diff --git a/(p,t) compression/LICENSE-Apache2.0 b/(p,t) compression/LICENSE-Apache2.0
new file mode 100644
index 0000000000000000000000000000000000000000..72f817fb44de8b9fd23fe71230b9dc5ccbe4ca35
--- /dev/null
+++ b/(p,t) compression/LICENSE-Apache2.0
@@ -0,0 +1,201 @@
+ Apache License
+ Version 2.0, January 2004
+ http://www.apache.org/licenses/
+
+ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+ 1. Definitions.
+
+ "License" shall mean the terms and conditions for use, reproduction,
+ and distribution as defined by Sections 1 through 9 of this document.
+
+ "Licensor" shall mean the copyright owner or entity authorized by
+ the copyright owner that is granting the License.
+
+ "Legal Entity" shall mean the union of the acting entity and all
+ other entities that control, are controlled by, or are under common
+ control with that entity. For the purposes of this definition,
+ "control" means (i) the power, direct or indirect, to cause the
+ direction or management of such entity, whether by contract or
+ otherwise, or (ii) ownership of fifty percent (50%) or more of the
+ outstanding shares, or (iii) beneficial ownership of such entity.
+
+ "You" (or "Your") shall mean an individual or Legal Entity
+ exercising permissions granted by this License.
+
+ "Source" form shall mean the preferred form for making modifications,
+ including but not limited to software source code, documentation
+ source, and configuration files.
+
+ "Object" form shall mean any form resulting from mechanical
+ transformation or translation of a Source form, including but
+ not limited to compiled object code, generated documentation,
+ and conversions to other media types.
+
+ "Work" shall mean the work of authorship, whether in Source or
+ Object form, made available under the License, as indicated by a
+ copyright notice that is included in or attached to the work
+ (an example is provided in the Appendix below).
+
+ "Derivative Works" shall mean any work, whether in Source or Object
+ form, that is based on (or derived from) the Work and for which the
+ editorial revisions, annotations, elaborations, or other modifications
+ represent, as a whole, an original work of authorship. For the purposes
+ of this License, Derivative Works shall not include works that remain
+ separable from, or merely link (or bind by name) to the interfaces of,
+ the Work and Derivative Works thereof.
+
+ "Contribution" shall mean any work of authorship, including
+ the original version of the Work and any modifications or additions
+ to that Work or Derivative Works thereof, that is intentionally
+ submitted to Licensor for inclusion in the Work by the copyright owner
+ or by an individual or Legal Entity authorized to submit on behalf of
+ the copyright owner. For the purposes of this definition, "submitted"
+ means any form of electronic, verbal, or written communication sent
+ to the Licensor or its representatives, including but not limited to
+ communication on electronic mailing lists, source code control systems,
+ and issue tracking systems that are managed by, or on behalf of, the
+ Licensor for the purpose of discussing and improving the Work, but
+ excluding communication that is conspicuously marked or otherwise
+ designated in writing by the copyright owner as "Not a Contribution."
+
+ "Contributor" shall mean Licensor and any individual or Legal Entity
+ on behalf of whom a Contribution has been received by Licensor and
+ subsequently incorporated within the Work.
+
+ 2. Grant of Copyright License. Subject to the terms and conditions of
+ this License, each Contributor hereby grants to You a perpetual,
+ worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+ copyright license to reproduce, prepare Derivative Works of,
+ publicly display, publicly perform, sublicense, and distribute the
+ Work and such Derivative Works in Source or Object form.
+
+ 3. Grant of Patent License. Subject to the terms and conditions of
+ this License, each Contributor hereby grants to You a perpetual,
+ worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+ (except as stated in this section) patent license to make, have made,
+ use, offer to sell, sell, import, and otherwise transfer the Work,
+ where such license applies only to those patent claims licensable
+ by such Contributor that are necessarily infringed by their
+ Contribution(s) alone or by combination of their Contribution(s)
+ with the Work to which such Contribution(s) was submitted. If You
+ institute patent litigation against any entity (including a
+ cross-claim or counterclaim in a lawsuit) alleging that the Work
+ or a Contribution incorporated within the Work constitutes direct
+ or contributory patent infringement, then any patent licenses
+ granted to You under this License for that Work shall terminate
+ as of the date such litigation is filed.
+
+ 4. Redistribution. You may reproduce and distribute copies of the
+ Work or Derivative Works thereof in any medium, with or without
+ modifications, and in Source or Object form, provided that You
+ meet the following conditions:
+
+ (a) You must give any other recipients of the Work or
+ Derivative Works a copy of this License; and
+
+ (b) You must cause any modified files to carry prominent notices
+ stating that You changed the files; and
+
+ (c) You must retain, in the Source form of any Derivative Works
+ that You distribute, all copyright, patent, trademark, and
+ attribution notices from the Source form of the Work,
+ excluding those notices that do not pertain to any part of
+ the Derivative Works; and
+
+ (d) If the Work includes a "NOTICE" text file as part of its
+ distribution, then any Derivative Works that You distribute must
+ include a readable copy of the attribution notices contained
+ within such NOTICE file, excluding those notices that do not
+ pertain to any part of the Derivative Works, in at least one
+ of the following places: within a NOTICE text file distributed
+ as part of the Derivative Works; within the Source form or
+ documentation, if provided along with the Derivative Works; or,
+ within a display generated by the Derivative Works, if and
+ wherever such third-party notices normally appear. The contents
+ of the NOTICE file are for informational purposes only and
+ do not modify the License. You may add Your own attribution
+ notices within Derivative Works that You distribute, alongside
+ or as an addendum to the NOTICE text from the Work, provided
+ that such additional attribution notices cannot be construed
+ as modifying the License.
+
+ You may add Your own copyright statement to Your modifications and
+ may provide additional or different license terms and conditions
+ for use, reproduction, or distribution of Your modifications, or
+ for any such Derivative Works as a whole, provided Your use,
+ reproduction, and distribution of the Work otherwise complies with
+ the conditions stated in this License.
+
+ 5. Submission of Contributions. Unless You explicitly state otherwise,
+ any Contribution intentionally submitted for inclusion in the Work
+ by You to the Licensor shall be under the terms and conditions of
+ this License, without any additional terms or conditions.
+ Notwithstanding the above, nothing herein shall supersede or modify
+ the terms of any separate license agreement you may have executed
+ with Licensor regarding such Contributions.
+
+ 6. Trademarks. This License does not grant permission to use the trade
+ names, trademarks, service marks, or product names of the Licensor,
+ except as required for reasonable and customary use in describing the
+ origin of the Work and reproducing the content of the NOTICE file.
+
+ 7. Disclaimer of Warranty. Unless required by applicable law or
+ agreed to in writing, Licensor provides the Work (and each
+ Contributor provides its Contributions) on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
+ implied, including, without limitation, any warranties or conditions
+ of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
+ PARTICULAR PURPOSE. You are solely responsible for determining the
+ appropriateness of using or redistributing the Work and assume any
+ risks associated with Your exercise of permissions under this License.
+
+ 8. Limitation of Liability. In no event and under no legal theory,
+ whether in tort (including negligence), contract, or otherwise,
+ unless required by applicable law (such as deliberate and grossly
+ negligent acts) or agreed to in writing, shall any Contributor be
+ liable to You for damages, including any direct, indirect, special,
+ incidental, or consequential damages of any character arising as a
+ result of this License or out of the use or inability to use the
+ Work (including but not limited to damages for loss of goodwill,
+ work stoppage, computer failure or malfunction, or any and all
+ other commercial damages or losses), even if such Contributor
+ has been advised of the possibility of such damages.
+
+ 9. Accepting Warranty or Additional Liability. While redistributing
+ the Work or Derivative Works thereof, You may choose to offer,
+ and charge a fee for, acceptance of support, warranty, indemnity,
+ or other liability obligations and/or rights consistent with this
+ License. However, in accepting such obligations, You may act only
+ on Your own behalf and on Your sole responsibility, not on behalf
+ of any other Contributor, and only if You agree to indemnify,
+ defend, and hold each Contributor harmless for any liability
+ incurred by, or claims asserted against, such Contributor by reason
+ of your accepting any such warranty or additional liability.
+
+ END OF TERMS AND CONDITIONS
+
+ APPENDIX: How to apply the Apache License to your work.
+
+ To apply the Apache License to your work, attach the following
+ boilerplate notice, with the fields enclosed by brackets "[]"
+ replaced with your own identifying information. (Don't include
+ the brackets!) The text should be enclosed in the appropriate
+ comment syntax for the file format. We also recommend that a
+ file or class name and description of purpose be included on the
+ same "printed page" as the copyright notice for easier
+ identification within third-party archives.
+
+ Copyright [yyyy] [name of copyright owner]
+
+ Licensed under the Apache License, Version 2.0 (the "License");
+ you may not use this file except in compliance with the License.
+ You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+ Unless required by applicable law or agreed to in writing, software
+ distributed under the License is distributed on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ See the License for the specific language governing permissions and
+ limitations under the License.
\ No newline at end of file
diff --git a/(p,t) compression/LICENSE-MIT.txt b/(p,t) compression/LICENSE-MIT.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6d33b12db6ddfca2826f665b907b66188822c129
--- /dev/null
+++ b/(p,t) compression/LICENSE-MIT.txt
@@ -0,0 +1,23 @@
+Copyright (c) 2012 Vladimir Keleshev, <vladimir@keleshev.com>
+
+Permission is hereby granted, free of charge, to any person
+obtaining a copy of this software and associated
+documentation files (the "Software"), to deal in the Software
+without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense,
+and/or sell copies of the Software, and to permit persons to
+whom the Software is furnished to do so, subject to the
+following conditions:
+
+The above copyright notice and this permission notice shall
+be included in all copies or substantial portions of the
+Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY
+KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR
+PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
+COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
+OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
+SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
\ No newline at end of file
diff --git a/(p,t) compression/Notice.txt b/(p,t) compression/Notice.txt
new file mode 100644
index 0000000000000000000000000000000000000000..308703a87659a660dc3f846ee01208f5f1c44fd5
--- /dev/null
+++ b/(p,t) compression/Notice.txt
@@ -0,0 +1,23 @@
+Neighborhood Preserving graph compression
+
+
+ all software is copyright 2021
+ Abd Errahmane Kiouche, licensed under the Apache License 2.0.
+
+
+
+docopt.cpp
+
+ Copyright (c) 2012 Vladimir Keleshev, <vladimir@keleshev.com>
+ Licensed under the MIT license (see LICENSE-MIT).
+ https://github.com/docopt/docopt.cpp
+
+ Files: docopt.cpp docopt.h docopt_private.h docopt_util.h docopt_value.h
+ Modifications: Remove "#pragma mark" directives.
+
+
+hash
+
+ Copyright 2016 Emaad Ahmed Manzoor
+ License: Apache License, Version 2.0
+ Files : hash.h
diff --git a/(p,t) compression/graph.cpp b/(p,t) compression/graph.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..5f9be2a24cc4e27f5f18f0d6cee002cca19a58d9
--- /dev/null
+++ b/(p,t) compression/graph.cpp
@@ -0,0 +1,65 @@
+//
+// Created by Kiouche on 1/20/2020.
+//
+
+#include <unordered_map>
+#include <unordered_set>
+#include <vector>
+#include "graph.h"
+#include "hash.h"
+
+
+
+
+
+namespace std {
+
+ vector<edge> get_edges(graph &g,bool directed){
+ vector<edge> edges;
+ unordered_set<edge> s_edges;
+ for (auto & s : g){
+ for (auto & d : s.second ){
+ edge e,r_e;
+ e.first = s.first;
+ e.second = d;
+ r_e.first = d;
+ r_e.second = s.first;
+ if(!directed) {
+ if (s_edges.find(e) == s_edges.end()) {
+ edges.push_back(e);
+ }
+ }
+ else edges.push_back(e);
+ s_edges.insert(e);
+ s_edges.insert(r_e);
+ }
+ }
+ return edges;
+ }
+
+ bool is_it_undirected(graph &g){
+ for (auto s : g){
+ for (auto d : s.second ){
+ if ( g[d].find(s.first)==g[d].end()) return false;
+ }
+ }
+ return true;
+ }
+
+ unordered_set<uint32_t > intersection(unordered_set<uint32_t> &s1,unordered_set<uint32_t> &s2){
+ unordered_set<uint32_t > intersection;
+ if (s1.size()< s2.size()){
+ for (auto n :s1){
+ if (s2.find(n)!=s2.end()) intersection.insert(n);
+ }
+ }
+ else{
+ for (auto n :s2){
+ if (s1.find(n)!=s1.end()) intersection.insert(n);
+ }
+ }
+ return intersection;
+ }
+
+
+}
\ No newline at end of file
diff --git a/(p,t) compression/graph.h b/(p,t) compression/graph.h
new file mode 100644
index 0000000000000000000000000000000000000000..fc9c71f35f04222a2a09347acc3fe4bc0dad0d4a
--- /dev/null
+++ b/(p,t) compression/graph.h
@@ -0,0 +1,36 @@
+//
+// Created by Kiouche on 1/20/2020.
+//
+
+#ifndef P_K_COMPRESSION_GRAPH_H
+#define P_K_COMPRESSION_GRAPH_H
+#include <unordered_map>
+#include <unordered_set>
+#include <vector>
+
+
+
+
+
+namespace std{
+
+ typedef unordered_map<uint32_t,unordered_map<int,unordered_set<uint32_t >>> node_neighbors; /// key 1 = node_id , key 2 = depth , value = nodes
+
+ typedef unordered_map<uint32_t , unordered_set<uint32_t >> graph; /// adjacency matrix , key = node_id
+
+ typedef pair<uint32_t , uint32_t> edge;
+
+ vector<edge> get_edges(graph &g,bool directed);
+
+
+ bool is_it_undirected(graph &g);
+
+
+ unordered_set<uint32_t > intersection(unordered_set<uint32_t> &s1,unordered_set<uint32_t> &s2);
+
+
+}
+
+
+
+#endif //P_K_COMPRESSION_GRAPH_H
diff --git a/(p,t) compression/hash.h b/(p,t) compression/hash.h
new file mode 100644
index 0000000000000000000000000000000000000000..3394fd28f4de154062a068b2340960ea6a60f20c
--- /dev/null
+++ b/(p,t) compression/hash.h
@@ -0,0 +1,43 @@
+//
+// Created by Kiouche on 1/20/2020.
+//
+
+#ifndef P_K_COMPRESSION_HASH_H
+#define P_K_COMPRESSION_HASH_H
+
+
+
+
+#include <string>
+#include <vector>
+
+namespace std {
+
+
+/* Combination hash from Boost */
+ template <class T>
+ inline void hash_combine(size_t& seed, const T& v)
+ {
+ hash<T> hasher;
+ seed ^= hasher(v) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
+ }
+
+ template<typename S, typename T> struct hash<pair<S, T>>
+{
+ inline size_t operator()(const pair<S, T>& v) const
+ {
+ size_t seed = 0;
+ hash_combine(seed, v.first);
+ hash_combine(seed, v.second);
+ return seed;
+ }
+
+};
+/* End combination hash from Boost */
+
+
+
+}
+
+
+#endif //P_K_COMPRESSION_HASH_H
diff --git a/(p,t) compression/io.cpp b/(p,t) compression/io.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..375bc75de8fdf88d72330115b9549131a51607c5
--- /dev/null
+++ b/(p,t) compression/io.cpp
@@ -0,0 +1,78 @@
+//
+// Created by Kiouche on 1/20/2020.
+//
+
+#include <fstream>
+#include <iostream>
+#include <string>
+#include <sstream>
+#include <unistd.h>
+#include <vector>
+#include "graph.h"
+#include "io.h"
+#include "hash.h"
+
+namespace std {
+
+ tuple<graph,unordered_map<edge , double>> read_graph_from_file(string filename,bool directed) {
+
+ ifstream f(filename);
+ string line;
+ graph g;
+ unordered_map<edge , double> edges_scores;
+ int loops = 0;
+
+ if (f.is_open()) {
+ while (getline(f, line)) {
+ uint32_t src_id, dst_id;
+ edge e,e_r;
+ double score;
+ stringstream ss;
+ ss.str(line);
+ ss >> src_id;
+ ss >> dst_id;
+ ss >> score;
+
+ if (src_id!=dst_id) {
+ e.first = src_id ; e.second = dst_id;
+ e_r.first = dst_id; e.second = src_id;
+ g[src_id].insert(dst_id);
+ if(!directed) g[dst_id].insert(src_id);
+ edges_scores[make_pair(src_id,dst_id)] = score ;
+ // if(!directed) edges_scores[e_r] = score;
+ }
+ else loops++;
+ }
+ } else {
+ cout << "Unable to open " << filename << " ! \n";
+ exit(-1);
+ }
+ cout << "number of nodes = " << g.size() << endl;
+ cout << "loops = " << loops << endl;
+ return {g,edges_scores};
+ }
+
+ void graph_to_file (po::variables_map &var,double runtime, double c_rate,vector<edge> &edges){
+
+ ofstream file;
+ file.open(var["output_file"].as<string>());
+ file << "Original graph" << "\t"<< var["input"].as<string>() <<endl;
+ file << "Directed" << "\t" << to_string(var["directed"].as<bool>()) << endl;
+ file << "Depth" << "\t" << to_string(var["depth"].as<int>()) << endl;
+ vector<double> p_values = var["proportions"].as<vector<double>>();
+ int depth = var["depth"].as<int>();
+ for (int i = 0;i<=depth;i++){
+ file << "k " + to_string(i) << "\t" << to_string(p_values.at(i)) << endl;
+ }
+ file << "execution time " << "\t" << to_string(runtime) << endl;
+ file << "compression rate " << "\t" << to_string(c_rate) << endl;
+
+ file << endl;
+
+ for (auto e : edges){
+ file << e.first <<"\t"<< e.second << endl;
+ }
+ file.close();
+ }
+
+}
\ No newline at end of file
diff --git a/(p,t) compression/io.h b/(p,t) compression/io.h
new file mode 100644
index 0000000000000000000000000000000000000000..6e901a5c3cdae018c2c5f43aaa88abcd00918b09
--- /dev/null
+++ b/(p,t) compression/io.h
@@ -0,0 +1,19 @@
+//
+// Created by Kiouche on 1/20/2020.
+//
+
+#ifndef P_K_COMPRESSION_IO_H
+#define P_K_COMPRESSION_IO_H
+#include "graph.h"
+#include <boost/program_options.hpp>
+
+namespace po = boost::program_options;
+
+
+namespace std {
+ tuple<graph,unordered_map<edge , double>> read_graph_from_file(string filename,bool directed);
+ void graph_to_file (po::variables_map &var,double runtime, double c_rate,vector<edge> &edges);
+
+}
+
+#endif //P_K_COMPRESSION_IO_H
diff --git a/(p,t) compression/main.cpp b/(p,t) compression/main.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..ce3bc9d20300afda0857d880878610a693c7c174
--- /dev/null
+++ b/(p,t) compression/main.cpp
@@ -0,0 +1,95 @@
+#include <iostream>
+#include <chrono>
+#include "p_k_compression.h"
+#include <boost/program_options.hpp>
+#include "graph.h"
+#include "io.h"
+#include <sstream>
+#include <string>
+#include <fstream>
+#include "hash.h"
+
+
+using namespace std;
+namespace po = boost::program_options;
+
+
+
+int main(int argc, char *argv[]) {
+
+ srand((unsigned)time(NULL));
+
+ po::options_description desc("Allowed options");
+ desc.add_options()
+ ("help", "produce help message")
+ ("input", po::value<string>(), "graph file name")
+ ("directed", po::value<bool>()->default_value(true), "is the graph directed?")
+ ("algorithm",po::value<string>()->default_value("Random"), "The compression Algorithm")
+ ("depth",po::value<int>()->default_value(2),"the depth of the compression")
+ ("proportions",po::value<std::vector<double> >()->multitoken(),"the preserving proportions")
+ ("output_file",po::value<string>(), "the path of the compressed graph");
+
+ po::variables_map var;
+ po::store(po::parse_command_line(argc, argv, desc), var);
+ po::notify(var);
+
+ if(var.count("help")) {
+ cout << desc << "\n";
+ return 0;
+ }
+
+ if(!var.count("input")) {
+ cout << "Missing argument --input.\n";
+ return 1;
+ }
+ if(!var.count("output_file")) {
+ cout << "Missing argument --output_file.\n";
+ return 1;
+ }
+
+ graph g2;
+
+ vector<int> s ;
+ vector<double> c ;
+ // perform 30 experiments
+ for (int i =0; i<30;i++) {
+ cout << i << endl;
+ string file_name = var["input"].as<string>() + to_string(i) + ".txt";
+ double compression_rate = 0;
+ auto[g, e_s] = read_graph_from_file(file_name, var["directed"].as<bool>());
+ auto start = chrono::steady_clock::now();
+
+ if (var["algorithm"].as<string>() == "Random") {
+ g2 = compress_graph_basic(g, var["depth"].as<int>(), var["proportions"].as<vector<double>>(),
+ var["directed"].as<bool>());
+
+ } else if (var["algorithm"].as<string>() == "LP") {
+ g2 = compress_graph_LP(g, e_s, var["depth"].as<int>(), var["proportions"].as<vector<double>>(),
+ var["directed"].as<bool>());
+
+ } else if (var["algorithm"].as<string>() == "SA") {
+ g2 = Simulated_annealing(1000, 10, 0.99, g, var["directed"].as<bool>(), var["depth"].as<int>(),
+ var["proportions"].as<vector<double>>());
+ }else if (var["algorithm"].as<string>() == "Greedy") {
+ g2 = compress_graph_greedy(g, var["depth"].as<int>(), var["proportions"].as<vector<double>>(),
+ var["directed"].as<bool>());
+
+ }
+
+ auto finish = chrono::steady_clock::now();
+ vector<edge> edges_original = get_edges(g, var["directed"].as<bool>());
+ vector<edge> edges_compressed = get_edges(g2, var["directed"].as<bool>());
+
+ double elapsed_time = chrono::duration_cast<chrono::duration<double>>(finish - start).count();
+ compression_rate = ((double) (edges_original.size() - edges_compressed.size()) /
+ edges_original.size());
+ c.push_back(compression_rate);
+ s.push_back(edges_compressed.size());
+ //graph_to_file(var, elapsed_time, compression_rate, edges_compressed);
+ cout << "compression time " << elapsed_time << endl;
+ cout << "compression rate " << compression_rate << endl;
+ }
+ for (int i = 0 ; i<30;i++) cout << c.at(i) << '\t' << s.at(i) << endl;
+
+ return 0;
+}
diff --git a/(p,t) compression/p_k_compression.cpp b/(p,t) compression/p_k_compression.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..e068a8a93c11c66baca87a7d605c372cc7277efd
--- /dev/null
+++ b/(p,t) compression/p_k_compression.cpp
@@ -0,0 +1,391 @@
+//
+// Created by Kiouche on 1/20/2020.
+//
+
+#include "p_k_compression.h"
+#include <chrono>
+#include <map>
+#include <list>
+#include <iostream>
+#include <algorithm>
+#include <random>
+#include <queue>
+
+#include "hash.h"
+
+
+
+namespace std {
+
+
+ bool test_insert(edge &e, bool directed,graph &constructed_graph,graph &compressed_graph ,int k, vector<double> &p){
+ uint32_t first, second;
+ first = e.first;
+ second = e.second;
+ if(!directed) {
+ if (constructed_graph[e.first].size() > constructed_graph[e.second].size()) {
+ first = e.second;
+ second = e.first;
+ }
+ }
+ bool insert = BFS(first,compressed_graph,constructed_graph,p,k);
+ if ( insert){
+ return true;
+ }
+ else if (!directed) {
+ return BFS(second,compressed_graph,constructed_graph,p,k);
+ }
+ else return insert;
+ }
+
+ void get_neighbors(uint32_t node, graph &g,unordered_map<int,unordered_set<uint32_t>> &neighbors,
+ int &maxDepth){
+
+ // Mark all the vertices as not visited
+ unordered_map<uint32_t , int> node_visited;
+ // Create a queue for BFS
+ deque<uint32_t> queue;
+ // array_queue *queue = new array_queue();
+ // Mark the current node as visited and enqueue it
+ node_visited[node]= 1;
+ queue.push_back(node);
+
+ int currentDepth = 1,
+ elementsToDepthIncrease = 1,
+ nextElementsToDepthIncrease = 0;
+
+ while(!queue.empty()) {
+ // Dequeue a vertex from queue and print it
+ uint32_t s = queue.front();
+ queue.pop_front();
+ // node_visited[s] = 1;
+ for (auto &v : g[s]){
+ if (node_visited[v]==0) {
+ nextElementsToDepthIncrease++;
+ node_visited[v]=1;
+ queue.push_back(v);
+ for (int i = currentDepth; i <= maxDepth; i++) neighbors[i].insert(v);
+ }
+ }
+ if (--elementsToDepthIncrease == 0) {
+ if (++currentDepth > maxDepth) break;
+ elementsToDepthIncrease = nextElementsToDepthIncrease;
+ nextElementsToDepthIncrease = 0;
+ }
+ }
+ }
+
+ bool check_constraints(graph &original_graph,graph &compressed_graph,vector<double> p, int k){
+
+ for (auto v : original_graph){
+ unordered_map<int,unordered_set<uint32_t>> n_v;
+ get_neighbors(v.first,compressed_graph,n_v,k);
+ for (int i=1;i<= k;i++){
+ unordered_set<uint32_t> nghs = intersection( n_v[i],original_graph[v.first]);
+ if ((double) nghs.size() < v.second.size()*p.at(i)){
+ cout << i << "---" << v.first << " " << nghs.size() << " "
+ << v.second.size() << endl;
+ return false;
+ }
+ }
+ }
+ return true;
+ }
+
+ bool BFS(uint32_t node, graph &g,graph &constructed_graph,vector<double> &p,int &maxDepth){
+
+ unordered_map<int,unordered_set<uint32_t>> neighbors;
+ // Mark all the vertices as not visited
+ unordered_map<uint32_t , int> node_visited;
+ // Create a queue for BFS
+ deque<uint32_t> queue;
+ // Mark the current node as visited and enqueue it
+ node_visited[node]= 1;
+ queue.push_back(node);
+
+ int currentDepth = 1,
+ elementsToDepthIncrease = 1,
+ nextElementsToDepthIncrease = 0;
+
+ while(!queue.empty()) {
+ // Dequeue a vertex from queue and print it
+ uint32_t s = queue.front();
+ queue.pop_front();
+ for (auto &v : g[s]){
+ if (node_visited[v]==0) {
+ nextElementsToDepthIncrease++;
+ node_visited[v]=1;
+ queue.push_back(v);
+ for (int i = currentDepth; i <= maxDepth; i++) neighbors[i].insert(v);
+ }
+ }
+ if (--elementsToDepthIncrease == 0) {
+ double nb_nghrs = constructed_graph[node].size();
+ unordered_set<uint32_t> s_neighbors = intersection( neighbors[currentDepth],constructed_graph[node]);
+ if ((double) s_neighbors.size() < nb_nghrs * p.at(currentDepth)) return true;
+ if (++currentDepth > maxDepth) break;
+ elementsToDepthIncrease = nextElementsToDepthIncrease;
+ nextElementsToDepthIncrease = 0;
+ }
+ }
+ if (currentDepth <= maxDepth){
+ for (int i= currentDepth;i<=maxDepth;i++){
+ double nb_nghrs = constructed_graph[node].size();
+ unordered_set<uint32_t> s_neighbors = intersection( neighbors[i],constructed_graph[node]);
+ if ((double) s_neighbors.size() < nb_nghrs * p.at(i)) return true;
+ }
+ }
+ return false;
+ }
+
+ graph compress_graph_LP(graph &initial_graph, unordered_map<edge,double> edges_scores, int k, vector<double> p,bool directed){
+
+ double compression_rate;
+ vector<edge> inserted_edges;
+
+ vector<pair<edge,double>> es_vec;
+
+ for ( auto & e : edges_scores ) es_vec.push_back(make_pair(e.first,e.second));
+ sort(es_vec.begin(), es_vec.end(), // sort by PL scores
+ [](const pair<edge,double> & l, const pair<edge,double>& r) {
+ return l.second > r.second;
+ });
+ cout << es_vec.size() << endl;
+ graph compressed_graph,constructed_graph;
+ int number_edges = 0;
+ int i=0;
+ for (auto e_s : es_vec){
+ edge e = e_s.first;
+ if (i%10000==0) cout << i<< endl;
+ i++;
+ constructed_graph[e.first].insert(e.second);
+ if(!directed) constructed_graph[e.second].insert(e.first);
+ bool insert =test_insert(e,directed,constructed_graph,compressed_graph,k,p);
+
+ if ( insert) {
+ inserted_edges.push_back(e);
+ number_edges++;
+ compressed_graph[e.first].insert(e.second);
+ if (!directed) compressed_graph[e.second].insert(e.first);
+ }
+ }
+ cout << "number of edges " << number_edges << endl;
+ if (check_constraints(initial_graph,compressed_graph,p,k)) cout << "feasible compression!"<< endl;
+ return compressed_graph;
+ }
+
+
+ graph compress_graph_basic(graph &initial_graph, int k, vector<double> p,bool directed){
+
+ double compression_rate;
+ vector<edge> inserted_edges;
+ vector<edge> s = get_edges(initial_graph,directed);
+ std::mt19937 g(rand());
+ std::shuffle(s.begin(), s.end(), g);
+
+ graph compressed_graph,constructed_graph;
+ int number_edges = 0;
+ int i=0;
+ for (auto e : s){
+ if (i%10000==0) cout << i<< endl;
+ i++;
+ constructed_graph[e.first].insert(e.second);
+ if(!directed) constructed_graph[e.second].insert(e.first);
+ bool insert =test_insert(e,directed,constructed_graph,compressed_graph,k,p);
+ if (insert){
+ inserted_edges.push_back(e);
+ number_edges++;
+ compressed_graph[e.first].insert(e.second);
+ if(!directed) compressed_graph[e.second].insert(e.first);
+ }
+ }
+ cout << "number of edges " << number_edges << endl;
+ if (check_constraints(initial_graph,compressed_graph,p,k)) cout << "feasible compression!"<< endl;
+ return compressed_graph;
+ }
+
+
+ vector<edge> perturbate_solution(vector<edge> &s){
+ vector<edge> s2;
+ for (auto e : s ) s2.push_back(e);
+ int max_perturbations = 2; //s.size()/100;
+ std::mt19937 gen(rand());
+ std::uniform_int_distribution<> dis(0, s.size()-1);
+ for (int i=0;i<max_perturbations;i++){
+ int r1,r2;
+ r1 = dis(gen);
+ r2 = dis(gen);
+ edge e = s2.at(r1);
+ s2.at(r1).first= s2.at(r2).first;
+ s2.at(r1).second= s2.at(r2).second;
+ s2.at(r2).first = e.first;
+ s2.at(r2).second = e.second;
+ }
+ return s2;
+ }
+
+
+ tuple<double,graph> evaluate_permutation ( vector<edge> &permutation,bool directed, vector<double> &p,
+ int k,graph &g){
+ //double compression_rate;
+ graph compressed_graph,constructed_graph;
+ int inserted_edges = 0;
+ for (auto e : permutation){
+ // update constructed graph
+ constructed_graph[e.first].insert(e.second);
+ if (!directed) constructed_graph[e.second].insert(e.first);
+ bool insert =test_insert(e,false,constructed_graph,compressed_graph,k,p);
+ if (insert){
+ inserted_edges++;
+ compressed_graph[e.first].insert(e.second);
+ if (!directed) compressed_graph[e.second].insert(e.first);
+ }
+ }
+
+ return make_tuple(inserted_edges,compressed_graph);
+ }
+
+
+
+ graph Simulated_annealing ( int max_iterations,
+ double initial_temperature,
+ double decrease_factor,
+ graph &initial_graph,
+ bool directed,
+ int k,vector<double> p){
+ auto start = chrono::steady_clock::now();
+ graph gr;
+ vector<edge> best_permutation;
+ /// generate initial solution
+ vector<edge> s = get_edges(initial_graph,false);
+ best_permutation = s;
+ std::mt19937 g(rand());
+ std::shuffle(s.begin(), s.end(), g);
+
+ double cost_s,cost_s2,T,best;
+ T= initial_temperature;
+ cost_s = get<0> (evaluate_permutation(s,directed,p,k,initial_graph));
+ gr = get<1> (evaluate_permutation(s,directed,p,k,initial_graph));
+ best = cost_s;
+ for (int i = 0;i<max_iterations;i++){
+ vector<edge> s2 = perturbate_solution(s);
+ cost_s2 = get<0> (evaluate_permutation(s2,directed, p,k,initial_graph));
+ if (cost_s2 < best){
+ best_permutation = s2;
+ gr = get<1> (evaluate_permutation(s2,directed,p,k,initial_graph));
+ best = cost_s2;
+ auto finish = chrono::steady_clock::now();
+ double elapsed_time= chrono::duration_cast<chrono::duration<double>>(finish - start).count();
+ //cout <<i<< '\t'<<best<< '\t' << elapsed_time << endl;
+ }
+ if (cost_s2 < cost_s){
+ s = s2;
+ cost_s = cost_s2;
+ }
+ else {
+ double r = ((double) rand() /(RAND_MAX));
+ if (std::exp( (cost_s -cost_s2) / T) > r ){
+ s = s2;
+ cost_s = cost_s2;
+ }
+ }
+ T = decrease_factor*T;
+ }
+
+ if ( check_constraints(initial_graph,gr,p,k)) {
+ cout << "feasible solution ! " << endl;
+ }
+
+ return gr;
+ }
+
+
+
+
+ graph compress_graph_greedy(graph &initial_graph, int k, vector<double> p,bool directed){
+
+ double compression_rate;
+ vector<edge> inserted_edges;
+ vector<edge> s = greedy_edges_order(initial_graph,directed,k);
+
+
+ graph compressed_graph,constructed_graph;
+ int number_edges = 0;
+ int i=0;
+ for (auto e : s){
+ if (i%10000==0) cout << i<< endl;
+ i++;
+ constructed_graph[e.first].insert(e.second);
+ if(!directed) constructed_graph[e.second].insert(e.first);
+ bool insert =test_insert(e,directed,constructed_graph,compressed_graph,k,p);
+ if (insert){
+ inserted_edges.push_back(e);
+ number_edges++;
+ compressed_graph[e.first].insert(e.second);
+ if(!directed) compressed_graph[e.second].insert(e.first);
+ }
+ }
+ cout << "number of edges " << number_edges << endl;
+ if (check_constraints(initial_graph,compressed_graph,p,k)) cout << "feasible compression!"<< endl;
+ return compressed_graph;
+ }
+
+ vector<edge> greedy_edges_order(graph &g,bool directed,int k){
+ vector<edge> edges = get_edges(g,directed);
+ map<pair<uint32_t ,uint32_t >,int> edge_score;
+ for (auto e : edges ){
+ unordered_set<uint32_t > neighbors_u;
+ unordered_set<uint32_t> neighbors_v;
+ neighbors_u = neighbors(g,k-1,e.first,e.second);
+ neighbors_v = neighbors(g,k-1,e.second,e.first);
+ for (auto n : neighbors_u){
+ if (g[n].find(e.second)!=g[n].end()) edge_score[e]=edge_score[e]+1;
+ }
+ for (auto n : neighbors_v){
+ if (g[n].find(e.first)!=g[n].end()) edge_score[e]=edge_score[e]+1;
+ }
+ }
+ sort(edges.begin(),edges.end(),[&]( const edge &e1, const edge &e2 )
+ { return edge_score[e1] > edge_score[e2];} );
+ return edges;
+ }
+
+
+ unordered_set<uint32_t> neighbors(graph &g,int max_depth,uint32_t u,uint32_t v){
+ unordered_set<uint32_t> nghrs;
+ // Mark all the vertices as not visited
+ unordered_map<uint32_t , int> node_visited;
+ // Create a queue for BFS
+ deque<uint32_t> queue;
+ // array_queue *queue = new array_queue();
+ // Mark the current node as visited and enqueue it
+ node_visited[u]= 1;
+ node_visited[v] = 1;
+ queue.push_back(u);
+ int currentDepth = 1,
+ elementsToDepthIncrease = 1,
+ nextElementsToDepthIncrease = 0;
+
+
+ while(!queue.empty()) {
+ // Dequeue a vertex from queue and print it
+ uint32_t s = queue.front();
+ queue.pop_front();
+ // node_visited[s] = 1;
+ for (auto &v : g[s]){
+ if (node_visited[v]==0) {
+ node_visited[v]=1;
+ queue.push_back(v);
+ nghrs.insert(v);
+ }
+ }
+ if (--elementsToDepthIncrease == 0) {
+ if (++currentDepth > max_depth) break;
+ elementsToDepthIncrease = nextElementsToDepthIncrease;
+ nextElementsToDepthIncrease = 0;
+ }
+ }
+ return nghrs;
+ }
+
+}
\ No newline at end of file
diff --git a/(p,t) compression/p_k_compression.h b/(p,t) compression/p_k_compression.h
new file mode 100644
index 0000000000000000000000000000000000000000..5f96fdeff2c09c30e961a0106b29887327019ae9
--- /dev/null
+++ b/(p,t) compression/p_k_compression.h
@@ -0,0 +1,57 @@
+//
+// Created by Kiouche on 1/20/2020.
+//
+
+#ifndef P_K_COMPRESSION_P_K_COMPRESSION_H
+#define P_K_COMPRESSION_P_K_COMPRESSION_H
+#include "graph.h"
+
+namespace std {
+
+
+ bool check_constraints(graph &original_graph,graph &compressed_graph,vector<double> p, int k);
+
+
+ bool BFS(uint32_t node, graph &g,graph &constructed_graph,vector<double> &p,int &maxDepth);
+
+ bool test_insert(edge &e, bool directed,graph &constructed_graph,graph &compressed_graph ,int k, vector<double> &p);
+
+ graph compress_graph_LP(graph &initial_graph, unordered_map<edge,double> edges_scores, int k, vector<double> p,bool directed);
+
+ void get_neighbors(uint32_t node, graph &g,unordered_map<int,unordered_set<uint32_t>> &neighbors,
+ int &maxDepth);
+ graph Greedy_compression(graph &initial_graph,unordered_map<edge,double> edges_scores, int k, vector<double> p,bool directed);
+ graph compress_graph_basic(graph &initial_graph, int k, vector<double> p,bool directed);
+
+ graph random_compression_graph(graph &initial_graph,bool directed);
+
+ vector<edge> perturbate_solution(vector<edge> &s);
+
+ graph Simulated_annealing ( int max_iterations,
+ double initial_temperature,
+ double decrease_factor,
+ graph &initial_graph,
+ bool directed,
+ int k,vector<double> p);
+
+
+
+
+
+
+
+ tuple<double,graph> evaluate_permutation ( vector<edge> &permutation,bool directed, vector<double> &p,
+ int k,graph &g);
+
+
+ graph compress_graph_greedy(graph &initial_graph, int k, vector<double> p,bool directed);
+
+
+
+ unordered_set<uint32_t> neighbors(graph &g,int max_depth,uint32_t u,uint32_t v);
+ vector<edge> greedy_edges_order(graph &g,bool directed,int k);
+
+
+}
+
+#endif //P_K_COMPRESSION_P_K_COMPRESSION_H
diff --git a/LICENSE b/LICENSE
new file mode 100644
index 0000000000000000000000000000000000000000..6b468505443f1f339f919b1ecf7718480f689fca
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,201 @@
+ Apache License
+ Version 2.0, January 2004
+ http://www.apache.org/licenses/
+
+ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+ 1. Definitions.
+
+ "License" shall mean the terms and conditions for use, reproduction,
+ and distribution as defined by Sections 1 through 9 of this document.
+
+ "Licensor" shall mean the copyright owner or entity authorized by
+ the copyright owner that is granting the License.
+
+ "Legal Entity" shall mean the union of the acting entity and all
+ other entities that control, are controlled by, or are under common
+ control with that entity. For the purposes of this definition,
+ "control" means (i) the power, direct or indirect, to cause the
+ direction or management of such entity, whether by contract or
+ otherwise, or (ii) ownership of fifty percent (50%) or more of the
+ outstanding shares, or (iii) beneficial ownership of such entity.
+
+ "You" (or "Your") shall mean an individual or Legal Entity
+ exercising permissions granted by this License.
+
+ "Source" form shall mean the preferred form for making modifications,
+ including but not limited to software source code, documentation
+ source, and configuration files.
+
+ "Object" form shall mean any form resulting from mechanical
+ transformation or translation of a Source form, including but
+ not limited to compiled object code, generated documentation,
+ and conversions to other media types.
+
+ "Work" shall mean the work of authorship, whether in Source or
+ Object form, made available under the License, as indicated by a
+ copyright notice that is included in or attached to the work
+ (an example is provided in the Appendix below).
+
+ "Derivative Works" shall mean any work, whether in Source or Object
+ form, that is based on (or derived from) the Work and for which the
+ editorial revisions, annotations, elaborations, or other modifications
+ represent, as a whole, an original work of authorship. For the purposes
+ of this License, Derivative Works shall not include works that remain
+ separable from, or merely link (or bind by name) to the interfaces of,
+ the Work and Derivative Works thereof.
+
+ "Contribution" shall mean any work of authorship, including
+ the original version of the Work and any modifications or additions
+ to that Work or Derivative Works thereof, that is intentionally
+ submitted to Licensor for inclusion in the Work by the copyright owner
+ or by an individual or Legal Entity authorized to submit on behalf of
+ the copyright owner. For the purposes of this definition, "submitted"
+ means any form of electronic, verbal, or written communication sent
+ to the Licensor or its representatives, including but not limited to
+ communication on electronic mailing lists, source code control systems,
+ and issue tracking systems that are managed by, or on behalf of, the
+ Licensor for the purpose of discussing and improving the Work, but
+ excluding communication that is conspicuously marked or otherwise
+ designated in writing by the copyright owner as "Not a Contribution."
+
+ "Contributor" shall mean Licensor and any individual or Legal Entity
+ on behalf of whom a Contribution has been received by Licensor and
+ subsequently incorporated within the Work.
+
+ 2. Grant of Copyright License. Subject to the terms and conditions of
+ this License, each Contributor hereby grants to You a perpetual,
+ worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+ copyright license to reproduce, prepare Derivative Works of,
+ publicly display, publicly perform, sublicense, and distribute the
+ Work and such Derivative Works in Source or Object form.
+
+ 3. Grant of Patent License. Subject to the terms and conditions of
+ this License, each Contributor hereby grants to You a perpetual,
+ worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+ (except as stated in this section) patent license to make, have made,
+ use, offer to sell, sell, import, and otherwise transfer the Work,
+ where such license applies only to those patent claims licensable
+ by such Contributor that are necessarily infringed by their
+ Contribution(s) alone or by combination of their Contribution(s)
+ with the Work to which such Contribution(s) was submitted. If You
+ institute patent litigation against any entity (including a
+ cross-claim or counterclaim in a lawsuit) alleging that the Work
+ or a Contribution incorporated within the Work constitutes direct
+ or contributory patent infringement, then any patent licenses
+ granted to You under this License for that Work shall terminate
+ as of the date such litigation is filed.
+
+ 4. Redistribution. You may reproduce and distribute copies of the
+ Work or Derivative Works thereof in any medium, with or without
+ modifications, and in Source or Object form, provided that You
+ meet the following conditions:
+
+ (a) You must give any other recipients of the Work or
+ Derivative Works a copy of this License; and
+
+ (b) You must cause any modified files to carry prominent notices
+ stating that You changed the files; and
+
+ (c) You must retain, in the Source form of any Derivative Works
+ that You distribute, all copyright, patent, trademark, and
+ attribution notices from the Source form of the Work,
+ excluding those notices that do not pertain to any part of
+ the Derivative Works; and
+
+ (d) If the Work includes a "NOTICE" text file as part of its
+ distribution, then any Derivative Works that You distribute must
+ include a readable copy of the attribution notices contained
+ within such NOTICE file, excluding those notices that do not
+ pertain to any part of the Derivative Works, in at least one
+ of the following places: within a NOTICE text file distributed
+ as part of the Derivative Works; within the Source form or
+ documentation, if provided along with the Derivative Works; or,
+ within a display generated by the Derivative Works, if and
+ wherever such third-party notices normally appear. The contents
+ of the NOTICE file are for informational purposes only and
+ do not modify the License. You may add Your own attribution
+ notices within Derivative Works that You distribute, alongside
+ or as an addendum to the NOTICE text from the Work, provided
+ that such additional attribution notices cannot be construed
+ as modifying the License.
+
+ You may add Your own copyright statement to Your modifications and
+ may provide additional or different license terms and conditions
+ for use, reproduction, or distribution of Your modifications, or
+ for any such Derivative Works as a whole, provided Your use,
+ reproduction, and distribution of the Work otherwise complies with
+ the conditions stated in this License.
+
+ 5. Submission of Contributions. Unless You explicitly state otherwise,
+ any Contribution intentionally submitted for inclusion in the Work
+ by You to the Licensor shall be under the terms and conditions of
+ this License, without any additional terms or conditions.
+ Notwithstanding the above, nothing herein shall supersede or modify
+ the terms of any separate license agreement you may have executed
+ with Licensor regarding such Contributions.
+
+ 6. Trademarks. This License does not grant permission to use the trade
+ names, trademarks, service marks, or product names of the Licensor,
+ except as required for reasonable and customary use in describing the
+ origin of the Work and reproducing the content of the NOTICE file.
+
+ 7. Disclaimer of Warranty. Unless required by applicable law or
+ agreed to in writing, Licensor provides the Work (and each
+ Contributor provides its Contributions) on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
+ implied, including, without limitation, any warranties or conditions
+ of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
+ PARTICULAR PURPOSE. You are solely responsible for determining the
+ appropriateness of using or redistributing the Work and assume any
+ risks associated with Your exercise of permissions under this License.
+
+ 8. Limitation of Liability. In no event and under no legal theory,
+ whether in tort (including negligence), contract, or otherwise,
+ unless required by applicable law (such as deliberate and grossly
+ negligent acts) or agreed to in writing, shall any Contributor be
+ liable to You for damages, including any direct, indirect, special,
+ incidental, or consequential damages of any character arising as a
+ result of this License or out of the use or inability to use the
+ Work (including but not limited to damages for loss of goodwill,
+ work stoppage, computer failure or malfunction, or any and all
+ other commercial damages or losses), even if such Contributor
+ has been advised of the possibility of such damages.
+
+ 9. Accepting Warranty or Additional Liability. While redistributing
+ the Work or Derivative Works thereof, You may choose to offer,
+ and charge a fee for, acceptance of support, warranty, indemnity,
+ or other liability obligations and/or rights consistent with this
+ License. However, in accepting such obligations, You may act only
+ on Your own behalf and on Your sole responsibility, not on behalf
+ of any other Contributor, and only if You agree to indemnify,
+ defend, and hold each Contributor harmless for any liability
+ incurred by, or claims asserted against, such Contributor by reason
+ of your accepting any such warranty or additional liability.
+
+ END OF TERMS AND CONDITIONS
+
+ APPENDIX: How to apply the Apache License to your work.
+
+ To apply the Apache License to your work, attach the following
+ boilerplate notice, with the fields enclosed by brackets "{}"
+ replaced with your own identifying information. (Don't include
+ the brackets!) The text should be enclosed in the appropriate
+ comment syntax for the file format. We also recommend that a
+ file or class name and description of purpose be included on the
+ same "printed page" as the copyright notice for easier
+ identification within third-party archives.
+
+ Copyright 2021 Abd Errahmane Kiouche
+
+ Licensed under the Apache License, Version 2.0 (the "License");
+ you may not use this file except in compliance with the License.
+ You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+ Unless required by applicable law or agreed to in writing, software
+ distributed under the License is distributed on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ See the License for the specific language governing permissions and
+ limitations under the License.