/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * Copyright (C) 2003-2010

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_GROSSO_LOCATELLI_PULLAN_MC_H

#define LEMON_GROSSO_LOCATELLI_PULLAN_MC_H

/// \ingroup approx_algs

///

/// \file

/// \brief The iterated local search algorithm of Grosso, Locatelli, and Pullan

/// for the maximum clique problem

#include <vector>

#include <limits>

#include <lemon/core.h>

#include <lemon/random.h>

namespace lemon {

  /// \addtogroup approx_algs

  /// @{

  /// \brief Implementation of the iterated local search algorithm of Grosso,

  /// Locatelli, and Pullan for the maximum clique problem

  ///

  /// \ref GrossoLocatelliPullanMc implements the iterated local search

  /// algorithm of Grosso, Locatelli, and Pullan for solving the \e maximum

  /// \e clique \e problem \cite grosso08maxclique.

  /// It is to find the largest complete subgraph (\e clique) in an

  /// undirected graph, i.e., the largest set of nodes where each

  /// pair of nodes is connected.

  ///

  /// This class provides a simple but highly efficient and robust heuristic

  /// method that quickly finds a quite large clique, but not necessarily the

  /// largest one.

  /// The algorithm performs a certain number of iterations to find several

  /// cliques and selects the largest one among them. Various limits can be

  /// specified to control the running time and the effectiveness of the

  /// search process.

  ///

  /// \tparam GR The undirected graph type the algorithm runs on.

  ///

  /// \note %GrossoLocatelliPullanMc provides three different node selection

  /// rules, from which the most powerful one is used by default.

  /// For more information, see \ref SelectionRule.

  template <typename GR>

  class GrossoLocatelliPullanMc

  {

  public:

    /// \brief Constants for specifying the node selection rule.

    ///

    /// Enum type containing constants for specifying the node selection rule

    /// for the \ref run() function.

    ///

    /// During the algorithm, nodes are selected for addition to the current

    /// clique according to the applied rule.

    /// In general, the PENALTY_BASED rule turned out to be the most powerful

    /// and the most robust, thus it is the default option.

    /// However, another selection rule can be specified using the \ref run()

    /// function with the proper parameter.

    enum SelectionRule {

      /// A node is selected randomly without any evaluation at each step.

      RANDOM,

      /// A node of maximum degree is selected randomly at each step.

      DEGREE_BASED,

      /// A node of minimum penalty is selected randomly at each step.

      /// The node penalties are updated adaptively after each stage of the

      /// search process.

      PENALTY_BASED

    };

    /// \brief Constants for the causes of search termination.

    ///

    /// Enum type containing constants for the different causes of search

    /// termination. The \ref run() function returns one of these values.

    enum TerminationCause {

      /// The iteration count limit is reached.

      ITERATION_LIMIT,

      /// The step count limit is reached.

      STEP_LIMIT,

      /// The clique size limit is reached.

      SIZE_LIMIT

    };

  private:

    TEMPLATE_GRAPH_TYPEDEFS(GR);

    typedef std::vector<int> IntVector;

    typedef std::vector<char> BoolVector;

    typedef std::vector<BoolVector> BoolMatrix;

    // Note: vector<char> is used instead of vector<bool> for efficiency reasons

    // The underlying graph

    const GR &_graph;

    IntNodeMap _id;

    // Internal matrix representation of the graph

    BoolMatrix _gr;

    int _n;

    // Search options

    bool _delta_based_restart;

    int _restart_delta_limit;

    // Search limits

    int _iteration_limit;

    int _step_limit;

    int _size_limit;

    // The current clique

    BoolVector _clique;

    int _size;

    // The best clique found so far

    BoolVector _best_clique;

    int _best_size;

    // The "distances" of the nodes from the current clique.

    // _delta[u] is the number of nodes in the clique that are

    // not connected with u.

    IntVector _delta;

    // The current tabu set

    BoolVector _tabu;

    // Random number generator

    Random _rnd;

  private:

    // Implementation of the RANDOM node selection rule.

    class RandomSelectionRule

    {

    private:

      // References to the algorithm instance

      const BoolVector &_clique;

      const IntVector  &_delta;

      const BoolVector &_tabu;

      Random &_rnd;

      // Pivot rule data

      int _n;

    public:

      // Constructor

      RandomSelectionRule(GrossoLocatelliPullanMc &mc) :

        _clique(mc._clique), _delta(mc._delta), _tabu(mc._tabu),

        _rnd(mc._rnd), _n(mc._n)

      {}

      // Return a node index for a feasible add move or -1 if no one exists

      int nextFeasibleAddNode() const {

        int start_node = _rnd[_n];

        for (int i = start_node; i != _n; i++) {

          if (_delta[i] == 0 && !_tabu[i]) return i;

        }

        for (int i = 0; i != start_node; i++) {

          if (_delta[i] == 0 && !_tabu[i]) return i;

        }

        return -1;

      }

      // Return a node index for a feasible swap move or -1 if no one exists

      int nextFeasibleSwapNode() const {

        int start_node = _rnd[_n];

        for (int i = start_node; i != _n; i++) {

          if (!_clique[i] && _delta[i] == 1 && !_tabu[i]) return i;

        }

        for (int i = 0; i != start_node; i++) {

          if (!_clique[i] && _delta[i] == 1 && !_tabu[i]) return i;

        }

        return -1;

      }

      // Return a node index for an add move or -1 if no one exists

      int nextAddNode() const {

        int start_node = _rnd[_n];

        for (int i = start_node; i != _n; i++) {

          if (_delta[i] == 0) return i;

        }

        for (int i = 0; i != start_node; i++) {

          if (_delta[i] == 0) return i;

        }

        return -1;

      }

      // Update internal data structures between stages (if necessary)

      void update() {}

    }; //class RandomSelectionRule

    // Implementation of the DEGREE_BASED node selection rule.

    class DegreeBasedSelectionRule

    {

    private:

      // References to the algorithm instance

      const BoolVector &_clique;

      const IntVector  &_delta;

      const BoolVector &_tabu;

      Random &_rnd;

      // Pivot rule data

      int _n;

      IntVector _deg;

    public:

      // Constructor

      DegreeBasedSelectionRule(GrossoLocatelliPullanMc &mc) :

        _clique(mc._clique), _delta(mc._delta), _tabu(mc._tabu),

        _rnd(mc._rnd), _n(mc._n), _deg(_n)

      {

        for (int i = 0; i != _n; i++) {

          int d = 0;

          BoolVector &row = mc._gr[i];

          for (int j = 0; j != _n; j++) {

            if (row[j]) d++;

          }

          _deg[i] = d;

        }

      }

      // Return a node index for a feasible add move or -1 if no one exists

      int nextFeasibleAddNode() const {

        int start_node = _rnd[_n];

        int node = -1, max_deg = -1;

        for (int i = start_node; i != _n; i++) {

          if (_delta[i] == 0 && !_tabu[i] && _deg[i] > max_deg) {

            node = i;

            max_deg = _deg[i];

          }

        }

        for (int i = 0; i != start_node; i++) {

          if (_delta[i] == 0 && !_tabu[i] && _deg[i] > max_deg) {

            node = i;

            max_deg = _deg[i];

          }

        }

        return node;

      }

      // Return a node index for a feasible swap move or -1 if no one exists

      int nextFeasibleSwapNode() const {

        int start_node = _rnd[_n];

        int node = -1, max_deg = -1;

        for (int i = start_node; i != _n; i++) {

          if (!_clique[i] && _delta[i] == 1 && !_tabu[i] &&

              _deg[i] > max_deg) {

            node = i;

            max_deg = _deg[i];

          }

        }

        for (int i = 0; i != start_node; i++) {

          if (!_clique[i] && _delta[i] == 1 && !_tabu[i] &&

              _deg[i] > max_deg) {

            node = i;

            max_deg = _deg[i];

          }

        }

        return node;

      }

      // Return a node index for an add move or -1 if no one exists

      int nextAddNode() const {

        int start_node = _rnd[_n];

        int node = -1, max_deg = -1;

        for (int i = start_node; i != _n; i++) {

          if (_delta[i] == 0 && _deg[i] > max_deg) {

            node = i;

            max_deg = _deg[i];

          }

        }

        for (int i = 0; i != start_node; i++) {

          if (_delta[i] == 0 && _deg[i] > max_deg) {

            node = i;

            max_deg = _deg[i];

          }

        }

        return node;

      }

      // Update internal data structures between stages (if necessary)

      void update() {}

    }; //class DegreeBasedSelectionRule

    // Implementation of the PENALTY_BASED node selection rule.

    class PenaltyBasedSelectionRule

    {

    private:

      // References to the algorithm instance

      const BoolVector &_clique;

      const IntVector  &_delta;

      const BoolVector &_tabu;

      Random &_rnd;

      // Pivot rule data

      int _n;

      IntVector _penalty;

    public:

      // Constructor

      PenaltyBasedSelectionRule(GrossoLocatelliPullanMc &mc) :

        _clique(mc._clique), _delta(mc._delta), _tabu(mc._tabu),

        _rnd(mc._rnd), _n(mc._n), _penalty(_n, 0)

      {}

      // Return a node index for a feasible add move or -1 if no one exists

      int nextFeasibleAddNode() const {

        int start_node = _rnd[_n];

        int node = -1, min_p = std::numeric_limits<int>::max();

        for (int i = start_node; i != _n; i++) {

          if (_delta[i] == 0 && !_tabu[i] && _penalty[i] < min_p) {

            node = i;

            min_p = _penalty[i];

          }

        }

        for (int i = 0; i != start_node; i++) {

          if (_delta[i] == 0 && !_tabu[i] && _penalty[i] < min_p) {

            node = i;

            min_p = _penalty[i];

          }

        }

        return node;

      }

      // Return a node index for a feasible swap move or -1 if no one exists

      int nextFeasibleSwapNode() const {

        int start_node = _rnd[_n];

        int node = -1, min_p = std::numeric_limits<int>::max();

        for (int i = start_node; i != _n; i++) {

          if (!_clique[i] && _delta[i] == 1 && !_tabu[i] &&

              _penalty[i] < min_p) {

            node = i;

            min_p = _penalty[i];

          }

        }

        for (int i = 0; i != start_node; i++) {

          if (!_clique[i] && _delta[i] == 1 && !_tabu[i] &&

              _penalty[i] < min_p) {

            node = i;

            min_p = _penalty[i];

          }

        }

        return node;

      }

      // Return a node index for an add move or -1 if no one exists

      int nextAddNode() const {

        int start_node = _rnd[_n];

        int node = -1, min_p = std::numeric_limits<int>::max();

        for (int i = start_node; i != _n; i++) {

          if (_delta[i] == 0 && _penalty[i] < min_p) {

            node = i;

            min_p = _penalty[i];

          }

        }

        for (int i = 0; i != start_node; i++) {

          if (_delta[i] == 0 && _penalty[i] < min_p) {

            node = i;

            min_p = _penalty[i];

          }

        }

        return node;

      }

      // Update internal data structures between stages (if necessary)

      void update() {}

    }; //class PenaltyBasedSelectionRule

  public:

    /// \brief Constructor.

    ///

    /// Constructor.

    /// The global \ref rnd "random number generator instance" is used

    /// during the algorithm.

    ///

    /// \param graph The undirected graph the algorithm runs on.

    GrossoLocatelliPullanMc(const GR& graph) :

      _graph(graph), _id(_graph), _rnd(rnd)

    {

      initOptions();

    }

    /// \brief Constructor with random seed.

    ///

    /// Constructor with random seed.

    ///

    /// \param graph The undirected graph the algorithm runs on.

    /// \param seed Seed value for the internal random number generator

    /// that is used during the algorithm.

    GrossoLocatelliPullanMc(const GR& graph, int seed) :

      _graph(graph), _id(_graph), _rnd(seed)

    {

      initOptions();

    }

    /// \brief Constructor with random number generator.

    ///

    /// Constructor with random number generator.

    ///

    /// \param graph The undirected graph the algorithm runs on.

    /// \param random A random number generator that is used during the

    /// algorithm.

    GrossoLocatelliPullanMc(const GR& graph, const Random& random) :

      _graph(graph), _id(_graph), _rnd(random)

    {

      initOptions();

    }

    /// \name Execution Control

    /// The \ref run() function can be used to execute the algorithm.\n

    /// The functions \ref iterationLimit(int), \ref stepLimit(int), and 

    /// \ref sizeLimit(int) can be used to specify various limits for the

    /// search process.

    /// @{

    /// \brief Sets the maximum number of iterations.

    ///

    /// This function sets the maximum number of iterations.

    /// Each iteration of the algorithm finds a maximal clique (but not

    /// necessarily the largest one) by performing several search steps

    /// (node selections).

    ///

    /// This limit controls the running time and the success of the

    /// algorithm. For larger values, the algorithm runs slower, but it more

    /// likely finds larger cliques. For smaller values, the algorithm is

    /// faster but probably gives worse results.

    /// 

    /// The default value is \c 1000.

    /// \c -1 means that number of iterations is not limited.

    ///

    /// \warning You should specify a reasonable limit for the number of

    /// iterations and/or the number of search steps.

    ///

    /// \return <tt>(*this)</tt>

    ///

    /// \sa stepLimit(int)

    /// \sa sizeLimit(int)

    GrossoLocatelliPullanMc& iterationLimit(int limit) {

      _iteration_limit = limit;

      return *this;

    }

    /// \brief Sets the maximum number of search steps.

    ///

    /// This function sets the maximum number of elementary search steps.

    /// Each iteration of the algorithm finds a maximal clique (but not

    /// necessarily the largest one) by performing several search steps

    /// (node selections).

    ///

    /// This limit controls the running time and the success of the

    /// algorithm. For larger values, the algorithm runs slower, but it more

    /// likely finds larger cliques. For smaller values, the algorithm is

    /// faster but probably gives worse results.

    /// 

    /// The default value is \c -1, which means that number of steps

    /// is not limited explicitly. However, the number of iterations is

    /// limited and each iteration performs a finite number of search steps.

    ///

    /// \warning You should specify a reasonable limit for the number of

    /// iterations and/or the number of search steps.

    ///

    /// \return <tt>(*this)</tt>

    ///

    /// \sa iterationLimit(int)

    /// \sa sizeLimit(int)

    GrossoLocatelliPullanMc& stepLimit(int limit) {

      _step_limit = limit;

      return *this;

    }

    /// \brief Sets the desired clique size.

    ///

    /// This function sets the desired clique size that serves as a search

    /// limit. If a clique of this size (or a larger one) is found, then the

    /// algorithm terminates.

    /// 

    /// This function is especially useful if you know an exact upper bound

    /// for the size of the cliques in the graph or if any clique above 

    /// a certain size limit is sufficient for your application.

    /// 

    /// The default value is \c -1, which means that the size limit is set to

    /// the number of nodes in the graph.

    ///

    /// \return <tt>(*this)</tt>

    ///

    /// \sa iterationLimit(int)

    /// \sa stepLimit(int)

    GrossoLocatelliPullanMc& sizeLimit(int limit) {

      _size_limit = limit;

      return *this;

    }

    /// \brief The maximum number of iterations.

    ///

    /// This function gives back the maximum number of iterations.

    /// \c -1 means that no limit is specified.

    ///

    /// \sa iterationLimit(int)

    int iterationLimit() const {

      return _iteration_limit;

    }

    /// \brief The maximum number of search steps.

    ///

    /// This function gives back the maximum number of search steps.

    /// \c -1 means that no limit is specified.

    ///

    /// \sa stepLimit(int)

    int stepLimit() const {

      return _step_limit;

    }

    /// \brief The desired clique size.

    ///

    /// This function gives back the desired clique size that serves as a

    /// search limit. \c -1 means that this limit is set to the number of

    /// nodes in the graph.

    ///

    /// \sa sizeLimit(int)

    int sizeLimit() const {

      return _size_limit;

    }

    /// \brief Runs the algorithm.

    ///

    /// This function runs the algorithm. If one of the specified limits

    /// is reached, the search process terminates.

    ///

    /// \param rule The node selection rule. For more information, see

    /// \ref SelectionRule.

    ///

    /// \return The termination cause of the search. For more information,

    /// see \ref TerminationCause.

    TerminationCause run(SelectionRule rule = PENALTY_BASED)

    {

      init();

      switch (rule) {

        case RANDOM:

          return start<RandomSelectionRule>();

        case DEGREE_BASED:

          return start<DegreeBasedSelectionRule>();

        default:

          return start<PenaltyBasedSelectionRule>();

      }

    }

    /// @}

    /// \name Query Functions

    /// The results of the algorithm can be obtained using these functions.\n

    /// The run() function must be called before using them. 

    /// @{

    /// \brief The size of the found clique

    ///

    /// This function returns the size of the found clique.

    ///

    /// \pre run() must be called before using this function.

    int cliqueSize() const {

      return _best_size;

    }

    /// \brief Gives back the found clique in a \c bool node map

    ///

    /// This function gives back the characteristic vector of the found

    /// clique in the given node map.

    /// It must be a \ref concepts::WriteMap "writable" node map with

    /// \c bool (or convertible) value type.

    ///

    /// \pre run() must be called before using this function.

    template <typename CliqueMap>

    void cliqueMap(CliqueMap &map) const {

      for (NodeIt n(_graph); n != INVALID; ++n) {

        map[n] = static_cast<bool>(_best_clique[_id[n]]);

      }

    }

    /// \brief Iterator to list the nodes of the found clique

    ///

    /// This iterator class lists the nodes of the found clique.

    /// Before using it, you must allocate a GrossoLocatelliPullanMc instance

    /// and call its \ref GrossoLocatelliPullanMc::run() "run()" method.

    ///

    /// The following example prints out the IDs of the nodes in the found

    /// clique.

    /// \code

    ///   GrossoLocatelliPullanMc<Graph> mc(g);

    ///   mc.run();

    ///   for (GrossoLocatelliPullanMc<Graph>::CliqueNodeIt n(mc);

    ///        n != INVALID; ++n)

    ///   {

    ///     std::cout << g.id(n) << std::endl;

    ///   }

    /// \endcode

    class CliqueNodeIt

    {

    private:

      NodeIt _it;

      BoolNodeMap _map;

    public:

      /// Constructor

      /// Constructor.

      /// \param mc The algorithm instance.

      CliqueNodeIt(const GrossoLocatelliPullanMc &mc)

       : _map(mc._graph)

      {

        mc.cliqueMap(_map);

        for (_it = NodeIt(mc._graph); _it != INVALID && !_map[_it]; ++_it) ;

      }

      /// Conversion to \c Node

      operator Node() const { return _it; }

      bool operator==(Invalid) const { return _it == INVALID; }

      bool operator!=(Invalid) const { return _it != INVALID; }

      /// Next node

      CliqueNodeIt &operator++() {

        for (++_it; _it != INVALID && !_map[_it]; ++_it) ;

        return *this;

      }

      /// Postfix incrementation

      /// Postfix incrementation.

      ///

      /// \warning This incrementation returns a \c Node, not a

      /// \c CliqueNodeIt as one may expect.

      typename GR::Node operator++(int) {

        Node n=*this;

        ++(*this);

        return n;

      }

    };

    /// @}

  private:

    // Initialize search options and limits

    void initOptions() {

      // Search options

      _delta_based_restart = true;

      _restart_delta_limit = 4;

      // Search limits

      _iteration_limit = 1000;

      _step_limit = -1;             // this is disabled by default

      _size_limit = -1;             // this is disabled by default

    }

    // Adds a node to the current clique

    void addCliqueNode(int u) {

      if (_clique[u]) return;

      _clique[u] = true;

      _size++;

      BoolVector &row = _gr[u];

      for (int i = 0; i != _n; i++) {

        if (!row[i]) _delta[i]++;

      }

    }

    // Removes a node from the current clique

    void delCliqueNode(int u) {

      if (!_clique[u]) return;

      _clique[u] = false;

      _size--;

      BoolVector &row = _gr[u];

      for (int i = 0; i != _n; i++) {

        if (!row[i]) _delta[i]--;

      }

    }

    // Initialize data structures

    void init() {

      _n = countNodes(_graph);

      int ui = 0;

      for (NodeIt u(_graph); u != INVALID; ++u) {

        _id[u] = ui++;

      }

      _gr.clear();

      _gr.resize(_n, BoolVector(_n, false));

      ui = 0;

      for (NodeIt u(_graph); u != INVALID; ++u) {

        for (IncEdgeIt e(_graph, u); e != INVALID; ++e) {

          int vi = _id[_graph.runningNode(e)];

          _gr[ui][vi] = true;

          _gr[vi][ui] = true;

        }

        ++ui;

      }

      _clique.clear();

      _clique.resize(_n, false);

      _size = 0;

      _best_clique.clear();

      _best_clique.resize(_n, false);

      _best_size = 0;

      _delta.clear();

      _delta.resize(_n, 0);

      _tabu.clear();

      _tabu.resize(_n, false);

    }

    // Executes the algorithm

    template <typename SelectionRuleImpl>

    TerminationCause start() {

      if (_n == 0) return SIZE_LIMIT;

      if (_n == 1) {

        _best_clique[0] = true;

        _best_size = 1;

        return SIZE_LIMIT;

      }

      // Iterated local search algorithm

      const int max_size = _size_limit >= 0 ? _size_limit : _n;

      const int max_restart = _iteration_limit >= 0 ?

        _iteration_limit : std::numeric_limits<int>::max();

      const int max_select = _step_limit >= 0 ?

        _step_limit : std::numeric_limits<int>::max();

      SelectionRuleImpl sel_method(*this);

      int select = 0, restart = 0;

      IntVector restart_nodes;

      while (select < max_select && restart < max_restart) {

        // Perturbation/restart

        restart++;

        if (_delta_based_restart) {

          restart_nodes.clear();

          for (int i = 0; i != _n; i++) {

            if (_delta[i] >= _restart_delta_limit)

              restart_nodes.push_back(i);

          }

        }

        int rs_node = -1;

        if (restart_nodes.size() > 0) {

          rs_node = restart_nodes[_rnd[restart_nodes.size()]];

        } else {

          rs_node = _rnd[_n];

        }

        BoolVector &row = _gr[rs_node];

        for (int i = 0; i != _n; i++) {

          if (_clique[i] && !row[i]) delCliqueNode(i);

        }

        addCliqueNode(rs_node);

        // Local search

        _tabu.clear();

        _tabu.resize(_n, false);

        bool tabu_empty = true;

        int max_swap = _size;

        while (select < max_select) {

          select++;

          int u;

          if ((u = sel_method.nextFeasibleAddNode()) != -1) {

            // Feasible add move

            addCliqueNode(u);

            if (tabu_empty) max_swap = _size;

          }

          else if ((u = sel_method.nextFeasibleSwapNode()) != -1) {

            // Feasible swap move

            int v = -1;

            BoolVector &row = _gr[u];

            for (int i = 0; i != _n; i++) {

              if (_clique[i] && !row[i]) {

                v = i;

                break;

              }

            }

            addCliqueNode(u);

            delCliqueNode(v);

            _tabu[v] = true;

            tabu_empty = false;

            if (--max_swap <= 0) break;

          }

          else if ((u = sel_method.nextAddNode()) != -1) {

            // Non-feasible add move

            addCliqueNode(u);

          }

          else break;

        }

        if (_size > _best_size) {

          _best_clique = _clique;

          _best_size = _size;

          if (_best_size >= max_size) return SIZE_LIMIT;

        }

        sel_method.update();

      }

      return (restart >= max_restart ? ITERATION_LIMIT : STEP_LIMIT);

    }

  }; //class GrossoLocatelliPullanMc

  ///@}

} //namespace lemon

#endif //LEMON_GROSSO_LOCATELLI_PULLAN_MC_H