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Diffstat (limited to 'include/gudhi/Graph_matching.h')
| -rw-r--r-- | include/gudhi/Graph_matching.h | 174 |
1 files changed, 174 insertions, 0 deletions
diff --git a/include/gudhi/Graph_matching.h b/include/gudhi/Graph_matching.h new file mode 100644 index 00000000..f51e22e9 --- /dev/null +++ b/include/gudhi/Graph_matching.h @@ -0,0 +1,174 @@ +/* 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_ |