dust3d/thirdparty/QuadriFlow/3rd/lemon-1.3.1/lemon/grosso_locatelli_pullan_mc.h

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/* -*- mode: C++; indent-tabs-mode: nil; -*-
*
* This file is a part of LEMON, a generic C++ optimization library.
*
* Copyright (C) 2003-2013
* 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