# Changeset 358:7f26c4b32651 in lemon

Ignore:
Timestamp:
10/28/08 23:10:27 (11 years ago)
Branch:
default
Phase:
public
Message:

Minor doc improvements related to Suurballe (#47)

Files:
2 edited

### Legend:

Unmodified
 r357 /// @{ /// \brief Implementation of an algorithm for finding arc-disjoint /// paths between two nodes having minimum total length. /// \brief Algorithm for finding arc-disjoint paths between two nodes /// having minimum total length. /// /// \ref lemon::Suurballe "Suurballe" implements an algorithm for /// finding arc-disjoint paths having minimum total length (cost) /// from a given source node to a given target node in a directed /// digraph. /// from a given source node to a given target node in a digraph. /// /// In fact, this implementation is the specialization of the /// \ref CapacityScaling "successive shortest path" algorithm. /// /// \tparam Digraph The directed digraph type the algorithm runs on. /// \tparam Digraph The digraph type the algorithm runs on. /// The default value is \c ListDigraph. /// \tparam LengthMap The type of the length (cost) map. /// The default value is Digraph::ArcMap. /// /// \warning Length values should be \e non-negative \e integers. /// \note For finding node-disjoint paths this algorithm can be used /// with \ref SplitDigraphAdaptor. /// /// \author Attila Bernath and Peter Kovacs template < typename Digraph, #ifdef DOXYGEN template #else template < typename Digraph = ListDigraph, typename LengthMap = typename Digraph::template ArcMap > #endif class Suurballe { private: /// \brief Special implementation of the \ref Dijkstra algorithm /// \brief Special implementation of the Dijkstra algorithm /// for finding shortest paths in the residual network. /// private: // The directed digraph the algorithm runs on // The digraph the algorithm runs on const Digraph &_graph; _dist(digraph), _pred(pred), _s(s), _t(t) {} /// \brief Runs the algorithm. Returns \c true if a path is found /// \brief Run the algorithm. It returns \c true if a path is found /// from the source node to the target node. bool run() { _proc_nodes.clear(); // Processing nodes // Process nodes while (!heap.empty() && heap.top() != _t) { Node u = heap.top(), v; _proc_nodes.push_back(u); // Traversing outgoing arcs // Traverse outgoing arcs for (OutArcIt e(_graph, u); e != INVALID; ++e) { if (_flow[e] == 0) { } // Traversing incoming arcs // Traverse incoming arcs for (InArcIt e(_graph, u); e != INVALID; ++e) { if (_flow[e] == 1) { if (heap.empty()) return false; // Updating potentials of processed nodes // Update potentials of processed nodes Length t_dist = heap.prio(); for (int i = 0; i < int(_proc_nodes.size()); ++i) private: // The directed digraph the algorithm runs on // The digraph the algorithm runs on const Digraph &_graph; // The length map /// Constructor. /// /// \param digraph The directed digraph the algorithm runs on. /// \param digraph The digraph the algorithm runs on. /// \param length The length (cost) values of the arcs. /// \param s The source node. } /// \brief Sets the flow map. /// /// Sets the flow map. /// \brief Set the flow map. /// /// This function sets the flow map. /// /// The found flow contains only 0 and 1 values. It is the union of } /// \brief Sets the potential map. /// /// Sets the potential map. /// \brief Set the potential map. /// /// This function sets the potential map. /// /// The potentials provide the dual solution of the underlying /// @{ /// \brief Runs the algorithm. /// /// Runs the algorithm. /// \brief Run the algorithm. /// /// This function runs the algorithm. /// /// \param k The number of paths to be found. /// /// \return \c k if there are at least \c k arc-disjoint paths /// from \c s to \c t. Otherwise it returns the number of /// \return \c k if there are at least \c k arc-disjoint paths from /// \c s to \c t in the digraph. Otherwise it returns the number of /// arc-disjoint paths found. /// } /// \brief Initializes the algorithm. /// /// Initializes the algorithm. /// \brief Initialize the algorithm. /// /// This function initializes the algorithm. void init() { // Initializing maps // Initialize maps if (!_flow) { _flow = new FlowMap(_graph); } /// \brief Executes the successive shortest path algorithm to find /// \brief Execute the successive shortest path algorithm to find /// an optimal flow. /// /// Executes the successive shortest path algorithm to find a /// minimum cost flow, which is the union of \c k or less /// This function executes the successive shortest path algorithm to /// find a minimum cost flow, which is the union of \c k or less /// arc-disjoint paths. /// /// \return \c k if there are at least \c k arc-disjoint paths /// from \c s to \c t. Otherwise it returns the number of /// \return \c k if there are at least \c k arc-disjoint paths from /// \c s to \c t in the digraph. Otherwise it returns the number of /// arc-disjoint paths found. /// /// \pre \ref init() must be called before using this function. int findFlow(int k = 2) { // Finding shortest paths // Find shortest paths _path_num = 0; while (_path_num < k) { // Running Dijkstra // Run Dijkstra if (!_dijkstra->run()) break; ++_path_num; // Setting the flow along the found shortest path // Set the flow along the found shortest path Node u = _target; Arc e; } /// \brief Computes the paths from the flow. /// /// Computes the paths from the flow. /// \brief Compute the paths from the flow. /// /// This function computes the paths from the flow. /// /// \pre \ref init() and \ref findFlow() must be called before using /// this function. void findPaths() { // Creating the residual flow map (the union of the paths not // found so far) // Create the residual flow map (the union of the paths not found // so far) FlowMap res_flow(_graph); for(ArcIt a(_graph);a!=INVALID;++a) res_flow[a]=(*_flow)[a]; for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a]; paths.clear(); /// \name Query Functions /// The result of the algorithm can be obtained using these /// The results of the algorithm can be obtained using these /// functions. /// \n The algorithm should be executed before using them. /// @{ /// \brief Returns a const reference to the arc map storing the /// \brief Return a const reference to the arc map storing the /// found flow. /// /// Returns a const reference to the arc map storing the flow that /// is the union of the found arc-disjoint paths. /// /// \pre \ref run() or findFlow() must be called before using this /// function. /// This function returns a const reference to the arc map storing /// the flow that is the union of the found arc-disjoint paths. /// /// \pre \ref run() or \ref findFlow() must be called before using /// this function. const FlowMap& flowMap() const { return *_flow; } /// \brief Returns a const reference to the node map storing the /// \brief Return a const reference to the node map storing the /// found potentials (the dual solution). /// /// Returns a const reference to the node map storing the found /// potentials that provide the dual solution of the underlying /// minimum cost flow problem. /// /// \pre \ref run() or findFlow() must be called before using this /// function. /// This function returns a const reference to the node map storing /// the found potentials that provide the dual solution of the /// underlying minimum cost flow problem. /// /// \pre \ref run() or \ref findFlow() must be called before using /// this function. const PotentialMap& potentialMap() const { return *_potential; } /// \brief Returns the flow on the given arc. /// /// Returns the flow on the given arc. /// \brief Return the flow on the given arc. /// /// This function returns the flow on the given arc. /// It is \c 1 if the arc is involved in one of the found paths, /// otherwise it is \c 0. /// /// \pre \ref run() or findFlow() must be called before using this /// function. /// \pre \ref run() or \ref findFlow() must be called before using /// this function. int flow(const Arc& arc) const { return (*_flow)[arc]; } /// \brief Returns the potential of the given node. /// /// Returns the potential of the given node. /// /// \pre \ref run() or findFlow() must be called before using this /// function. /// \brief Return the potential of the given node. /// /// This function returns the potential of the given node. /// /// \pre \ref run() or \ref findFlow() must be called before using /// this function. Length potential(const Node& node) const { return (*_potential)[node]; } /// \brief Returns the total length (cost) of the found paths (flow). /// /// Returns the total length (cost) of the found paths (flow). /// The complexity of the function is \f$O(e) \f$. /// /// \pre \ref run() or findFlow() must be called before using this /// function. /// \brief Return the total length (cost) of the found paths (flow). /// /// This function returns the total length (cost) of the found paths /// (flow). The complexity of the function is \f$O(e) \f$. /// /// \pre \ref run() or \ref findFlow() must be called before using /// this function. Length totalLength() const { Length c = 0; } /// \brief Returns the number of the found paths. /// /// Returns the number of the found paths. /// /// \pre \ref run() or findFlow() must be called before using this /// function. /// \brief Return the number of the found paths. /// /// This function returns the number of the found paths. /// /// \pre \ref run() or \ref findFlow() must be called before using /// this function. int pathNum() const { return _path_num; } /// \brief Returns a const reference to the specified path. /// /// Returns a const reference to the specified path. /// \brief Return a const reference to the specified path. /// /// This function returns a const reference to the specified path. /// /// \param i The function returns the \c i-th path. /// \c i must be between \c 0 and %pathNum()-1. /// /// \pre \ref run() or findPaths() must be called before using this /// function. /// \pre \ref run() or \ref findPaths() must be called before using /// this function. Path path(int i) const { return paths[i];