max/edmonds-matching-algorithm
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use union-find structure for rho

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This commit is contained in:
Maximilian Keßler 2023-11-06 18:45:08 +01:00
parent 1d75066eea
commit 497d601ffc
Signed by: max
GPG Key ID: BCC5A619923C0BA5
2 changed files with 37 additions and 38 deletions
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54
src/edmonds.cpp
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@ -8,7 +8,7 @@ using namespace ED;
namespace Edmonds { namespace Edmonds {
void check_integrity(GraphAttributes const & attrs) void check_integrity(GraphAttributes & attrs)
{ {
for(NodeId id = 0; id < attrs.num_nodes(); ++id) for(NodeId id = 0; id < attrs.num_nodes(); ++id)
{ {
@ -22,13 +22,13 @@ void check_integrity(GraphAttributes const & attrs)
if (attrs.is_out_of_forest(id)) if (attrs.is_out_of_forest(id))
{ {
assert(attrs.phi[id] == id); assert(attrs.phi[id] == id);
assert(attrs.rho[id] == id); assert(attrs.rho(id) == id);
} }
else else
{ {
// check for a path to the root, i.e. ρ(node) // check for a path to the root, i.e. ρ(node)
NodeId cur_node = id; NodeId cur_node = id;
while(cur_node != attrs.rho[cur_node]) while(cur_node != attrs.rho(cur_node))
{ {
// If the condition was true, then cur_node is outer, part of a blossom // If the condition was true, then cur_node is outer, part of a blossom
// and we want to follow its path // and we want to follow its path
@ -36,8 +36,8 @@ void check_integrity(GraphAttributes const & attrs)
// and point to vertices that have the same rho // and point to vertices that have the same rho
assert(attrs.mu[cur_node] != cur_node); assert(attrs.mu[cur_node] != cur_node);
assert(attrs.phi[cur_node] != cur_node); assert(attrs.phi[cur_node] != cur_node);
assert(attrs.rho[attrs.mu[cur_node]] == attrs.rho[cur_node]); assert(attrs.rho(attrs.mu[cur_node]) == attrs.rho(cur_node));
assert(attrs.rho[attrs.phi[cur_node]] == attrs.rho[cur_node]); assert(attrs.rho(attrs.phi[cur_node]) == attrs.rho(cur_node));
// now, walk along the matched edge // now, walk along the matched edge
cur_node = attrs.mu[cur_node]; cur_node = attrs.mu[cur_node];
@ -46,7 +46,7 @@ void check_integrity(GraphAttributes const & attrs)
// - not be the identity // - not be the identity
// - result in a node that has the same rho // - result in a node that has the same rho
assert(attrs.phi[cur_node] != cur_node); assert(attrs.phi[cur_node] != cur_node);
assert(attrs.rho[attrs.phi[cur_node]] == attrs.rho[cur_node]); assert(attrs.rho(attrs.phi[cur_node]) == attrs.rho(cur_node));
cur_node = attrs.mu[attrs.phi[cur_node]]; cur_node = attrs.mu[attrs.phi[cur_node]];
} }
@ -54,7 +54,7 @@ void check_integrity(GraphAttributes const & attrs)
if (not attrs.is_outer(id)) if (not attrs.is_outer(id))
{ {
assert(attrs.rho[id] == id); assert(attrs.rho(id) == id);
} }
} }
} }
@ -103,7 +103,7 @@ __attribute__((noinline))
void augment(GraphAttributes & attrs, std::vector<NodeId> const & x_path, std::vector<NodeId> const & y_path, void augment(GraphAttributes & attrs, std::vector<NodeId> const & x_path, std::vector<NodeId> const & y_path,
std::stack<NodeId> & outer_unvisited_nodes) std::stack<NodeId> & outer_unvisited_nodes)
{ {
//std::cout << "Augment" << std::endl; std::cout << "Augment" << std::endl;
// Paths are disjoint -> augment // Paths are disjoint -> augment
attrs.mu[x_path.front()] = y_path.front(); attrs.mu[x_path.front()] = y_path.front();
attrs.mu[y_path.front()] = x_path.front(); attrs.mu[y_path.front()] = x_path.front();
@ -124,7 +124,7 @@ void augment(GraphAttributes & attrs, std::vector<NodeId> const & x_path, std::v
} }
__attribute__((noinline)) __attribute__((noinline))
std::tuple<NodeId, size_type, size_type> find_blossom_root_id(GraphAttributes const & attrs, std::vector<NodeId> const & x_path, std::vector<NodeId> const & y_path) std::tuple<NodeId, size_type, size_type> find_blossom_root_id(GraphAttributes & attrs, std::vector<NodeId> const & x_path, std::vector<NodeId> const & y_path)
{ {
size_t distance_from_x = x_path.size() - 1; size_t distance_from_x = x_path.size() - 1;
size_t distance_from_y = y_path.size() - 1; size_t distance_from_y = y_path.size() - 1;
@ -135,7 +135,7 @@ std::tuple<NodeId, size_type, size_type> find_blossom_root_id(GraphAttributes co
--distance_from_y; --distance_from_y;
} }
// found first vertex of x_path \cap y_path // found first vertex of x_path \cap y_path
while (attrs.rho[x_path[distance_from_x]] != x_path[distance_from_x]) while (attrs.rho(x_path[distance_from_x]) != x_path[distance_from_x])
{ {
++distance_from_x; ++distance_from_x;
++distance_from_y; ++distance_from_y;
@ -153,7 +153,7 @@ void update_phialong_blossom_paths(GraphAttributes & attrs, std::vector<NodeId>
// Update φ along the paths to encode the ear decomposition // Update φ along the paths to encode the ear decomposition
for (size_t i = 1; i <= distance_from_x; i += 2) for (size_t i = 1; i <= distance_from_x; i += 2)
{ {
if (attrs.rho[attrs.phi[x_path[i]]] != blossom_root_id) if (attrs.rho(attrs.phi[x_path[i]]) != blossom_root_id)
{ {
attrs.phi[attrs.phi[x_path[i]]] = x_path[i]; attrs.phi[attrs.phi[x_path[i]]] = x_path[i];
} }
@ -161,36 +161,23 @@ void update_phialong_blossom_paths(GraphAttributes & attrs, std::vector<NodeId>
for (size_t i = 1; i <= distance_from_y; i += 2) for (size_t i = 1; i <= distance_from_y; i += 2)
{ {
if (attrs.rho[attrs.phi[y_path[i]]] != blossom_root_id) if (attrs.rho(attrs.phi[y_path[i]]) != blossom_root_id)
{ {
attrs.phi[attrs.phi[y_path[i]]] = y_path[i]; attrs.phi[attrs.phi[y_path[i]]] = y_path[i];
} }
} }
// Link x and y // Link x and y
if (attrs.rho[x_path.front()] != blossom_root_id) if (attrs.rho(x_path.front()) != blossom_root_id)
{ {
attrs.phi[x_path.front()] = y_path.front(); attrs.phi[x_path.front()] = y_path.front();
} }
if (attrs.rho[y_path.front()] != blossom_root_id) if (attrs.rho(y_path.front()) != blossom_root_id)
{ {
attrs.phi[y_path.front()] = x_path.front(); attrs.phi[y_path.front()] = x_path.front();
} }
} }
__attribute__((noinline))
void contract_rho(GraphAttributes & attrs, NodeId blossom_root_id)
{
// Iterating over whole attrs.
for (NodeId node_id = 0; node_id < attrs.num_nodes(); ++node_id)
{
if (attrs.rho[attrs.rho[node_id]] == blossom_root_id)
{
attrs.rho[node_id] = blossom_root_id;
}
}
}
__attribute__((noinline)) __attribute__((noinline))
void update_rho(GraphAttributes & attrs, std::vector<NodeId> const & x_path, std::vector<NodeId> const & y_path, void update_rho(GraphAttributes & attrs, std::vector<NodeId> const & x_path, std::vector<NodeId> const & y_path,
std::tuple<NodeId, size_type, size_type> const & blossom_root_description, std::tuple<NodeId, size_type, size_type> const & blossom_root_description,
@ -205,7 +192,7 @@ void update_rho(GraphAttributes & attrs, std::vector<NodeId> const & x_path, std
auto const [blossom_root_id, distance_from_x, distance_from_y] = blossom_root_description; auto const [blossom_root_id, distance_from_x, distance_from_y] = blossom_root_description;
for (size_t i = 0; i <= distance_from_x; ++i) for (size_t i = 0; i <= distance_from_x; ++i)
{ {
attrs.rho[x_path[i]] = blossom_root_id; attrs.rho_[x_path[i]] = blossom_root_id;
if (not attrs.scanned[x_path[i]]) if (not attrs.scanned[x_path[i]])
{ {
outer_unvisited_nodes.push(x_path[i]); outer_unvisited_nodes.push(x_path[i]);
@ -213,20 +200,19 @@ void update_rho(GraphAttributes & attrs, std::vector<NodeId> const & x_path, std
} }
for (size_t i = 0; i <= distance_from_y; ++i) for (size_t i = 0; i <= distance_from_y; ++i)
{ {
attrs.rho[y_path[i]] = blossom_root_id; attrs.rho_[y_path[i]] = blossom_root_id;
if (not attrs.scanned[y_path[i]]) if (not attrs.scanned[y_path[i]])
{ {
outer_unvisited_nodes.push(y_path[i]); outer_unvisited_nodes.push(y_path[i]);
} }
} }
contract_rho(attrs, blossom_root_id);
} }
__attribute__((noinline)) __attribute__((noinline))
void contract_blossom(GraphAttributes & attrs, std::vector<NodeId> const & x_path, std::vector<NodeId> const & y_path, void contract_blossom(GraphAttributes & attrs, std::vector<NodeId> const & x_path, std::vector<NodeId> const & y_path,
std::stack<NodeId> & outer_unvisited_nodes) std::stack<NodeId> & outer_unvisited_nodes)
{ {
//std::cout << "Contract blossom" << std::endl; std::cout << "Contract blossom" << std::endl;
std::tuple<NodeId, size_type, size_type> const blossom_root_description = find_blossom_root_id(attrs, x_path, y_path); std::tuple<NodeId, size_type, size_type> const blossom_root_description = find_blossom_root_id(attrs, x_path, y_path);
update_phialong_blossom_paths(attrs, x_path, y_path, blossom_root_description); update_phialong_blossom_paths(attrs, x_path, y_path, blossom_root_description);
@ -253,16 +239,16 @@ void maximum_matching_from_initial_matching(Graph const & graph, GraphAttributes
for(NodeId neighbor_id : graph.node(id).neighbors()) for(NodeId neighbor_id : graph.node(id).neighbors())
{ {
check_integrity(attrs); check_integrity(attrs);
//std::cout << "Check passed" << std::endl; std::cout << "Check passed" << std::endl;
if (attrs.is_out_of_forest(neighbor_id)) if (attrs.is_out_of_forest(neighbor_id))
{ {
//std::cout << "Grow forest" << std::endl; std::cout << "Grow forest" << std::endl;
// Grow Forest // Grow Forest
attrs.phi[neighbor_id] = id; attrs.phi[neighbor_id] = id;
assert(attrs.mu[neighbor_id] != neighbor_id); assert(attrs.mu[neighbor_id] != neighbor_id);
outer_unvisited_nodes.push(attrs.mu[neighbor_id]); outer_unvisited_nodes.push(attrs.mu[neighbor_id]);
} }
else if (attrs.is_outer(neighbor_id) and attrs.rho[id] != attrs.rho[neighbor_id]) else if (attrs.is_outer(neighbor_id) and attrs.rho(id) != attrs.rho(neighbor_id))
{ {
std::vector<NodeId> x_path = path_to_forest_root(attrs, id); std::vector<NodeId> x_path = path_to_forest_root(attrs, id);
std::vector<NodeId> y_path = path_to_forest_root(attrs, neighbor_id); std::vector<NodeId> y_path = path_to_forest_root(attrs, neighbor_id);

21
src/graph_attributes.h
View File

@ -20,10 +20,12 @@ namespace ED
void reset_forest(); void reset_forest();
NodeId rho(NodeId id);
void reset_matching(); void reset_matching();
std::vector<NodeId> phi; std::vector<NodeId> phi;
std::vector<NodeId> rho; std::vector<NodeId> rho_;
std::vector<NodeId> mu; std::vector<NodeId> mu;
std::vector<bool> scanned; std::vector<bool> scanned;
}; };
@ -31,7 +33,7 @@ namespace ED
inline inline
GraphAttributes::GraphAttributes(const ED::NodeId num_nodes): GraphAttributes::GraphAttributes(const ED::NodeId num_nodes):
phi(num_nodes), phi(num_nodes),
rho(num_nodes), rho_(num_nodes),
mu(num_nodes), mu(num_nodes),
scanned(num_nodes) scanned(num_nodes)
{ {
@ -41,7 +43,7 @@ namespace ED
inline inline
NodeId GraphAttributes::num_nodes() const NodeId GraphAttributes::num_nodes() const
{ {
assert(phi.size() == rho.size()); assert(phi.size() == rho_.size());
assert(phi.size() == mu.size()); assert(phi.size() == mu.size());
assert(phi.size() == scanned.size()); assert(phi.size() == scanned.size());
return phi.size(); return phi.size();
@ -68,10 +70,21 @@ namespace ED
void GraphAttributes::reset_forest() void GraphAttributes::reset_forest()
{ {
std::iota(phi.begin(), phi.end(), 0); std::iota(phi.begin(), phi.end(), 0);
std::iota(rho.begin(), rho.end(), 0); std::iota(rho_.begin(), rho_.end(), 0);
std::fill(scanned.begin(), scanned.end(), false); std::fill(scanned.begin(), scanned.end(), false);
} }
inline
NodeId GraphAttributes::rho(NodeId id)
{
while(rho_[id] != id)
{
rho_[id] = rho_[rho_[id]];
id = rho_[id];
}
return id;
}
inline inline
void GraphAttributes::reset_matching() void GraphAttributes::reset_matching()
{ {