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extern/quadriflow/3rd/lemon-1.3.1/lemon/hartmann_orlin_mmc.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_HARTMANN_ORLIN_MMC_H
#define LEMON_HARTMANN_ORLIN_MMC_H
/// \ingroup min_mean_cycle
///
/// \file
/// \brief Hartmann-Orlin's algorithm for finding a minimum mean cycle.
#include <vector>
#include <limits>
#include <lemon/core.h>
#include <lemon/path.h>
#include <lemon/tolerance.h>
#include <lemon/connectivity.h>
namespace lemon {
/// \brief Default traits class of HartmannOrlinMmc class.
///
/// Default traits class of HartmannOrlinMmc class.
/// \tparam GR The type of the digraph.
/// \tparam CM The type of the cost map.
/// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
#ifdef DOXYGEN
template <typename GR, typename CM>
#else
template <typename GR, typename CM,
bool integer = std::numeric_limits<typename CM::Value>::is_integer>
#endif
struct HartmannOrlinMmcDefaultTraits
{
/// The type of the digraph
typedef GR Digraph;
/// The type of the cost map
typedef CM CostMap;
/// The type of the arc costs
typedef typename CostMap::Value Cost;
/// \brief The large cost type used for internal computations
///
/// The large cost type used for internal computations.
/// It is \c long \c long if the \c Cost type is integer,
/// otherwise it is \c double.
/// \c Cost must be convertible to \c LargeCost.
typedef double LargeCost;
/// The tolerance type used for internal computations
typedef lemon::Tolerance<LargeCost> Tolerance;
/// \brief The path type of the found cycles
///
/// The path type of the found cycles.
/// It must conform to the \ref lemon::concepts::Path "Path" concept
/// and it must have an \c addFront() function.
typedef lemon::Path<Digraph> Path;
};
// Default traits class for integer cost types
template <typename GR, typename CM>
struct HartmannOrlinMmcDefaultTraits<GR, CM, true>
{
typedef GR Digraph;
typedef CM CostMap;
typedef typename CostMap::Value Cost;
#ifdef LEMON_HAVE_LONG_LONG
typedef long long LargeCost;
#else
typedef long LargeCost;
#endif
typedef lemon::Tolerance<LargeCost> Tolerance;
typedef lemon::Path<Digraph> Path;
};
/// \addtogroup min_mean_cycle
/// @{
/// \brief Implementation of the Hartmann-Orlin algorithm for finding
/// a minimum mean cycle.
///
/// This class implements the Hartmann-Orlin algorithm for finding
/// a directed cycle of minimum mean cost in a digraph
/// \cite hartmann93finding, \cite dasdan98minmeancycle.
/// This method is based on \ref KarpMmc "Karp"'s original algorithm, but
/// applies an early termination scheme. It makes the algorithm
/// significantly faster for some problem instances, but slower for others.
/// The algorithm runs in time O(nm) and uses space O(n<sup>2</sup>+m).
///
/// \tparam GR The type of the digraph the algorithm runs on.
/// \tparam CM The type of the cost map. The default
/// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
/// \tparam TR The traits class that defines various types used by the
/// algorithm. By default, it is \ref HartmannOrlinMmcDefaultTraits
/// "HartmannOrlinMmcDefaultTraits<GR, CM>".
/// In most cases, this parameter should not be set directly,
/// consider to use the named template parameters instead.
#ifdef DOXYGEN
template <typename GR, typename CM, typename TR>
#else
template < typename GR,
typename CM = typename GR::template ArcMap<int>,
typename TR = HartmannOrlinMmcDefaultTraits<GR, CM> >
#endif
class HartmannOrlinMmc
{
public:
/// The type of the digraph
typedef typename TR::Digraph Digraph;
/// The type of the cost map
typedef typename TR::CostMap CostMap;
/// The type of the arc costs
typedef typename TR::Cost Cost;
/// \brief The large cost type
///
/// The large cost type used for internal computations.
/// By default, it is \c long \c long if the \c Cost type is integer,
/// otherwise it is \c double.
typedef typename TR::LargeCost LargeCost;
/// The tolerance type
typedef typename TR::Tolerance Tolerance;
/// \brief The path type of the found cycles
///
/// The path type of the found cycles.
/// Using the \ref lemon::HartmannOrlinMmcDefaultTraits
/// "default traits class",
/// it is \ref lemon::Path "Path<Digraph>".
typedef typename TR::Path Path;
/// \brief The
/// \ref lemon::HartmannOrlinMmcDefaultTraits "traits class"
/// of the algorithm
typedef TR Traits;
private:
TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
// Data sturcture for path data
struct PathData
{
LargeCost dist;
Arc pred;
PathData(LargeCost d, Arc p = INVALID) :
dist(d), pred(p) {}
};
typedef typename Digraph::template NodeMap<std::vector<PathData> >
PathDataNodeMap;
private:
// The digraph the algorithm runs on
const Digraph &_gr;
// The cost of the arcs
const CostMap &_cost;
// Data for storing the strongly connected components
int _comp_num;
typename Digraph::template NodeMap<int> _comp;
std::vector<std::vector<Node> > _comp_nodes;
std::vector<Node>* _nodes;
typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
// Data for the found cycles
bool _curr_found, _best_found;
LargeCost _curr_cost, _best_cost;
int _curr_size, _best_size;
Node _curr_node, _best_node;
int _curr_level, _best_level;
Path *_cycle_path;
bool _local_path;
// Node map for storing path data
PathDataNodeMap _data;
// The processed nodes in the last round
std::vector<Node> _process;
Tolerance _tolerance;
// Infinite constant
const LargeCost INF;
public:
/// \name Named Template Parameters
/// @{
template <typename T>
struct SetLargeCostTraits : public Traits {
typedef T LargeCost;
typedef lemon::Tolerance<T> Tolerance;
};
/// \brief \ref named-templ-param "Named parameter" for setting
/// \c LargeCost type.
///
/// \ref named-templ-param "Named parameter" for setting \c LargeCost
/// type. It is used for internal computations in the algorithm.
template <typename T>
struct SetLargeCost
: public HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > {
typedef HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > Create;
};
template <typename T>
struct SetPathTraits : public Traits {
typedef T Path;
};
/// \brief \ref named-templ-param "Named parameter" for setting
/// \c %Path type.
///
/// \ref named-templ-param "Named parameter" for setting the \c %Path
/// type of the found cycles.
/// It must conform to the \ref lemon::concepts::Path "Path" concept
/// and it must have an \c addFront() function.
template <typename T>
struct SetPath
: public HartmannOrlinMmc<GR, CM, SetPathTraits<T> > {
typedef HartmannOrlinMmc<GR, CM, SetPathTraits<T> > Create;
};
/// @}
protected:
HartmannOrlinMmc() {}
public:
/// \brief Constructor.
///
/// The constructor of the class.
///
/// \param digraph The digraph the algorithm runs on.
/// \param cost The costs of the arcs.
HartmannOrlinMmc( const Digraph &digraph,
const CostMap &cost ) :
_gr(digraph), _cost(cost), _comp(digraph), _out_arcs(digraph),
_best_found(false), _best_cost(0), _best_size(1),
_cycle_path(NULL), _local_path(false), _data(digraph),
INF(std::numeric_limits<LargeCost>::has_infinity ?
std::numeric_limits<LargeCost>::infinity() :
std::numeric_limits<LargeCost>::max())
{}
/// Destructor.
~HartmannOrlinMmc() {
if (_local_path) delete _cycle_path;
}
/// \brief Set the path structure for storing the found cycle.
///
/// This function sets an external path structure for storing the
/// found cycle.
///
/// If you don't call this function before calling \ref run() or
/// \ref findCycleMean(), a local \ref Path "path" structure
/// will be allocated. The destuctor deallocates this automatically
/// allocated object, of course.
///
/// \note The algorithm calls only the \ref lemon::Path::addFront()
/// "addFront()" function of the given path structure.
///
/// \return <tt>(*this)</tt>
HartmannOrlinMmc& cycle(Path &path) {
if (_local_path) {
delete _cycle_path;
_local_path = false;
}
_cycle_path = &path;
return *this;
}
/// \brief Set the tolerance used by the algorithm.
///
/// This function sets the tolerance object used by the algorithm.
///
/// \return <tt>(*this)</tt>
HartmannOrlinMmc& tolerance(const Tolerance& tolerance) {
_tolerance = tolerance;
return *this;
}
/// \brief Return a const reference to the tolerance.
///
/// This function returns a const reference to the tolerance object
/// used by the algorithm.
const Tolerance& tolerance() const {
return _tolerance;
}
/// \name Execution control
/// The simplest way to execute the algorithm is to call the \ref run()
/// function.\n
/// If you only need the minimum mean cost, you may call
/// \ref findCycleMean().
/// @{
/// \brief Run the algorithm.
///
/// This function runs the algorithm.
/// It can be called more than once (e.g. if the underlying digraph
/// and/or the arc costs have been modified).
///
/// \return \c true if a directed cycle exists in the digraph.
///
/// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
/// \code
/// return mmc.findCycleMean() && mmc.findCycle();
/// \endcode
bool run() {
return findCycleMean() && findCycle();
}
/// \brief Find the minimum cycle mean.
///
/// This function finds the minimum mean cost of the directed
/// cycles in the digraph.
///
/// \return \c true if a directed cycle exists in the digraph.
bool findCycleMean() {
// Initialization and find strongly connected components
init();
findComponents();
// Find the minimum cycle mean in the components
for (int comp = 0; comp < _comp_num; ++comp) {
if (!initComponent(comp)) continue;
processRounds();
// Update the best cycle (global minimum mean cycle)
if ( _curr_found && (!_best_found ||
_curr_cost * _best_size < _best_cost * _curr_size) ) {
_best_found = true;
_best_cost = _curr_cost;
_best_size = _curr_size;
_best_node = _curr_node;
_best_level = _curr_level;
}
}
return _best_found;
}
/// \brief Find a minimum mean directed cycle.
///
/// This function finds a directed cycle of minimum mean cost
/// in the digraph using the data computed by findCycleMean().
///
/// \return \c true if a directed cycle exists in the digraph.
///
/// \pre \ref findCycleMean() must be called before using this function.
bool findCycle() {
if (!_best_found) return false;
IntNodeMap reached(_gr, -1);
int r = _best_level + 1;
Node u = _best_node;
while (reached[u] < 0) {
reached[u] = --r;
u = _gr.source(_data[u][r].pred);
}
r = reached[u];
Arc e = _data[u][r].pred;
_cycle_path->addFront(e);
_best_cost = _cost[e];
_best_size = 1;
Node v;
while ((v = _gr.source(e)) != u) {
e = _data[v][--r].pred;
_cycle_path->addFront(e);
_best_cost += _cost[e];
++_best_size;
}
return true;
}
/// @}
/// \name Query Functions
/// The results of the algorithm can be obtained using these
/// functions.\n
/// The algorithm should be executed before using them.
/// @{
/// \brief Return the total cost of the found cycle.
///
/// This function returns the total cost of the found cycle.
///
/// \pre \ref run() or \ref findCycleMean() must be called before
/// using this function.
Cost cycleCost() const {
return static_cast<Cost>(_best_cost);
}
/// \brief Return the number of arcs on the found cycle.
///
/// This function returns the number of arcs on the found cycle.
///
/// \pre \ref run() or \ref findCycleMean() must be called before
/// using this function.
int cycleSize() const {
return _best_size;
}
/// \brief Return the mean cost of the found cycle.
///
/// This function returns the mean cost of the found cycle.
///
/// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
/// following code.
/// \code
/// return static_cast<double>(alg.cycleCost()) / alg.cycleSize();
/// \endcode
///
/// \pre \ref run() or \ref findCycleMean() must be called before
/// using this function.
double cycleMean() const {
return static_cast<double>(_best_cost) / _best_size;
}
/// \brief Return the found cycle.
///
/// This function returns a const reference to the path structure
/// storing the found cycle.
///
/// \pre \ref run() or \ref findCycle() must be called before using
/// this function.
const Path& cycle() const {
return *_cycle_path;
}
///@}
private:
// Initialization
void init() {
if (!_cycle_path) {
_local_path = true;
_cycle_path = new Path;
}
_cycle_path->clear();
_best_found = false;
_best_cost = 0;
_best_size = 1;
_cycle_path->clear();
for (NodeIt u(_gr); u != INVALID; ++u)
_data[u].clear();
}
// Find strongly connected components and initialize _comp_nodes
// and _out_arcs
void findComponents() {
_comp_num = stronglyConnectedComponents(_gr, _comp);
_comp_nodes.resize(_comp_num);
if (_comp_num == 1) {
_comp_nodes[0].clear();
for (NodeIt n(_gr); n != INVALID; ++n) {
_comp_nodes[0].push_back(n);
_out_arcs[n].clear();
for (OutArcIt a(_gr, n); a != INVALID; ++a) {
_out_arcs[n].push_back(a);
}
}
} else {
for (int i = 0; i < _comp_num; ++i)
_comp_nodes[i].clear();
for (NodeIt n(_gr); n != INVALID; ++n) {
int k = _comp[n];
_comp_nodes[k].push_back(n);
_out_arcs[n].clear();
for (OutArcIt a(_gr, n); a != INVALID; ++a) {
if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
}
}
}
}
// Initialize path data for the current component
bool initComponent(int comp) {
_nodes = &(_comp_nodes[comp]);
int n = _nodes->size();
if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
return false;
}
for (int i = 0; i < n; ++i) {
_data[(*_nodes)[i]].resize(n + 1, PathData(INF));
}
return true;
}
// Process all rounds of computing path data for the current component.
// _data[v][k] is the cost of a shortest directed walk from the root
// node to node v containing exactly k arcs.
void processRounds() {
Node start = (*_nodes)[0];
_data[start][0] = PathData(0);
_process.clear();
_process.push_back(start);
int k, n = _nodes->size();
int next_check = 4;
bool terminate = false;
for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) {
processNextBuildRound(k);
if (k == next_check || k == n) {
terminate = checkTermination(k);
next_check = next_check * 3 / 2;
}
}
for ( ; k <= n && !terminate; ++k) {
processNextFullRound(k);
if (k == next_check || k == n) {
terminate = checkTermination(k);
next_check = next_check * 3 / 2;
}
}
}
// Process one round and rebuild _process
void processNextBuildRound(int k) {
std::vector<Node> next;
Node u, v;
Arc e;
LargeCost d;
for (int i = 0; i < int(_process.size()); ++i) {
u = _process[i];
for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
e = _out_arcs[u][j];
v = _gr.target(e);
d = _data[u][k-1].dist + _cost[e];
if (_tolerance.less(d, _data[v][k].dist)) {
if (_data[v][k].dist == INF) next.push_back(v);
_data[v][k] = PathData(d, e);
}
}
}
_process.swap(next);
}
// Process one round using _nodes instead of _process
void processNextFullRound(int k) {
Node u, v;
Arc e;
LargeCost d;
for (int i = 0; i < int(_nodes->size()); ++i) {
u = (*_nodes)[i];
for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
e = _out_arcs[u][j];
v = _gr.target(e);
d = _data[u][k-1].dist + _cost[e];
if (_tolerance.less(d, _data[v][k].dist)) {
_data[v][k] = PathData(d, e);
}
}
}
}
// Check early termination
bool checkTermination(int k) {
typedef std::pair<int, int> Pair;
typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0));
typename GR::template NodeMap<LargeCost> pi(_gr);
int n = _nodes->size();
LargeCost cost;
int size;
Node u;
// Search for cycles that are already found
_curr_found = false;
for (int i = 0; i < n; ++i) {
u = (*_nodes)[i];
if (_data[u][k].dist == INF) continue;
for (int j = k; j >= 0; --j) {
if (level[u].first == i && level[u].second > 0) {
// A cycle is found
cost = _data[u][level[u].second].dist - _data[u][j].dist;
size = level[u].second - j;
if (!_curr_found || cost * _curr_size < _curr_cost * size) {
_curr_cost = cost;
_curr_size = size;
_curr_node = u;
_curr_level = level[u].second;
_curr_found = true;
}
}
level[u] = Pair(i, j);
if (j != 0) {
u = _gr.source(_data[u][j].pred);
}
}
}
// If at least one cycle is found, check the optimality condition
LargeCost d;
if (_curr_found && k < n) {
// Find node potentials
for (int i = 0; i < n; ++i) {
u = (*_nodes)[i];
pi[u] = INF;
for (int j = 0; j <= k; ++j) {
if (_data[u][j].dist < INF) {
d = _data[u][j].dist * _curr_size - j * _curr_cost;
if (_tolerance.less(d, pi[u])) pi[u] = d;
}
}
}
// Check the optimality condition for all arcs
bool done = true;
for (ArcIt a(_gr); a != INVALID; ++a) {
if (_tolerance.less(_cost[a] * _curr_size - _curr_cost,
pi[_gr.target(a)] - pi[_gr.source(a)]) ) {
done = false;
break;
}
}
return done;
}
return (k == n);
}
}; //class HartmannOrlinMmc
///@}
} //namespace lemon
#endif //LEMON_HARTMANN_ORLIN_MMC_H