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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(s): Francois Godi
*
* Copyright (C) 2015 INRIA Saclay (France)
*
* 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 SRC_BOTTLENECK_INCLUDE_GUDHI_GRAPH_MATCHING_H_
#define SRC_BOTTLENECK_INCLUDE_GUDHI_GRAPH_MATCHING_H_
#include <deque>
#include <list>
#include <vector>
#include "gudhi/Layered_neighbors_finder.h"
namespace Gudhi {
namespace bottleneck {
template<typename Persistence_diagram1, typename Persistence_diagram2>
double bottleneck_distance(Persistence_diagram1& diag1, Persistence_diagram2& diag2, double e = 0.);
class Graph_matching {
public:
Graph_matching(const Persistence_diagrams_graph& g);
Graph_matching& operator=(const Graph_matching& m);
bool perfect() const;
bool multi_augment();
void set_r(double r);
private:
const Persistence_diagrams_graph& g;
double r;
std::vector<int> v_to_u;
std::list<int> unmatched_in_u;
Layered_neighbors_finder* layering() const;
bool augment(Layered_neighbors_finder* layered_nf, int u_start_index, int max_depth);
void update(std::deque<int>& path);
};
Graph_matching::Graph_matching(const Persistence_diagrams_graph& g)
: g(g), r(0), v_to_u(g.size()), unmatched_in_u() {
for (int u_point_index = 0; u_point_index < g.size(); ++u_point_index)
unmatched_in_u.emplace_back(u_point_index);
}
Graph_matching& Graph_matching::operator=(const Graph_matching& m) {
r = m.r;
v_to_u = m.v_to_u;
unmatched_in_u = m.unmatched_in_u;
return *this;
}
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();
double rn = sqrt(g.size());
int nblmax = layered_nf->vlayers_number()*2 + 1;
// verification of a necessary criterion
if ((unmatched_in_u.size() > rn && nblmax > rn) || nblmax == 0)
return false;
bool successful = false;
std::list<int>* tries = new std::list<int>(unmatched_in_u);
for (auto it = tries->cbegin(); it != tries->cend(); it++)
successful = successful || augment(layered_nf, *it, nblmax);
delete tries;
delete layered_nf;
return successful;
}
inline void Graph_matching::set_r(double r) {
this->r = r;
}
Layered_neighbors_finder* Graph_matching::layering() const {
bool end = false;
int layer = 0;
std::list<int> u_vertices(unmatched_in_u);
std::list<int> v_vertices;
Neighbors_finder nf(g, r);
Layered_neighbors_finder* layered_nf = new Layered_neighbors_finder(g, r);
for (int v_point_index = 0; v_point_index < g.size(); ++v_point_index)
nf.add(v_point_index);
while (!u_vertices.empty()) {
for (auto it = u_vertices.cbegin(); it != u_vertices.cend(); ++it) {
std::list<int>* u_succ = nf.pull_all_near(*it);
for (auto it = u_succ->cbegin(); it != u_succ->cend(); ++it) {
layered_nf->add(*it, layer);
v_vertices.emplace_back(*it);
}
delete u_succ;
}
u_vertices.clear();
for (auto it = v_vertices.cbegin(); it != v_vertices.cend(); it++) {
if (v_to_u.at(*it) == null_point_index())
end = true;
else
u_vertices.emplace_back(v_to_u.at(*it));
}
if (end)
return layered_nf;
v_vertices.clear();
layer++;
}
return layered_nf;
}
bool Graph_matching::augment(Layered_neighbors_finder *layered_nf, int u_start_index, int max_depth) {
std::deque<int> path;
path.emplace_back(u_start_index);
// start is a point from U
do {
if (static_cast<int>(path.size()) > max_depth) {
path.pop_back();
path.pop_back();
}
if (path.empty())
return false;
int w = path.back();
path.emplace_back(layered_nf->pull_near(w, 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());
path.pop_back();
update(path);
return true;
}
void Graph_matching::update(std::deque<int>& path) {
unmatched_in_u.remove(path.front());
for (auto it = path.cbegin(); it != path.cend(); ++it) {
int tmp = *it;
++it;
v_to_u[*it] = tmp;
}
}
template<typename Persistence_diagram1, typename Persistence_diagram2>
double bottleneck_distance(Persistence_diagram1& diag1, Persistence_diagram2& diag2, double e) {
Persistence_diagrams_graph g(diag1, diag2, e);
std::vector<double>* sd = g.sorted_distances();
int idmin = 0;
int idmax = sd->size() - 1;
double alpha = pow(sd->size(), 0.25);
Graph_matching m(g);
Graph_matching biggest_unperfect = m;
while (idmin != idmax) {
int pas = static_cast<int>((idmax - idmin) / alpha);
m.set_r(sd->at(idmin + pas));
while (m.multi_augment()) {}
if (m.perfect()) {
idmax = idmin + pas;
m = biggest_unperfect;
} else {
biggest_unperfect = m;
idmin = idmin + pas + 1;
}
}
double b = sd->at(idmin);
delete sd;
return b;
}
} // namespace bottleneck
} // namespace Gudhi
#endif // SRC_BOTTLENECK_INCLUDE_GUDHI_GRAPH_MATCHING_H_
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