1 | // -*- c++ -*- |
---|
2 | #ifndef HUGO_MINLENGTHPATHS_H |
---|
3 | #define HUGO_MINLENGTHPATHS_H |
---|
4 | |
---|
5 | ///\ingroup flowalgs |
---|
6 | ///\file |
---|
7 | ///\brief An algorithm for finding k paths of minimal total length. |
---|
8 | |
---|
9 | |
---|
10 | #include <hugo/maps.h> |
---|
11 | #include <vector> |
---|
12 | #include <hugo/min_cost_flows.h> |
---|
13 | |
---|
14 | namespace hugo { |
---|
15 | |
---|
16 | /// \addtogroup flowalgs |
---|
17 | /// @{ |
---|
18 | |
---|
19 | ///\brief Implementation of an algorithm for finding k edge-disjoint paths between 2 nodes |
---|
20 | /// of minimal total length |
---|
21 | /// |
---|
22 | /// The class \ref hugo::MinLengthPaths implements |
---|
23 | /// an algorithm for finding k edge-disjoint paths |
---|
24 | /// from a given source node to a given target node in an |
---|
25 | /// edge-weighted directed graph having minimal total weight (length). |
---|
26 | /// |
---|
27 | ///\warning Length values should be nonnegative. |
---|
28 | /// |
---|
29 | ///\param Graph The directed graph type the algorithm runs on. |
---|
30 | ///\param LengthMap The type of the length map (values should be nonnegative). |
---|
31 | /// |
---|
32 | ///\author Attila Bernath |
---|
33 | template <typename Graph, typename LengthMap> |
---|
34 | class MinLengthPaths{ |
---|
35 | |
---|
36 | |
---|
37 | typedef typename LengthMap::ValueType Length; |
---|
38 | |
---|
39 | typedef typename Graph::Node Node; |
---|
40 | typedef typename Graph::NodeIt NodeIt; |
---|
41 | typedef typename Graph::Edge Edge; |
---|
42 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
43 | typedef typename Graph::template EdgeMap<int> EdgeIntMap; |
---|
44 | |
---|
45 | typedef ConstMap<Edge,int> ConstMap; |
---|
46 | |
---|
47 | //Input |
---|
48 | const Graph& G; |
---|
49 | |
---|
50 | //Auxiliary variables |
---|
51 | //This is the capacity map for the mincostflow problem |
---|
52 | ConstMap const1map; |
---|
53 | //This MinCostFlows instance will actually solve the problem |
---|
54 | MinCostFlows<Graph, LengthMap, ConstMap> mincost_flow; |
---|
55 | |
---|
56 | //Container to store found paths |
---|
57 | std::vector< std::vector<Edge> > paths; |
---|
58 | |
---|
59 | public : |
---|
60 | |
---|
61 | |
---|
62 | /// The constructor of the class. |
---|
63 | |
---|
64 | ///\param _G The directed graph the algorithm runs on. |
---|
65 | ///\param _length The length (weight or cost) of the edges. |
---|
66 | MinLengthPaths(Graph& _G, LengthMap& _length) : G(_G), |
---|
67 | const1map(1), mincost_flow(_G, _length, const1map){} |
---|
68 | |
---|
69 | ///Runs the algorithm. |
---|
70 | |
---|
71 | ///Runs the algorithm. |
---|
72 | ///Returns k if there are at least k edge-disjoint paths from s to t. |
---|
73 | ///Otherwise it returns the number of found edge-disjoint paths from s to t. |
---|
74 | /// |
---|
75 | ///\param s The source node. |
---|
76 | ///\param t The target node. |
---|
77 | ///\param k How many paths are we looking for? |
---|
78 | /// |
---|
79 | int run(Node s, Node t, int k) { |
---|
80 | |
---|
81 | int i = mincost_flow.run(s,t,k); |
---|
82 | |
---|
83 | |
---|
84 | //Let's find the paths |
---|
85 | //We put the paths into stl vectors (as an inner representation). |
---|
86 | //In the meantime we lose the information stored in 'reversed'. |
---|
87 | //We suppose the lengths to be positive now. |
---|
88 | |
---|
89 | //We don't want to change the flow of mincost_flow, so we make a copy |
---|
90 | //The name here suggests that the flow has only 0/1 values. |
---|
91 | EdgeIntMap reversed(G); |
---|
92 | |
---|
93 | for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) |
---|
94 | reversed[e] = mincost_flow.getFlow()[e]; |
---|
95 | |
---|
96 | paths.clear(); |
---|
97 | //total_length=0; |
---|
98 | paths.resize(k); |
---|
99 | for (int j=0; j<i; ++j){ |
---|
100 | Node n=s; |
---|
101 | OutEdgeIt e; |
---|
102 | |
---|
103 | while (n!=t){ |
---|
104 | |
---|
105 | |
---|
106 | G.first(e,n); |
---|
107 | |
---|
108 | while (!reversed[e]){ |
---|
109 | ++e; |
---|
110 | } |
---|
111 | n = G.head(e); |
---|
112 | paths[j].push_back(e); |
---|
113 | //total_length += length[e]; |
---|
114 | reversed[e] = 1-reversed[e]; |
---|
115 | } |
---|
116 | |
---|
117 | } |
---|
118 | return i; |
---|
119 | } |
---|
120 | |
---|
121 | |
---|
122 | ///Returns the total length of the paths |
---|
123 | |
---|
124 | ///This function gives back the total length of the found paths. |
---|
125 | ///\pre \ref run() must |
---|
126 | ///be called before using this function. |
---|
127 | Length totalLength(){ |
---|
128 | return mincost_flow.totalLength(); |
---|
129 | } |
---|
130 | |
---|
131 | ///Returns the found flow. |
---|
132 | |
---|
133 | ///This function returns a const reference to the EdgeMap \c flow. |
---|
134 | ///\pre \ref run() must |
---|
135 | ///be called before using this function. |
---|
136 | const EdgeIntMap &getFlow() const { return mincost_flow.flow;} |
---|
137 | |
---|
138 | /// Returns the optimal dual solution |
---|
139 | |
---|
140 | ///This function returns a const reference to the NodeMap |
---|
141 | ///\c potential (the dual solution). |
---|
142 | /// \pre \ref run() must be called before using this function. |
---|
143 | const EdgeIntMap &getPotential() const { return mincost_flow.potential;} |
---|
144 | |
---|
145 | ///Checks whether the complementary slackness holds. |
---|
146 | |
---|
147 | ///This function checks, whether the given solution is optimal. |
---|
148 | ///It should return true after calling \ref run() |
---|
149 | ///Currently this function only checks optimality, |
---|
150 | ///doesn't bother with feasibility |
---|
151 | ///It is meant for testing purposes. |
---|
152 | /// |
---|
153 | bool checkComplementarySlackness(){ |
---|
154 | return mincost_flow.checkComplementarySlackness(); |
---|
155 | } |
---|
156 | |
---|
157 | ///Read the found paths. |
---|
158 | |
---|
159 | ///This function gives back the \c j-th path in argument p. |
---|
160 | ///Assumes that \c run() has been run and nothing changed since then. |
---|
161 | /// \warning It is assumed that \c p is constructed to |
---|
162 | ///be a path of graph \c G. |
---|
163 | ///If \c j is not less than the result of previous \c run, |
---|
164 | ///then the result here will be an empty path (\c j can be 0 as well). |
---|
165 | /// |
---|
166 | ///\param Path The type of the path structure to put the result to (must meet hugo path concept). |
---|
167 | ///\param p The path to put the result to |
---|
168 | ///\param j Which path you want to get from the found paths (in a real application you would get the found paths iteratively) |
---|
169 | template<typename Path> |
---|
170 | void getPath(Path& p, size_t j){ |
---|
171 | |
---|
172 | p.clear(); |
---|
173 | if (j>paths.size()-1){ |
---|
174 | return; |
---|
175 | } |
---|
176 | typename Path::Builder B(p); |
---|
177 | for(typename std::vector<Edge>::iterator i=paths[j].begin(); |
---|
178 | i!=paths[j].end(); ++i ){ |
---|
179 | B.pushBack(*i); |
---|
180 | } |
---|
181 | |
---|
182 | B.commit(); |
---|
183 | } |
---|
184 | |
---|
185 | }; //class MinLengthPaths |
---|
186 | |
---|
187 | ///@} |
---|
188 | |
---|
189 | } //namespace hugo |
---|
190 | |
---|
191 | #endif //HUGO_MINLENGTHPATHS_H |
---|