max/edmonds-matching-algorithm
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ensure all outer vertices are scanned

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Maximilian Keßler 2023-11-05 13:06:50 +01:00
parent 14474189c4
commit 1b9f930adf
Signed by: max
GPG Key ID: BCC5A619923C0BA5
1 changed files with 89 additions and 77 deletions
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166
src/edmonds.cpp
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@ -30,101 +30,113 @@ std::vector<NodeId> path_to_forest_root(Graph const & graph, NodeId id)
return retval;
}
NodeId find_outer_vertex(Graph const & graph)
{
for(NodeId id = 0; id < graph.num_nodes(); ++id)
{
if (not graph.node(id).scanned and graph.is_outer(id))
{
return id;
}
}
return invalid_node_id;
}
Graph maximum_matching_from_initial_matching(Graph & graph)
{
graph.reset_forest();
for(NodeId id = 0; id < graph.num_nodes(); ++id) {
if (graph.is_outer(id))
NodeId id;
while((id = find_outer_vertex(graph)) != invalid_node_id)
{
for(NodeId neighbor_id : graph.node(id).neighbors())
{
for(NodeId neighbor_id : graph.node(id).neighbors())
if (graph.is_out_of_forest(neighbor_id))
{
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);
// 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())
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)
{
// 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);
graph.node(x_path[i]).matched_neighbor = x_path[i+1];
graph.node(x_path[i+1]).matched_neighbor = x_path[i];
}
else
for(size_t i = 1; i < y_path.size(); i += 2)
{
// Paths are not disjoint -> shrink blossom
size_t distance_from_x = x_path.size() - 1;
size_t distance_from_y = y_path.size() - 1;
while (distance_from_x > 0 and distance_from_y > 0 and \
x_path[distance_from_x - 1] == y_path[distance_from_y - 1])
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
size_t distance_from_x = x_path.size() - 1;
size_t distance_from_y = y_path.size() - 1;
while (distance_from_x > 0 and distance_from_y > 0 and \
x_path[distance_from_x - 1] == y_path[distance_from_y - 1])
{
--distance_from_x;
--distance_from_y;
}
// found first vertex of x_path \cap y_path
while (graph.root_of_ear_component(x_path[distance_from_x]) != x_path[distance_from_x])
{
++distance_from_x;
++distance_from_y;
};
// found first vertex fixed by root_of_ear_component
NodeId blossom_root_id = x_path[distance_from_x];
for(size_t i = 1; i <= distance_from_x; i += 2)
{
if (graph.root_of_ear_component(graph.ear_or_root_neighbor(x_path[i])) != blossom_root_id)
{
--distance_from_x;
--distance_from_y;
graph.node(graph.ear_or_root_neighbor(x_path[i])).ear_or_root_neighbor = x_path[i];
}
// found first vertex of x_path \cap y_path
while (graph.root_of_ear_component(x_path[distance_from_x]) != x_path[distance_from_x])
}
for(size_t i = 1; i <= distance_from_y; i += 2)
{
if (graph.root_of_ear_component(graph.ear_or_root_neighbor(y_path[i])) != blossom_root_id)
{
++distance_from_x;
++distance_from_y;
};
// found first vertex fixed by root_of_ear_component
NodeId blossom_root_id = x_path[distance_from_x];
for(size_t i = 1; i <= distance_from_x; i += 2)
{
if (graph.root_of_ear_component(graph.ear_or_root_neighbor(x_path[i])) != blossom_root_id)
{
graph.node(graph.ear_or_root_neighbor(x_path[i])).ear_or_root_neighbor = x_path[i];
}
}
for(size_t i = 1; i <= distance_from_y; i += 2)
{
if (graph.root_of_ear_component(graph.ear_or_root_neighbor(y_path[i])) != blossom_root_id)
{
graph.node(graph.ear_or_root_neighbor(y_path[i])).ear_or_root_neighbor = y_path[i];
}
}
if (graph.root_of_ear_component(x_path.front()) != blossom_root_id)
{
graph.node(x_path.front()).ear_or_root_neighbor = y_path.front();
}
if (graph.root_of_ear_component(y_path.front()) != blossom_root_id)
{
graph.node(x_path.front()).ear_or_root_neighbor = x_path.front();
graph.node(graph.ear_or_root_neighbor(y_path[i])).ear_or_root_neighbor = y_path[i];
}
}
if (graph.root_of_ear_component(x_path.front()) != blossom_root_id)
{
graph.node(x_path.front()).ear_or_root_neighbor = y_path.front();
}
if (graph.root_of_ear_component(y_path.front()) != blossom_root_id)
{
graph.node(x_path.front()).ear_or_root_neighbor = x_path.front();
}
// Update root indices
for(size_t i = 0; i <= distance_from_x; ++i)
{
graph.node(x_path[i]).root_of_ear_component = blossom_root_id;
}
for(size_t i = 0; i <= distance_from_y; ++i)
{
graph.node(y_path[i]).root_of_ear_component = blossom_root_id;
}
// Update root indices
for(size_t i = 0; i <= distance_from_x; ++i)
{
graph.node(x_path[i]).root_of_ear_component = blossom_root_id;
}
for(size_t i = 0; i <= distance_from_y; ++i)
{
graph.node(y_path[i]).root_of_ear_component = blossom_root_id;
}
}
}
}
graph.node(id).scanned = true;
}
return graph;
};