Edit: /usr/include/boost/graph/howard_cycle_ratio.hpp (23107B)
// 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
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
/** @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. (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)
{
using namespace boost::placeholders;
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()
{
using namespace boost::placeholders;
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