问题
I've been struggling a lot to figure out how to do this. I'm interested in quickly finding the cut set of a graph. I know that BGL supports finding the cut set by iteration over the colorMap arguments supported by, e.g., edmonds_karp_max_flow. The Gomory Hu algorithm needs to make several calls to a minimum cut algorithm.
The result that I was hoping for was to have a multimap that contains: (color, vertex)
The following code is an attempt at rewriting the example from the Boost Graph Library to use a multimap for the associative_property_map. Compiling the code can be done with: clang -lboost_graph -o edmonds_karp edmonds_karp.cpp or g++ instead of clang. I don't get the errors that come out of.
#include <boost/config.hpp>
#include <iostream>
#include <string>
#include <boost/foreach.hpp>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/edmonds_karp_max_flow.hpp>
#include <boost/graph/graph_utility.hpp>
#include <boost/graph/read_dimacs.hpp>
#include <boost/lexical_cast.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/unordered_map.hpp>
int main()
{
using namespace boost;
typedef adjacency_list_traits < vecS, vecS, directedS > Traits;
typedef adjacency_list < listS, vecS, directedS,
property < vertex_name_t, std::string >,
property < edge_capacity_t, long,
property < edge_residual_capacity_t, long,
property < edge_reverse_t, Traits::edge_descriptor > > > > Graph;
Graph g;
property_map < Graph, edge_capacity_t >::type
capacity = get(edge_capacity, g);
property_map < Graph, edge_reverse_t >::type rev = get(edge_reverse, g);
property_map < Graph, edge_residual_capacity_t >::type
residual_capacity = get(edge_residual_capacity, g);
std::multimap<default_color_type, Traits::vertex_descriptor> colorMap;
boost::associative_property_map< std::map<default_color_type,
Traits::vertex_descriptor> >
color_map(colorMap);
Traits::vertex_descriptor s, t;
read_dimacs_max_flow(g, capacity, rev, s, t);
std::vector<Traits::edge_descriptor> pred(num_vertices(g));
long flow = edmonds_karp_max_flow
(g, s, t, capacity, residual_capacity, rev,
make_iterator_property_map(color_map.begin()),
&pred[0]);
std::cout << "c The total flow:" << std::endl;
std::cout << "s " << flow << std::endl << std::endl;
std::cout << "c flow values:" << std::endl;
graph_traits < Graph >::vertex_iterator u_iter, u_end;
graph_traits < Graph >::out_edge_iterator ei, e_end;
for (boost::tie(u_iter, u_end) = vertices(g); u_iter != u_end; ++u_iter)
for (boost::tie(ei, e_end) = out_edges(*u_iter, g); ei != e_end; ++ei)
if (capacity[*ei] > 0)
std::cout << "f " << *u_iter << " " << target(*ei, g) << " "
<< (capacity[*ei] - residual_capacity[*ei]) << std::endl;
// if using the original example, unedited, this piece of code works
// BOOST_FOREACH(default_color_type x, color){
// std::cout << x << std::endl;
// }
return EXIT_SUCCESS;
}
Hints will be greatly appreciated. Thank you.
回答1:
Here's a quick PoC based on Boost BiMap
typedef boost::bimap<bimaps::list_of<default_color_type>, bimaps::set_of<Traits::vertex_descriptor> > smart_map;
smart_map colorMap;
boost::associative_property_map<smart_map::right_map> color_map(colorMap.right);
I've taken a small sample from http://lpsolve.sourceforge.net/5.5/DIMACS_maxf.htm and you can see it Live On Coliru, output:
c The total flow:
s 15
c flow values:
f 0 1 5
f 0 2 10
f 1 3 5
f 1 4 0
f 2 3 5
f 2 4 5
f 3 5 10
f 4 5 5
ltr: 0 -> 5
ltr: 4 -> 0
ltr: 0 -> 1
ltr: 4 -> 2
ltr: 0 -> 3
ltr: 0 -> 4
rtl: 0 -> 4
rtl: 1 -> 0
rtl: 2 -> 4
rtl: 3 -> 0
rtl: 4 -> 0
rtl: 5 -> 0
Full Listing:
#include <boost/foreach.hpp>
#include <boost/bimap.hpp>
#include <boost/graph/adjacency_list.hpp>
#include <boost/bimap/list_of.hpp>
#include <boost/bimap/set_of.hpp>
#include <boost/graph/edmonds_karp_max_flow.hpp>
#include <boost/graph/graph_utility.hpp>
#include <boost/graph/read_dimacs.hpp>
#include <boost/lexical_cast.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/unordered_map.hpp>
int main() {
using namespace boost;
typedef adjacency_list_traits<vecS, vecS, directedS> Traits;
typedef adjacency_list<
listS, vecS, directedS, property<vertex_name_t, std::string>,
property<edge_capacity_t, long,
property<edge_residual_capacity_t, long,
property<edge_reverse_t, Traits::edge_descriptor> > > > Graph;
Graph g;
property_map<Graph, edge_capacity_t>::type capacity = get(edge_capacity, g);
property_map<Graph, edge_reverse_t>::type rev = get(edge_reverse, g);
property_map<Graph, edge_residual_capacity_t>::type residual_capacity = get(edge_residual_capacity, g);
typedef boost::bimap<bimaps::list_of<default_color_type>, bimaps::set_of<Traits::vertex_descriptor> > smart_map;
smart_map colorMap;
boost::associative_property_map<smart_map::right_map> color_map(colorMap.right);
Traits::vertex_descriptor s, t;
read_dimacs_max_flow(g, capacity, rev, s, t);
std::vector<Traits::edge_descriptor> pred(num_vertices(g));
long flow = edmonds_karp_max_flow(
g, s, t, capacity, residual_capacity, rev,
color_map, &pred[0]);
std::cout << "c The total flow:" << std::endl;
std::cout << "s " << flow << std::endl << std::endl;
std::cout << "c flow values:" << std::endl;
graph_traits<Graph>::vertex_iterator u_iter, u_end;
graph_traits<Graph>::out_edge_iterator ei, e_end;
for (boost::tie(u_iter, u_end) = vertices(g); u_iter != u_end; ++u_iter)
for (boost::tie(ei, e_end) = out_edges(*u_iter, g); ei != e_end; ++ei)
if (capacity[*ei] > 0)
std::cout << "f " << *u_iter << " " << target(*ei, g) << " " << (capacity[*ei] - residual_capacity[*ei])
<< std::endl;
for (auto const& e : colorMap.left) std::cout << "ltr: " << e.first << " -> " << e.second << "\n";
for (auto const& e : colorMap.right) std::cout << "rtl: " << e.first << " -> " << e.second << "\n";
return EXIT_SUCCESS;
}
UPDATE
Using Boost MultiIndex to create a bidirectional mapping:
struct VertexColor {
Traits::vertex_descriptor vertex;
boost::default_color_type color;
};
typedef boost::multi_index_container<
VertexColor,
bmi::indexed_by<
bmi::hashed_non_unique<bmi::tag<struct by_color>, bmi::member<VertexColor, boost::default_color_type, &VertexColor::color> >,
bmi::ordered_unique <bmi::tag<struct by_vertex>, bmi::member<VertexColor, Traits::vertex_descriptor, &VertexColor::vertex> >
>
> smart_map;
Now, using Boost Property Map to model a ReadWritePropertyMap:
struct bidi_color_map {
typedef smart_map::index<by_vertex>::type impl_t;
bidi_color_map(impl_t& ref) : ref_(&ref) {}
impl_t &get() { return *ref_; }
impl_t const &get() const { return *ref_; }
private:
impl_t* ref_;
};
namespace boost {
template <> struct property_traits<bidi_color_map> {
typedef default_color_type value_type;
typedef default_color_type reference;
typedef Traits::vertex_descriptor key_type;
typedef read_write_property_map_tag category;
};
}
boost::property_traits<bidi_color_map>::reference get(bidi_color_map const& idx, boost::property_traits<bidi_color_map>::key_type const& key) {
auto it = idx.get().find(key);
if (it != idx.get().end())
return it->color;
else
throw std::range_error("key not found in index");
}
void put(bidi_color_map& idx, boost::property_traits<bidi_color_map>::key_type const& key, boost::property_traits<bidi_color_map>::value_type val) {
auto it = idx.get().find(key);
if (it != idx.get().end())
idx.get().modify(it, [val](VertexColor& p) { p.color = val; });
else
idx.get().insert({key,val});
}
Now you can just pass that as the colormap:
smart_map colorMap;
bidi_color_map color_map(colorMap.get<by_vertex>());
See it Live On Coliru as well
来源：https://stackoverflow.com/questions/26697477/cut-set-of-a-graph-boost-graph-library