1 | // -*- c++ -*- |
---|
2 | #ifndef LEMON_MINLENGTHPATHS_H |
---|
3 | #define LEMON_MINLENGTHPATHS_H |
---|
4 | |
---|
5 | ///\ingroup galgs |
---|
6 | ///\file |
---|
7 | ///\brief An algorithm for finding k paths of minimal total length. |
---|
8 | |
---|
9 | #include <iostream> |
---|
10 | #include <lemon/dijkstra.h> |
---|
11 | #include <lemon/graph_wrapper.h> |
---|
12 | #include <lemon/maps.h> |
---|
13 | #include <vector> |
---|
14 | |
---|
15 | |
---|
16 | namespace lemon { |
---|
17 | |
---|
18 | /// \addtogroup galgs |
---|
19 | /// @{ |
---|
20 | |
---|
21 | ///\brief Implementation of an algorithm for finding k paths between 2 nodes |
---|
22 | /// of minimal total length |
---|
23 | /// |
---|
24 | /// The class \ref lemon::MinLengthPaths "MinLengthPaths" implements |
---|
25 | /// an algorithm for finding k edge-disjoint paths |
---|
26 | /// from a given source node to a given target node in an |
---|
27 | /// edge-weighted directed graph having minimal total weigth (length). |
---|
28 | /// |
---|
29 | ///\author Attila Bernath |
---|
30 | template <typename Graph, typename LengthMap> |
---|
31 | class MinLengthPaths { |
---|
32 | |
---|
33 | typedef typename LengthMap::Value Length; |
---|
34 | |
---|
35 | typedef typename Graph::Node Node; |
---|
36 | typedef typename Graph::NodeIt NodeIt; |
---|
37 | typedef typename Graph::Edge Edge; |
---|
38 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
39 | typedef typename Graph::template EdgeMap<int> EdgeIntMap; |
---|
40 | |
---|
41 | typedef ConstMap<Edge,int> ConstMap; |
---|
42 | |
---|
43 | typedef ResGraphWrapper<const Graph,int,ConstMap,EdgeIntMap> ResGraphType; |
---|
44 | |
---|
45 | class ModLengthMap { |
---|
46 | typedef typename ResGraphType::template NodeMap<Length> NodeMap; |
---|
47 | const ResGraphType& G; |
---|
48 | const EdgeIntMap& rev; |
---|
49 | const LengthMap &ol; |
---|
50 | const NodeMap &pot; |
---|
51 | public : |
---|
52 | typedef typename LengthMap::Key Key; |
---|
53 | typedef typename LengthMap::Value Value; |
---|
54 | |
---|
55 | Value operator[](typename ResGraphType::Edge e) const { |
---|
56 | //if ( (1-2*rev[e])*ol[e]-(pot[G.target(e)]-pot[G.source(e)] ) <0 ){ |
---|
57 | // std::cout<<"Negative length!!"<<std::endl; |
---|
58 | //} |
---|
59 | return (1-2*rev[e])*ol[e]-(pot[G.target(e)]-pot[G.source(e)]); |
---|
60 | } |
---|
61 | |
---|
62 | ModLengthMap(const ResGraphType& _G, const EdgeIntMap& _rev, |
---|
63 | const LengthMap &o, const NodeMap &p) : |
---|
64 | G(_G), rev(_rev), ol(o), pot(p){}; |
---|
65 | };//ModLengthMap |
---|
66 | |
---|
67 | |
---|
68 | |
---|
69 | |
---|
70 | const Graph& G; |
---|
71 | const LengthMap& length; |
---|
72 | |
---|
73 | //auxiliary variables |
---|
74 | |
---|
75 | //The value is 1 iff the edge is reversed. |
---|
76 | //If the algorithm has finished, the edges of the seeked paths are |
---|
77 | //exactly those that are reversed |
---|
78 | EdgeIntMap reversed; |
---|
79 | |
---|
80 | //Container to store found paths |
---|
81 | std::vector< std::vector<Edge> > paths; |
---|
82 | //typedef DirPath<Graph> DPath; |
---|
83 | //DPath paths; |
---|
84 | |
---|
85 | |
---|
86 | Length total_length; |
---|
87 | |
---|
88 | public : |
---|
89 | |
---|
90 | |
---|
91 | MinLengthPaths(Graph& _G, LengthMap& _length) : G(_G), |
---|
92 | length(_length), reversed(_G)/*, dijkstra_dist(_G)*/{ } |
---|
93 | |
---|
94 | |
---|
95 | ///Runs the algorithm. |
---|
96 | |
---|
97 | ///Runs the algorithm. |
---|
98 | ///Returns k if there are at least k edge-disjoint paths from s to t. |
---|
99 | ///Otherwise it returns the number of found edge-disjoint paths from s to t. |
---|
100 | int run(Node s, Node t, int k) { |
---|
101 | ConstMap const1map(1); |
---|
102 | |
---|
103 | |
---|
104 | //We need a residual graph, in which some of the edges are reversed |
---|
105 | ResGraphType res_graph(G, const1map, reversed); |
---|
106 | |
---|
107 | //Initialize the copy of the Dijkstra potential to zero |
---|
108 | typename ResGraphType::template NodeMap<Length> dijkstra_dist(res_graph); |
---|
109 | ModLengthMap mod_length(res_graph, reversed, length, dijkstra_dist); |
---|
110 | |
---|
111 | Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length); |
---|
112 | |
---|
113 | int i; |
---|
114 | for (i=0; i<k; ++i){ |
---|
115 | dijkstra.run(s); |
---|
116 | if (!dijkstra.reached(t)){ |
---|
117 | //There are no k paths from s to t |
---|
118 | break; |
---|
119 | }; |
---|
120 | |
---|
121 | { |
---|
122 | //We have to copy the potential |
---|
123 | typename ResGraphType::NodeIt n; |
---|
124 | for ( res_graph.first(n) ; res_graph.valid(n) ; res_graph.next(n) ) { |
---|
125 | dijkstra_dist[n] += dijkstra.distMap()[n]; |
---|
126 | } |
---|
127 | } |
---|
128 | |
---|
129 | |
---|
130 | //Reversing the sortest path |
---|
131 | Node n=t; |
---|
132 | Edge e; |
---|
133 | while (n!=s){ |
---|
134 | e = dijkstra.pred(n); |
---|
135 | n = dijkstra.predNode(n); |
---|
136 | reversed[e] = 1-reversed[e]; |
---|
137 | } |
---|
138 | |
---|
139 | |
---|
140 | } |
---|
141 | |
---|
142 | //Let's find the paths |
---|
143 | //We put the paths into stl vectors (as an inner representation). |
---|
144 | //In the meantime we lose the information stored in 'reversed'. |
---|
145 | //We suppose the lengths to be positive now. |
---|
146 | |
---|
147 | //Meanwhile we put the total length of the found paths |
---|
148 | //in the member variable total_length |
---|
149 | paths.clear(); |
---|
150 | total_length=0; |
---|
151 | paths.resize(k); |
---|
152 | for (int j=0; j<i; ++j){ |
---|
153 | Node n=s; |
---|
154 | OutEdgeIt e; |
---|
155 | |
---|
156 | while (n!=t){ |
---|
157 | |
---|
158 | |
---|
159 | G.first(e,n); |
---|
160 | |
---|
161 | while (!reversed[e]){ |
---|
162 | G.next(e); |
---|
163 | } |
---|
164 | n = G.target(e); |
---|
165 | paths[j].push_back(e); |
---|
166 | total_length += length[e]; |
---|
167 | reversed[e] = 1-reversed[e]; |
---|
168 | } |
---|
169 | |
---|
170 | } |
---|
171 | |
---|
172 | return i; |
---|
173 | } |
---|
174 | |
---|
175 | ///This function gives back the total length of the found paths. |
---|
176 | ///Assumes that \c run() has been run and nothing changed since then. |
---|
177 | Length totalLength(){ |
---|
178 | return total_length; |
---|
179 | } |
---|
180 | |
---|
181 | ///This function gives back the \c j-th path in argument p. |
---|
182 | ///Assumes that \c run() has been run and nothing changed since then. |
---|
183 | /// \warning It is assumed that \c p is constructed to be a path of graph \c G. If \c j is greater than the result of previous \c run, then the result here will be an empty path. |
---|
184 | template<typename DirPath> |
---|
185 | void getPath(DirPath& p, int j){ |
---|
186 | p.clear(); |
---|
187 | typename DirPath::Builder B(p); |
---|
188 | for(typename std::vector<Edge>::iterator i=paths[j].begin(); |
---|
189 | i!=paths[j].end(); ++i ){ |
---|
190 | B.pushBack(*i); |
---|
191 | } |
---|
192 | |
---|
193 | B.commit(); |
---|
194 | } |
---|
195 | |
---|
196 | }; //class MinLengthPaths |
---|
197 | |
---|
198 | ///@} |
---|
199 | |
---|
200 | } //namespace lemon |
---|
201 | |
---|
202 | #endif //LEMON_MINLENGTHPATHS_H |
---|