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/* This file is part of the Gudhi Library. The Gudhi library
* (Geometric Understanding in Higher Dimensions) is a generic C++
* library for computational topology.
*
* Author: Francois Godi
*
* Copyright (C) 2015 Inria
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef GRAPH_MATCHING_H_
#define GRAPH_MATCHING_H_
#include <gudhi/Neighbors_finder.h>
#include <vector>
#include <unordered_set>
#include <algorithm>
namespace Gudhi {
namespace persistence_diagram {
/** \internal \brief Structure representing a graph matching. The graph is a Persistence_diagrams_graph.
*
* \ingroup bottleneck_distance
*/
class Graph_matching {
public:
/** \internal \brief Constructor constructing an empty matching. */
explicit Graph_matching(Persistence_graph &g);
/** \internal \brief Is the matching perfect ? */
bool perfect() const;
/** \internal \brief Augments the matching with a maximal set of edge-disjoint shortest augmenting paths. */
bool multi_augment();
/** \internal \brief Sets the maximum length of the edges allowed to be added in the matching, 0 initially. */
void set_r(double r);
private:
Persistence_graph* gp;
double r;
/** \internal \brief Given a point from V, provides its matched point in U, null_point_index() if there isn't. */
std::vector<int> v_to_u;
/** \internal \brief All the unmatched points in U. */
std::unordered_set<int> unmatched_in_u;
/** \internal \brief Provides a Layered_neighbors_finder dividing the graph in layers. Basically a BFS. */
Layered_neighbors_finder layering() const;
/** \internal \brief Augments the matching with a simple path no longer than max_depth. Basically a DFS. */
bool augment(Layered_neighbors_finder & layered_nf, int u_start_index, int max_depth);
/** \internal \brief Update the matching with the simple augmenting path given as parameter. */
void update(std::vector<int> & path);
};
inline Graph_matching::Graph_matching(Persistence_graph& g)
: gp(&g), r(0.), v_to_u(g.size(), null_point_index()), unmatched_in_u(g.size()) {
for (int u_point_index = 0; u_point_index < g.size(); ++u_point_index)
unmatched_in_u.insert(u_point_index);
}
inline bool Graph_matching::perfect() const {
return unmatched_in_u.empty();
}
inline bool Graph_matching::multi_augment() {
if (perfect())
return false;
Layered_neighbors_finder layered_nf(layering());
int max_depth = layered_nf.vlayers_number()*2 - 1;
double rn = sqrt(gp->size());
// verification of a necessary criterion in order to shortcut if possible
if (max_depth < 0 || (unmatched_in_u.size() > rn && max_depth >= rn))
return false;
bool successful = false;
std::vector<int> tries(unmatched_in_u.cbegin(), unmatched_in_u.cend());
for (auto it = tries.cbegin(); it != tries.cend(); it++)
// 'augment' has side-effects which have to be always executed, don't change order
successful = augment(layered_nf, *it, max_depth) || successful;
return successful;
}
inline void Graph_matching::set_r(double r) {
this->r = r;
}
inline bool Graph_matching::augment(Layered_neighbors_finder & layered_nf, int u_start_index, int max_depth) {
// V vertices have at most one successor, thus when we backtrack from U we can directly pop_back 2 vertices.
std::vector<int> path;
path.emplace_back(u_start_index);
do {
if (static_cast<int> (path.size()) > max_depth) {
path.pop_back();
path.pop_back();
}
if (path.empty())
return false;
path.emplace_back(layered_nf.pull_near(path.back(), static_cast<int> (path.size()) / 2));
while (path.back() == null_point_index()) {
path.pop_back();
path.pop_back();
if (path.empty())
return false;
path.pop_back();
path.emplace_back(layered_nf.pull_near(path.back(), path.size() / 2));
}
path.emplace_back(v_to_u.at(path.back()));
} while (path.back() != null_point_index());
// if v_to_u.at(path.back()) has no successor, path.back() is an exposed vertex
path.pop_back();
update(path);
return true;
}
inline Layered_neighbors_finder Graph_matching::layering() const {
std::vector<int> u_vertices(unmatched_in_u.cbegin(), unmatched_in_u.cend());
std::vector<int> v_vertices;
Neighbors_finder nf(*gp, r);
for (int v_point_index = 0; v_point_index < gp->size(); ++v_point_index)
nf.add(v_point_index);
Layered_neighbors_finder layered_nf(*gp, r);
for (int layer = 0; !u_vertices.empty(); layer++) {
// one layer is one step in the BFS
for (auto it1 = u_vertices.cbegin(); it1 != u_vertices.cend(); ++it1) {
std::vector<int> u_succ(nf.pull_all_near(*it1));
for (auto it2 = u_succ.begin(); it2 != u_succ.end(); ++it2) {
layered_nf.add(*it2, layer);
v_vertices.emplace_back(*it2);
}
}
// When the above for finishes, we have progress of one half-step (from U to V) in the BFS
u_vertices.clear();
bool end = false;
for (auto it = v_vertices.cbegin(); it != v_vertices.cend(); it++)
if (v_to_u.at(*it) == null_point_index())
// we stop when a nearest exposed V vertex (from U exposed vertices) has been found
end = true;
else
u_vertices.emplace_back(v_to_u.at(*it));
// When the above for finishes, we have progress of one half-step (from V to U) in the BFS
if (end)
return layered_nf;
v_vertices.clear();
}
return layered_nf;
}
inline void Graph_matching::update(std::vector<int>& path) {
// Must return 1.
unmatched_in_u.erase(path.front());
for (auto it = path.cbegin(); it != path.cend(); ++it) {
// Be careful, the iterator is incremented twice each time
int tmp = *it;
v_to_u[*(++it)] = tmp;
}
}
} // namespace persistence_diagram
} // namespace Gudhi
#endif // GRAPH_MATCHING_H_
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