Start implementation of matching algorithm

This commit is contained in:
Maximilian Keßler 2023-11-04 18:29:49 +01:00
parent a35d86d0d4
commit e568e298f0
Signed by: max
GPG key ID: BCC5A619923C0BA5
2 changed files with 79 additions and 3 deletions

View file

@ -1,8 +1,76 @@
#include "edmonds.h" #include "edmonds.h"
namespace Edmonds { using namespace ED;
ED::Graph maximum_matching(ED::Graph & graph)
{
namespace Edmonds {
std::vector<NodeId> path_to_forest_root(Graph const & graph, NodeId id)
{
std::vector<NodeId> retval;
retval.push_back(id);
while (graph.matched_neighbor(id) != id)
{
id = graph.matched_neighbor(id);
retval.push_back(id);
// Note that it is guaranteed that this does not produce a loop:
// We are traversing the path to a root of the forest,
// but we know that each root is exposed by M, so after traversing
// the matching edge, we cannot have reached a root.
id = graph.ear_or_root_neighbor(id);
retval.push_back(id);
}
return retval;
}
Graph maximum_matching(Graph & graph)
{
graph.reset_forest();
for(NodeId id = 0; id < graph.num_nodes(); ++id) {
if (graph.is_out_of_forest(id))
{
for(NodeId neighbor_id : graph.node(id).neighbors())
{
if (graph.is_out_of_forest(neighbor_id))
{
// Grow Forest
graph.node(neighbor_id).ear_or_root_neighbor = id;
}
else if (graph.is_outer(neighbor_id) and \
graph.root_of_ear_component(id) != graph.root_of_ear_component(neighbor_id))
{
std::vector<NodeId> x_path = path_to_forest_root(graph, id);
std::vector<NodeId> y_path = path_to_forest_root(graph, neighbor_id);
if (x_path.back() != y_path.back())
{
// Paths are disjoint -> augment
graph.node(x_path.front()).matched_neighbor = y_path.front();
graph.node(y_path.front()).matched_neighbor = x_path.front();
// TODO: put this into own method?
for(size_t i = 1; i < x_path.size(); i += 2)
{
graph.node(x_path[i]).matched_neighbor = x_path[i+1];
graph.node(x_path[i+1]).matched_neighbor = x_path[i];
}
for(size_t i = 1; i < y_path.size(); i += 2)
{
graph.node(y_path[i]).matched_neighbor = y_path[i+1];
graph.node(y_path[i+1]).matched_neighbor = y_path[i];
}
// Note that since this is tail-recursion, this will not generate
// new stack frames in OPT mode
return maximum_matching(graph);
}
else
{
// Paths are not disjoint -> shrink blossom
}
}
}
}
}
}; };
} }

View file

@ -146,6 +146,8 @@ public:
**/ **/
Node const & node(NodeId const id) const; Node const & node(NodeId const id) const;
Node & node(NodeId const id);
/** /**
@brief Adds the edge <tt> {node1_id, node2_id} </tt> to this graph. @brief Adds the edge <tt> {node1_id, node2_id} </tt> to this graph.
@ -224,6 +226,12 @@ Node const & Graph::node(NodeId const id) const
{ {
return _nodes[id]; return _nodes[id];
} }
inline
Node & Graph::node(NodeId const id)
{
return _nodes[id];
}
//END: Inline section //END: Inline section