bfs" template class - rather than as function.
51 The class has two template parameters: \b GR and \b TR.<br>
52 GR is the digraph the algorithm runs on. It has \ref lemon::ListDigraph "ListDigraph" as default type.
53 TR is a Traits class commonly used to easy the parametrization of templates. In most cases you
54 wont need to modify the default type \ref lemon::BfsDefaultTraits "BfsDefaultTraits<GR>".
56 To use the class, declare it!
58 Bfs<ListGraph> bfs(gr);
60 Note the lack of second template argument because of the default parameter.
62 It provides a simple but powerful interface to control the execution.
64 int dist = bfs.run(s,t);
66 It finds the shortest path from node \c s to node \c t and returns it, or zero
67 if there is no path from \c s to \c t.<br>
68 If you want the shortest path from a specified node to all other node, just write:
72 Now the distances and path information are stored in maps which you can access with
73 member functions like \ref lemon::Bfs::distMap "distMap()" or \ref lemon::Bfs::predMap "predMap()".<br>
74 Or more directly with other member functions like \ref lemon::Bfs::predNode "predNode()". Once the algorithm
75 is finished (or to be precise reached that node) \ref lemon::Bfs::dist "dist()" or \ref lemon::Bfs::predNode
76 "predNode()" can be called.
78 For an example let's say we want to print the shortest path of those nodes which
79 are in a certain distance.
83 for( ListGraph::NodeIt n(gr); n != INVALID; ++n ) {
84 if( bfs.reached(n) && bfs.dist(n) <= max_dist ) {
85 std::cout << gr.id(n);
87 Node prev = bfs.prevNode(n);
88 while( prev != INVALID ) {
89 std::cout << "<-" << gr.id(prev);
90 prev = bfs.prevNode(n);
93 std::cout << std::endl;
98 In the previous code we only used \c run(). Now we introduce the way you can directly
99 control the execution of the algorithm.
101 First you have to initialize the variables with \ref lemon::Bfs::init "init()".
106 Then you add one or more source nodes to the queue. They will be processed, as they would
107 be reached by the algorithm before. And yes - you can add more sources during the execution.
109 bfs.addSource(node_1);
110 bfs.addSource(node_2);
114 And finally you can start the process with \ref lemon::Bfs::start "start()", or
115 you can write your own loop to process the nodes one-by-one.
118 Since Dfs is very similar to Bfs with a few tiny differences we only see a bit more complex example
119 to demonstrate Dfs's capabilities.
121 We will see a program, which solves the problem of <b>topological ordering</b>.
122 We need to know in which order we should put on our clothes. The program will do the following:
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.
129 \dontinclude topological_ordering.cc
130 First of all we will need an own \ref lemon::Dfs::ProcessedMap "ProcessedMap". The ordering
131 will be done through it.
134 The class meets the \ref concepts::WriteMap "WriteMap" concept. In it's \c set() method the only thing
135 we need to do is insert the key - that is the node whose processing just finished - into the beginning
137 Although we implemented this needed helper class ourselves it was not necessary.
138 The \ref lemon::FrontInserterBoolMap "FrontInserterBoolMap" class does exactly
139 what we needed. To be correct it's more general - and it's all in \c LEMON. But
140 we wanted to show you, how easy is to add additional functionality.
142 First we declare the needed data structures: the digraph and a map to store the nodes' label.
146 Now we build a digraph. But keep in mind that it must be DAG because cyclic digraphs has no topological
153 Then add arcs which represent the precedences between those items.
157 See how easy is to access the internal information of this algorithm trough maps.
158 We only need to set our own map as the class's \ref lemon::Dfs::ProcessedMap "ProcessedMap".
162 And now comes the third part. Write out the list in reverse order. But the list was
163 composed in reverse way (with \c push_front() instead of \c push_back() so we just iterate it.
167 The program is to be found in the \ref demo directory: \ref topological_ordering.cc
169 \todo Check the linking of the demo file, the code samples are missing.
171 More algorithms are described in the \ref algorithms2 "second part".
174 [SEC]sec_shortest_paths[SEC] Shortest Paths
176 See \ref Dijkstra and \ref BellmanFord.
179 If you want to solve some transportation problems in a network then you
180 will want to find shortest paths between nodes of a graph. This is
181 usually solved using Dijkstra's algorithm. A utility that solves this is
182 the LEMON Dijkstra class. The following code is a simple program using
183 the LEMON Dijkstra class: it calculates the shortest path between node s
184 and t in a graph g. We omit the part reading the graph g and the length
189 In LEMON, the algorithms are implemented basically as classes, but
190 for some of them, function-type interfaces are also available
191 for the sake of convenience.
192 For instance, the Dijkstra algorithm is implemented in the \ref Dijkstra
193 template class, but the \ref dijkstra() function is also defined,
194 which can still be used quite flexibly due to named parameters.
196 The original sample code could also use the class interface as follows.
199 Dijkstra<ListDigraph> dijkstra(g, length);
200 dijkstra.distMap(dist);
202 dijkstra.addSource(u);
206 The previous code is obviously longer than the original, but the
207 execution can be controlled to a higher extent. While using the function-type
208 interface, only one source can be added to the algorithm, the class
209 interface makes it possible to specify several root nodes.
210 Moreover, the algorithm can also be executed step-by-step. For instance,
211 the following code can be used instead of \ref dijkstra.start().
214 while (!dijkstra.emptyQueue()) {
215 ListDigraph::Node n = dijkstra.processNextNode();
216 cout << g.id(n) << ' ' << dijkstra.dist(g) << endl;
221 [SEC]sec_max_flow[SEC] Maximum Flows