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ecency-mobile/ios/Pods/boost-for-react-native/boost/graph/howard_cycle_ratio.hpp

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// Copyright (C) 2006-2009 Dmitry Bufistov and Andrey Parfenov
// Use, modification and distribution is subject to the Boost Software
// License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_GRAPH_CYCLE_RATIO_HOWARD_HPP
#define BOOST_GRAPH_CYCLE_RATIO_HOWARD_HPP
#include <vector>
#include <list>
#include <algorithm>
#include <limits>
#include <boost/bind.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/type_traits/remove_const.hpp>
#include <boost/concept_check.hpp>
#include <boost/pending/queue.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/graph_concepts.hpp>
#include <boost/concept/assert.hpp>
/** @file howard_cycle_ratio.hpp
* @brief The implementation of the maximum/minimum cycle ratio/mean algorithm.
* @author Dmitry Bufistov
* @author Andrey Parfenov
*/
namespace boost {
/**
* The mcr_float is like numeric_limits, but only for floating point types
* and only defines infinity() and epsilon(). This class is primarily used
* to encapsulate a less-precise epsilon than natively supported by the
* floating point type.
*/
template <typename Float = double> struct mcr_float {
typedef Float value_type;
static Float infinity()
{ return std::numeric_limits<value_type>::infinity(); }
static Float epsilon()
{ return Float(-0.005); }
};
namespace detail {
template <typename FloatTraits> struct
min_comparator_props {
typedef std::greater<typename FloatTraits::value_type> comparator;
static const int multiplier = 1;
};
template <typename FloatTraits> struct
max_comparator_props {
typedef std::less<typename FloatTraits::value_type> comparator;
static const int multiplier = -1;
};
template <typename FloatTraits, typename ComparatorProps>
struct float_wrapper {
typedef typename FloatTraits::value_type value_type;
typedef ComparatorProps comparator_props_t;
typedef typename ComparatorProps::comparator comparator;
static value_type infinity()
{ return FloatTraits::infinity() * ComparatorProps::multiplier; }
static value_type epsilon()
{ return FloatTraits::epsilon() * ComparatorProps::multiplier; }
};
/*! @class mcr_howard
* @brief Calculates optimum (maximum/minimum) cycle ratio of a directed graph.
* Uses Howard's iteration policy algorithm. </br>(It is described in the paper
* "Experimental Analysis of the Fastest Optimum Cycle Ratio and Mean Algorithm"
* by Ali Dasdan).
*/
template <typename FloatTraits,
typename Graph, typename VertexIndexMap,
typename EdgeWeight1, typename EdgeWeight2>
class mcr_howard
{
public:
typedef typename FloatTraits::value_type float_t;
typedef typename FloatTraits::comparator_props_t cmp_props_t;
typedef typename FloatTraits::comparator comparator_t;
typedef enum{ my_white = 0, my_black } my_color_type;
typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
typedef typename graph_traits<Graph>::edge_descriptor edge_t;
typedef typename graph_traits<Graph>::vertices_size_type vn_t;
typedef std::vector<float_t> vp_t;
typedef typename boost::iterator_property_map<
typename vp_t::iterator, VertexIndexMap
> distance_map_t; //V -> float_t
typedef typename std::vector<edge_t> ve_t;
typedef std::vector<my_color_type> vcol_t;
typedef typename ::boost::iterator_property_map<
typename ve_t::iterator, VertexIndexMap
> policy_t; //Vertex -> Edge
typedef typename ::boost::iterator_property_map<
typename vcol_t::iterator, VertexIndexMap
> color_map_t;
typedef typename std::list<vertex_t> pinel_t;// The in_edges list of the policy graph
typedef typename std::vector<pinel_t> inedges1_t;
typedef typename ::boost::iterator_property_map<
typename inedges1_t::iterator, VertexIndexMap
> inedges_t;
typedef typename std::vector<edge_t> critical_cycle_t;
//Bad vertex flag. If true, then the vertex is "bad".
// Vertex is "bad" if its out_degree is equal to zero.
typedef typename boost::iterator_property_map<
std::vector<int>::iterator, VertexIndexMap
> badv_t;
/*!
* Constructor
* \param g = (V, E) - a directed multigraph.
* \param vim Vertex Index Map. Read property Map: V -> [0, num_vertices(g)).
* \param ewm edge weight map. Read property map: E -> R
* \param ew2m edge weight map. Read property map: E -> R+
* \param infty A big enough value to guaranty that there exist a cycle with
* better ratio.
* \param cmp The compare operator for float_ts.
*/
mcr_howard(const Graph &g, VertexIndexMap vim,
EdgeWeight1 ewm, EdgeWeight2 ew2m) :
m_g(g), m_vim(vim), m_ew1m(ewm), m_ew2m(ew2m),
m_bound(mcr_bound()),
m_cr(m_bound),
m_V(num_vertices(m_g)),
m_dis(m_V, 0), m_dm(m_dis.begin(), m_vim),
m_policyc(m_V), m_policy(m_policyc.begin(), m_vim),
m_inelc(m_V), m_inel(m_inelc.begin(), m_vim),
m_badvc(m_V, false), m_badv(m_badvc.begin(), m_vim),
m_colcv(m_V),
m_col_bfs(m_V)
{ }
/*!
* \return maximum/minimum_{for all cycles C}
* [sum_{e in C} w1(e)] / [sum_{e in C} w2(e)],
* or FloatTraits::infinity() if graph has no cycles.
*/
float_t ocr_howard()
{
construct_policy_graph();
int k = 0;
float_t mcr = 0;
do
{
mcr = policy_mcr();
++k;
}
while (try_improve_policy(mcr) && k < 100); //To avoid infinite loop
const float_t eps_ = -0.00000001 * cmp_props_t::multiplier;
if (m_cmp(mcr, m_bound + eps_))
{
return FloatTraits::infinity();
}
else
{
return mcr;
}
}
virtual ~mcr_howard() {}
protected:
virtual void store_critical_edge(edge_t, critical_cycle_t &) {}
virtual void store_critical_cycle(critical_cycle_t &) {}
private:
/*!
* \return lower/upper bound for the maximal/minimal cycle ratio
*/
float_t mcr_bound()
{
typename graph_traits<Graph>::vertex_iterator vi, vie;
typename graph_traits<Graph>::out_edge_iterator oei, oeie;
float_t cz = (std::numeric_limits<float_t>::max)(); //Closest to zero value
float_t s = 0;
const float_t eps_ = std::numeric_limits<float_t>::epsilon();
for (boost::tie(vi, vie) = vertices(m_g); vi != vie; ++vi)
{
for (boost::tie(oei, oeie) = out_edges(*vi, m_g); oei != oeie; ++oei)
{
s += std::abs(m_ew1m[*oei]);
float_t a = std::abs(m_ew2m[*oei]);
if ( a > eps_ && a < cz)
{
cz = a;
}
}
}
return cmp_props_t::multiplier * (s / cz);
}
/*!
* Constructs an arbitrary policy graph.
*/
void construct_policy_graph()
{
m_sink = graph_traits<Graph>().null_vertex();
typename graph_traits<Graph>::vertex_iterator vi, vie;
typename graph_traits<Graph>::out_edge_iterator oei, oeie;
for ( boost::tie(vi, vie) = vertices(m_g); vi != vie; ++vi )
{
boost::tie(oei, oeie) = out_edges(*vi, m_g);
typename graph_traits<Graph>::out_edge_iterator mei =
std::max_element(oei, oeie,
boost::bind(m_cmp,
boost::bind(&EdgeWeight1::operator[], m_ew1m, _1),
boost::bind(&EdgeWeight1::operator[], m_ew1m, _2)
)
);
if (mei == oeie)
{
if (m_sink == graph_traits<Graph>().null_vertex())
{
m_sink = *vi;
}
m_badv[*vi] = true;
m_inel[m_sink].push_back(*vi);
}
else
{
m_inel[target(*mei, m_g)].push_back(*vi);
m_policy[*vi] = *mei;
}
}
}
/*! Sets the distance value for all vertices "v" such that there is
* a path from "v" to "sv". It does "inverse" breadth first visit of the policy
* graph, starting from the vertex "sv".
*/
void mcr_bfv(vertex_t sv, float_t cr, color_map_t c)
{
boost::queue<vertex_t> Q;
c[sv] = my_black;
Q.push(sv);
while (!Q.empty())
{
vertex_t v = Q.top(); Q.pop();
for (typename pinel_t::const_iterator itr = m_inel[v].begin();
itr != m_inel[v].end(); ++itr)
//For all in_edges of the policy graph
{
if (*itr != sv)
{
if (m_badv[*itr])
{
m_dm[*itr] = m_dm[v] + m_bound - cr;
}
else
{
m_dm[*itr] = m_dm[v] + m_ew1m[m_policy[*itr]] -
m_ew2m[m_policy[*itr]] * cr;
}
c[*itr] = my_black;
Q.push(*itr);
}
}
}
}
/*!
* \param sv an arbitrary (undiscovered) vertex of the policy graph.
* \return a vertex in the policy graph that belongs to a cycle.
* Performs a depth first visit until a cycle edge is found.
*/
vertex_t find_cycle_vertex(vertex_t sv)
{
vertex_t gv = sv;
std::fill(m_colcv.begin(), m_colcv.end(), my_white);
color_map_t cm(m_colcv.begin(), m_vim);
do
{
cm[gv] = my_black;
if (! m_badv[gv])
{
gv = target(m_policy[gv], m_g);
}
else
{
gv = m_sink;
}
}
while (cm[gv] != my_black);
return gv;
}
/*!
* \param sv - vertex that belongs to a cycle in the policy graph.
*/
float_t cycle_ratio(vertex_t sv)
{
if (sv == m_sink) return m_bound;
std::pair<float_t, float_t> sums_(float_t(0), float_t(0));
vertex_t v = sv;
critical_cycle_t cc;
do
{
store_critical_edge(m_policy[v], cc);
sums_.first += m_ew1m[m_policy[v]];
sums_.second += m_ew2m[m_policy[v]];
v = target(m_policy[v], m_g);
}
while (v != sv);
float_t cr = sums_.first / sums_.second;
if ( m_cmp(m_cr, cr) )
{
m_cr = cr;
store_critical_cycle(cc);
}
return cr;
}
/*!
* Finds the optimal cycle ratio of the policy graph
*/
float_t policy_mcr()
{
std::fill(m_col_bfs.begin(), m_col_bfs.end(), my_white);
color_map_t vcm_ = color_map_t(m_col_bfs.begin(), m_vim);
typename graph_traits<Graph>::vertex_iterator uv_itr, vie;
boost::tie(uv_itr, vie) = vertices(m_g);
float_t mcr = m_bound;
while ( (uv_itr = std::find_if(uv_itr, vie,
boost::bind(std::equal_to<my_color_type>(),
my_white,
boost::bind(&color_map_t::operator[], vcm_, _1)
)
)
) != vie )
///While there are undiscovered vertices
{
vertex_t gv = find_cycle_vertex(*uv_itr);
float_t cr = cycle_ratio(gv) ;
mcr_bfv(gv, cr, vcm_);
if ( m_cmp(mcr, cr) ) mcr = cr;
++uv_itr;
}
return mcr;
}
/*!
* Changes the edge m_policy[s] to the new_edge.
*/
void improve_policy(vertex_t s, edge_t new_edge)
{
vertex_t t = target(m_policy[s], m_g);
typename property_traits<VertexIndexMap>::value_type ti = m_vim[t];
m_inelc[ti].erase( std::find(m_inelc[ti].begin(), m_inelc[ti].end(), s));
m_policy[s] = new_edge;
t = target(new_edge, m_g);
m_inel[t].push_back(s); ///Maintain in_edge list
}
/*!
* A negative cycle detector.
*/
bool try_improve_policy(float_t cr)
{
bool improved = false;
typename graph_traits<Graph>::vertex_iterator vi, vie;
typename graph_traits<Graph>::out_edge_iterator oei, oeie;
const float_t eps_ = FloatTraits::epsilon();
for (boost::tie(vi, vie) = vertices(m_g); vi != vie; ++vi)
{
if (!m_badv[*vi])
{
for (boost::tie(oei, oeie) = out_edges(*vi, m_g); oei != oeie; ++oei)
{
vertex_t t = target(*oei, m_g);
//Current distance from *vi to some vertex
float_t dis_ = m_ew1m[*oei] - m_ew2m[*oei] * cr + m_dm[t];
if ( m_cmp(m_dm[*vi] + eps_, dis_) )
{
improve_policy(*vi, *oei);
m_dm[*vi] = dis_;
improved = true;
}
}
}
else
{
float_t dis_ = m_bound - cr + m_dm[m_sink];
if ( m_cmp(m_dm[*vi] + eps_, dis_) )
{
m_dm[*vi] = dis_;
}
}
}
return improved;
}
private:
const Graph &m_g;
VertexIndexMap m_vim;
EdgeWeight1 m_ew1m;
EdgeWeight2 m_ew2m;
comparator_t m_cmp;
float_t m_bound; //> The lower/upper bound to the maximal/minimal cycle ratio
float_t m_cr; //>The best cycle ratio that has been found so far
vn_t m_V; //>The number of the vertices in the graph
vp_t m_dis; //>Container for the distance map
distance_map_t m_dm; //>Distance map
ve_t m_policyc; //>Container for the policy graph
policy_t m_policy; //>The interface for the policy graph
inedges1_t m_inelc; //>Container fot in edges list
inedges_t m_inel; //>Policy graph, input edges list
std::vector<int> m_badvc;
badv_t m_badv; //Marks "bad" vertices
vcol_t m_colcv, m_col_bfs; //Color maps
vertex_t m_sink; //To convert any graph to "good"
};
/*! \class mcr_howard1
* \brief Finds optimum cycle raio and a critical cycle
*/
template <typename FloatTraits,
typename Graph, typename VertexIndexMap,
typename EdgeWeight1, typename EdgeWeight2>
class mcr_howard1 : public
mcr_howard<FloatTraits, Graph, VertexIndexMap,
EdgeWeight1, EdgeWeight2>
{
public:
typedef mcr_howard<FloatTraits, Graph, VertexIndexMap,
EdgeWeight1, EdgeWeight2> inhr_t;
mcr_howard1(const Graph &g, VertexIndexMap vim,
EdgeWeight1 ewm, EdgeWeight2 ew2m) :
inhr_t(g, vim, ewm, ew2m)
{ }
void get_critical_cycle(typename inhr_t::critical_cycle_t &cc)
{ return cc.swap(m_cc); }
protected:
void store_critical_edge(typename inhr_t::edge_t ed,
typename inhr_t::critical_cycle_t &cc)
{ cc.push_back(ed); }
void store_critical_cycle(typename inhr_t::critical_cycle_t &cc)
{ m_cc.swap(cc); }
private:
typename inhr_t::critical_cycle_t m_cc; //Critical cycle
};
/*!
* \param g a directed multigraph.
* \param vim Vertex Index Map. A map V->[0, num_vertices(g))
* \param ewm Edge weight1 map.
* \param ew2m Edge weight2 map.
* \param pcc pointer to the critical edges list.
* \return Optimum cycle ratio of g or FloatTraits::infinity() if g has no cycles.
*/
template <typename FT,
typename TG, typename TVIM,
typename TEW1, typename TEW2,
typename EV>
typename FT::value_type
optimum_cycle_ratio(const TG &g, TVIM vim, TEW1 ewm, TEW2 ew2m, EV* pcc)
{
typedef typename graph_traits<TG>::directed_category DirCat;
BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true));
BOOST_CONCEPT_ASSERT(( IncidenceGraphConcept<TG> ));
BOOST_CONCEPT_ASSERT(( VertexListGraphConcept<TG> ));
typedef typename graph_traits<TG>::vertex_descriptor Vertex;
BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept<TVIM, Vertex> ));
typedef typename graph_traits<TG>::edge_descriptor Edge;
BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept<TEW1, Edge> ));
BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept<TEW2, Edge> ));
if(pcc == 0) {
return detail::mcr_howard<FT,TG, TVIM, TEW1, TEW2>(
g, vim, ewm, ew2m
).ocr_howard();
}
detail::mcr_howard1<FT, TG, TVIM, TEW1, TEW2> obj(g, vim, ewm, ew2m);
double ocr = obj.ocr_howard();
obj.get_critical_cycle(*pcc);
return ocr;
}
} // namespace detail
// Algorithms
// Maximum Cycle Ratio
template <
typename FloatTraits,
typename Graph,
typename VertexIndexMap,
typename EdgeWeight1Map,
typename EdgeWeight2Map>
inline typename FloatTraits::value_type
maximum_cycle_ratio(const Graph &g, VertexIndexMap vim, EdgeWeight1Map ew1m,
EdgeWeight2Map ew2m,
std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0,
FloatTraits = FloatTraits())
{
typedef detail::float_wrapper<
FloatTraits, detail::max_comparator_props<FloatTraits>
> Traits;
return detail::optimum_cycle_ratio<Traits>(g, vim, ew1m, ew2m, pcc);
}
template <
typename Graph,
typename VertexIndexMap,
typename EdgeWeight1Map,
typename EdgeWeight2Map>
inline double
maximum_cycle_ratio(const Graph &g, VertexIndexMap vim,
EdgeWeight1Map ew1m, EdgeWeight2Map ew2m,
std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0)
{ return maximum_cycle_ratio(g, vim, ew1m, ew2m, pcc, mcr_float<>()); }
// Minimum Cycle Ratio
template <
typename FloatTraits,
typename Graph,
typename VertexIndexMap,
typename EdgeWeight1Map,
typename EdgeWeight2Map>
typename FloatTraits::value_type
minimum_cycle_ratio(const Graph &g, VertexIndexMap vim,
EdgeWeight1Map ew1m, EdgeWeight2Map ew2m,
std::vector<typename graph_traits<Graph>::edge_descriptor> *pcc = 0,
FloatTraits = FloatTraits())
{
typedef detail::float_wrapper<
FloatTraits, detail::min_comparator_props<FloatTraits>
> Traits;
return detail::optimum_cycle_ratio<Traits>(g, vim, ew1m, ew2m, pcc);
}
template <
typename Graph,
typename VertexIndexMap,
typename EdgeWeight1Map,
typename EdgeWeight2Map>
inline double
minimum_cycle_ratio(const Graph &g, VertexIndexMap vim,
EdgeWeight1Map ew1m, EdgeWeight2Map ew2m,
std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0)
{ return minimum_cycle_ratio(g, vim, ew1m, ew2m, pcc, mcr_float<>()); }
// Maximum Cycle Mean
template <
typename FloatTraits,
typename Graph,
typename VertexIndexMap,
typename EdgeWeightMap,
typename EdgeIndexMap>
inline typename FloatTraits::value_type
maximum_cycle_mean(const Graph &g, VertexIndexMap vim,
EdgeWeightMap ewm, EdgeIndexMap eim,
std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0,
FloatTraits ft = FloatTraits())
{
typedef typename remove_const<
typename property_traits<EdgeWeightMap>::value_type
>::type Weight;
typename std::vector<Weight> ed_w2(boost::num_edges(g), 1);
return maximum_cycle_ratio(g, vim, ewm,
make_iterator_property_map(ed_w2.begin(), eim),
pcc, ft);
}
template <
typename Graph,
typename VertexIndexMap,
typename EdgeWeightMap,
typename EdgeIndexMap>
inline double
maximum_cycle_mean(const Graph& g, VertexIndexMap vim,
EdgeWeightMap ewm, EdgeIndexMap eim,
std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0)
{ return maximum_cycle_mean(g, vim, ewm, eim, pcc, mcr_float<>()); }
// Minimum Cycle Mean
template <
typename FloatTraits,
typename Graph,
typename VertexIndexMap,
typename EdgeWeightMap,
typename EdgeIndexMap>
inline typename FloatTraits::value_type
minimum_cycle_mean(const Graph &g, VertexIndexMap vim,
EdgeWeightMap ewm, EdgeIndexMap eim,
std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0,
FloatTraits ft = FloatTraits())
{
typedef typename remove_const<
typename property_traits<EdgeWeightMap>::value_type
>::type Weight;
typename std::vector<Weight> ed_w2(boost::num_edges(g), 1);
return minimum_cycle_ratio(g, vim, ewm,
make_iterator_property_map(ed_w2.begin(), eim),
pcc, ft);
}
template <
typename Graph,
typename VertexIndexMap,
typename EdgeWeightMap,
typename EdgeIndexMap>
inline double
minimum_cycle_mean(const Graph &g, VertexIndexMap vim,
EdgeWeightMap ewm, EdgeIndexMap eim,
std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0)
{ return minimum_cycle_mean(g, vim, ewm, eim, pcc, mcr_float<>()); }
} //namespace boost
#endif
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