Finding: backedge reuse from the head of DFS tree doesn't work

orientation before mutation

README.md

@@ -0,0 +1,2 @@
+The objective of this branch is to measure the number of removed edges between
+preserved and mutated parts of the DFS tree.

deferred_planarity_test/include/mps.h

@@ -33,6 +33,12 @@ enum node_type {
 	AE_VIRTUAL_ROOT = 3
 };
 
+enum back_edge_type {
+    RETAINED = 0,
+    MUTATED_REMOVE = 1,
+    NON_MUTATED_REMOVE = 2
+};
+
 class node
 {
 public:
@@ -56,8 +62,16 @@ public:
 	node* adj(int i);
 	void set_adj_list(vector<node*> vec);
 	void DFS_visit(vector<node*> &dfsList, int &index);
-	void guided_DFS_visit(vector<node*> &dfsList, vector<node*> &node_list, int &index, vector<int> rev_post_order);
-	void mutated_DFS_visit(vector<node*> &dfsList, vector<node*> &node_list, int &index, vector<int> rev_post_order, int &mutate_point);
+	void guided_DFS_visit(vector<node*> &dfsList, 
+                          vector<node*> &node_list, 
+                          int &return_index, 
+                          vector<int> rev_post_order);
+	void mutated_DFS_visit(vector<node*> &dfsList, 
+                           vector<node*> &node_list, 
+                           int &index, 
+                           int &traversal_index, 
+                           vector<int> rev_post_order, 
+                           int mutate_point);
 
 	//PARENT-CHILDREN
 	void set_parent(node* n) ;
@@ -147,14 +161,20 @@ public:
 	maximal_planar_subgraph_finder();
 	~maximal_planar_subgraph_finder();
 	int find_mps(string input_file);
-	int compute_removed_edge_size(string input_file, vector<int> post_order);
+	int compute_removed_edge_size(string input_file, vector<int> post_order, int mutate_point);
+	void print_removed_edge_stats(string input_file, vector<int> post_order, int mutate_point);
 	vector<int> generate_post_order(string input_file);
-	vector<int> generate_mutated_post_order(string input_file, vector<int> post_order);
+	vector<int> generate_guided_post_order(string input_file, vector<int> post_order);
+	vector<int> generate_mutated_post_order(string input_file, vector<int> post_order, int mutate_point);
+    void set_mutate_point(int mutate_point);
+    int get_mutate_point();
 	node* get_new_node(node_type t);
     void read_from_gml(string input_file);
-	int output_removed_edge_size();
-	vector<int> postOrderTraversal();
-	vector<int> mutatedPostOrderTraversal(vector<int> post_order);
+	void output_print_removed_edge_stats();
+	int output_int_removed_edge_size();
+    vector<int> return_post_order();
+	void postOrderTraversal();
+	void mutatedPostOrderTraversal(vector<int> post_order, int mutate_point);
 	void guidedPostOrderTraversal(vector<int> post_order);
     void set_post_order(vector<int> post_order);
 	void sort_adj_list();
@@ -182,8 +202,9 @@ private:
 	vector<pair<node*, node*> > _edge_list; // Edges in DFS-tree. These edges must be contained in the maximal planar subgraph that we found.
 	vector<node*> _post_order_list; //The sorted version (increasing with post-order-index) of _node_list.
 	vector<pair<node*, node*> > _back_edge_list; // Edges other than that in DFS-tree. (The first node's index is higher than the second's.)
-	vector<bool> _is_back_edge_eliminate; //Record that if the back-edge has been eliminated or not.
+	vector<back_edge_type> _is_back_edge_eliminate; //Record that if the back-edge has been eliminated or not.
 	vector<node*> _new_node_list; //Newly added nodes.
+    int _mutate_point; // store the mutate_point
 };
 
 #endif

deferred_planarity_test/makefile

@@ -31,4 +31,4 @@ $(BIN_DIR) $(OBJ_DIR):
 
 .PHONY: clean
 clean:
-	rm -r $(BIN_DIR) $(OBJ_DIR)
+	rm -r $(OBJ_DIR)

deferred_planarity_test/src/main.cpp

@@ -11,51 +11,57 @@
 #include <iterator>
 #include <random>
 #include <vector>
- 
 #include <ogdf/fileformats/GraphIO.h>
-#define START_TEMP 100
 
 using namespace std;
 
-int compute_removed_edge_size(string input_file, vector<int> post_order);
 
+// functions defined in mps_test.cpp
+int compute_removed_edge_size(string input_file, vector<int> post_order, int mutate_point);
+void print_removed_edge_stats(string input_file, vector<int> post_order, int mutate_point);
 vector<int> generate_post_order(string input_file);
-vector<int> generate_mutated_post_order(string input_file, vector<int> post_order);
+vector<int> generate_guided_post_order(string input_file, vector<int> post_order);
+vector<int> generate_mutated_post_order_at_x(string input_file, vector<int> post_order, int mutate_point);
 
-double temp_decay(int k, int k_max) {
-    return 1.0 - ((k + 1.0) / (k_max));
+
+void vector_printer(vector<int> state) {
+    for (int i = 0; i < state.size(); ++i) {
+        std::cout << state[i] << ",";
+    }
+    std::cout << std::endl;
 }
 
-vector<int> sa_solve(string input_file, int k_max) {
 
-    // create sampling function
-    std::random_device rd;
-    std::mt19937 rng(rd());
-    std::uniform_real_distribution<> distribution(0.0, 1.0);
 
+void measure_removed_edges(string input_file, int k_max, int mutate_point) {
     // generate first state
     vector<int> state_old = generate_post_order(input_file);
     vector<int> state_new;
-    int e_old = compute_removed_edge_size(input_file, state_old);
-    int e_new = 0;
-    int delta = 0;
-    // initialize terms
-    double temp;
+
+
+    int removed_old = compute_removed_edge_size(input_file, state_old, mutate_point);
+    int removed_new;
 
     for (int k = 0; k < k_max; ++k) {
-        temp = START_TEMP * temp_decay(k, k_max);
+        std::cout << "first post order" << std::endl;
+        vector_printer(state_old);
 
-        state_new = generate_mutated_post_order(input_file, state_old);
-        e_new = compute_removed_edge_size(input_file, state_new);
-        delta = e_new - e_old;
+        // run mutation on canonical representation directly
+        state_new = generate_mutated_post_order_at_x(input_file, state_old, mutate_point);
+        // rotate output of mutated state to canonical representation
+        state_new = generate_guided_post_order(input_file, state_new);
+        // tree produced should be the same as tree from mutation
+        removed_new = compute_removed_edge_size(input_file, state_new, mutate_point);
+
+        std::cout << "mutated post order" << std::endl;
+        vector_printer(state_new);
+
+        
+        // std::cout << "removed edges in old: " << removed_old << std::endl;
+        // std::cout << "removed edges in new: " << removed_new << std::endl;
+        print_removed_edge_stats(input_file, state_new, mutate_point);
 
-        if (std::exp( -(delta) / temp) > distribution(rng)) {
-            state_old = state_new; 
-            e_old = e_new;
     }
-    }
-
-    return state_old;
 
 }
 
@@ -78,16 +84,10 @@ int get_graph_size(string input_file) {
 int main(int argc, char* argv[]) {
     string input_file = argv[1];
     int k_max = std::stoi(argv[2]);
+    int mutate_point = std::stoi(argv[3]);
 
     // generate order here
-    vector<int> post_order = sa_solve(input_file, k_max);
-
-    // std::copy(post_order.begin(), post_order.end(), std::ostream_iterator<int>(std::cout, " "));
-    // std::cout << std::endl;
-
-    // print order
-    int removed_edges = compute_removed_edge_size(input_file, post_order);
-    std::cout << "Number of removed edges: " << removed_edges << std::endl;
+    measure_removed_edges(input_file, k_max, mutate_point);
 
 	return 0;
 }

deferred_planarity_test/src/mps.cpp

@@ -3,6 +3,7 @@
 //-----------------------------------------------------------------------------------
 
 #include "mps.h"
+#include <cassert>
 
 // constructor can be made empty
 maximal_planar_subgraph_finder::maximal_planar_subgraph_finder() {}
@@ -19,8 +20,29 @@ maximal_planar_subgraph_finder::get_new_node(node_type t) {
 	return _new_node_list[_new_node_list.size()-1];
 }
 
-//Determine the post-order-list by a DFS-traversal.
+// setter and getter for mutate_point
+void
+maximal_planar_subgraph_finder::set_mutate_point(int mutate_point) {
+    _mutate_point = mutate_point;
+}
+
+int
+maximal_planar_subgraph_finder::get_mutate_point() {
+    return _mutate_point;
+}
+
 vector<int>
+maximal_planar_subgraph_finder::return_post_order() {
+    vector<int> post_order;
+    for (int i = 0; i < _post_order_list.size(); ++i) {
+        post_order.push_back(_post_order_list[i]->node_id());
+    }
+    return post_order;
+}
+
+
+//Determine the post-order-list by a DFS-traversal.
+void
 maximal_planar_subgraph_finder::postOrderTraversal() {
 	node::init_mark();
 	int postOrderID = 0;
@@ -29,12 +51,6 @@ maximal_planar_subgraph_finder::postOrderTraversal() {
 			_node_list[i]->DFS_visit(_post_order_list, postOrderID);
 		}
 	}
-
-    vector<int> post_order;
-    for (int i = 0; i < _post_order_list.size(); ++i) {
-        post_order.push_back(_post_order_list[i]->node_id());
-    }
-    return post_order;
 }
 
 
@@ -72,37 +88,27 @@ maximal_planar_subgraph_finder::guidedPostOrderTraversal(vector<int> post_order)
 }
 
 //Determine the post-order-list by a DFS-traversal.
-vector<int> 
-maximal_planar_subgraph_finder::mutatedPostOrderTraversal(vector<int> post_order) {
+void
+maximal_planar_subgraph_finder::mutatedPostOrderTraversal(vector<int> post_order, int mutate_point) {
 	node::init_mark();
 
+    // reverse post_order because reversed post_order is the traversal of the DFS tree from the starting node
     vector<int> rev_post_order;
     for (int i = post_order.size() - 1; i >= 0; --i) {
         rev_post_order.push_back(post_order[i]);
     }
 	int postOrderID = 0;
+    int traversal_index = 0;
 
     // introduce random selection
-    std::random_device rd;
-    std::mt19937 rng(rd());
     // Define the range [0, n]
     int n = _node_list.size() - 1;  // Change 'n' to your desired upper bound
-    // Create a uniform distribution for the range [0, n]
-    std::uniform_int_distribution<int> distribution(0, n);
-    // Generate a random number between 0 and n (inclusive)
-    int mutate_point = distribution(rng);
-    // std::cout << "the mutate point: " << mutate_point << std::endl;
+    // assert(mutate_point < n);
 
     // set loop variables
     int start = rev_post_order[0];
     int i = start;
 
-    // if mutate_point = 0
-    if (mutate_point == 0) {
-        // generate another point
-        start = distribution(rng); 
-    }
-
 
     int end_condition = _node_list.size();
     while (true)
@@ -111,27 +117,17 @@ maximal_planar_subgraph_finder::mutatedPostOrderTraversal(vector<int> post_order
         {
             if (!_node_list[i]->is_marked())
             {
-                _node_list[i]->mutated_DFS_visit(_post_order_list, _node_list, postOrderID, rev_post_order, mutate_point);
+                _node_list[i]->mutated_DFS_visit(_post_order_list, _node_list, postOrderID, traversal_index, rev_post_order, mutate_point);
             }
             break;
         }
         // std::cout << _node_list[i]->node_id() << ", " << !_node_list[i]->is_marked() << std::endl;
         if (!_node_list[i]->is_marked())
         {
-            _node_list[i]->mutated_DFS_visit(_post_order_list, _node_list, postOrderID, rev_post_order, mutate_point);
+            _node_list[i]->mutated_DFS_visit(_post_order_list, _node_list, postOrderID, traversal_index, rev_post_order, mutate_point);
         }
         i = (i + 1) % end_condition;
     }
-
-    vector<int> return_order;
-    for (int i = 0; i < _post_order_list.size(); ++i) {
-        return_order.push_back(_post_order_list[i]->node_id());
-    }
-
-    // we have to reverse the order as we add to list in the forward direction of recursion
-    // unlike that of previous methods where we add to list in the return direction of recursion
-    std::reverse(return_order.begin(), return_order.end());
-    return return_order;
 }
 
 
@@ -173,7 +169,7 @@ maximal_planar_subgraph_finder::determine_edges() {
 			if (_post_order_list[i]->adj(j)->post_order_index() > i) break;
 			if (_post_order_list[i]->adj(j)->get_1st_label() == i) continue;
 			_back_edge_list.push_back(pair<node*, node*> (_post_order_list[i], _post_order_list[i]->adj(j)));
-			_is_back_edge_eliminate.push_back(false);
+			_is_back_edge_eliminate.push_back(RETAINED);
 		}
 	}
 	for (int i = 0; i < _post_order_list.size(); ++i) {
@@ -184,14 +180,36 @@ maximal_planar_subgraph_finder::determine_edges() {
 //The main part of the whole algorithm: Back-edge-traversal
 void 
 maximal_planar_subgraph_finder::back_edge_traversal() {
-	node* i_node = 0;
-	node* current_node = 0;
+	node* i_node = nullptr;
+	node* current_node = nullptr;
+    int dfs_mutate_point = get_mutate_point();
+    int node_list_last_index = _node_list.size() - 1;
+    // dfs_mutate_point starts counting from the DFS head
+    // post_order starts from the last leaf of the DFS tree
+    // hence we start counting from the post_order last index
+    int post_order_mutate_point = node_list_last_index - dfs_mutate_point; 
+    // std::cout << "post_order_mutate_point: " << post_order_mutate_point << std::endl;
+    // back_edge first node is higher than the second
 	for (int i = 0; i < _back_edge_list.size(); ++i) {
+        // current node is the lower 
 		current_node = _back_edge_list[i].second;
 		i_node = _back_edge_list[i].first;
-		if (!back_edge_traversal(current_node, i_node->post_order_index())) _is_back_edge_eliminate[i] = true;
+        // back_edge_traversal returns true if it should be included
+        // false otherwise
+		if (!back_edge_traversal(current_node, i_node->post_order_index())) {
+            // if current_node is higher than post_order_mutate_point
+            // then it is the preserved section
+            if (current_node->post_order_index() > post_order_mutate_point) {
+                std::cout << "(" << current_node->node_id() << "[" << current_node->post_order_index() << "]"
+                << "," << i_node->node_id() << "[" << i_node->post_order_index() << "]" << ") ";
+                _is_back_edge_eliminate[i] = NON_MUTATED_REMOVE;
+            } else {
+                _is_back_edge_eliminate[i] = MUTATED_REMOVE;
             }
         } 
+	}
+    std::cout << std::endl;
+}
 
 //sub-function for the for-loop of back_edge_traversal().
 bool maximal_planar_subgraph_finder::back_edge_traversal(node* traverse_node, int index) {

deferred_planarity_test/src/mps_test.cpp

@@ -4,21 +4,29 @@
 
 #include "mps.h"
 #include <ogdf/fileformats/GraphIO.h>
+#include <algorithm>
+#include <vector>
+
 
 //-----------------------------------------------------------------------------------
 // Finding MPS
 //-----------------------------------------------------------------------------------
 
-// programs to call from main:
+// functions to call from main:
 
 int find_mps(string input_file) {
 	maximal_planar_subgraph_finder m;
 	return m.find_mps(input_file);
 }
 
-int compute_removed_edge_size(string input_file, vector<int> post_order) {
+int compute_removed_edge_size(string input_file, vector<int> post_order, int mutate_point) {
     maximal_planar_subgraph_finder m;
-    return m.compute_removed_edge_size(input_file, post_order);
+    return m.compute_removed_edge_size(input_file, post_order, mutate_point);
+}
+
+void print_removed_edge_stats(string input_file, vector<int> post_order, int mutate_point) {
+    maximal_planar_subgraph_finder m;
+    m.print_removed_edge_stats(input_file, post_order, mutate_point);
 }
 
 vector<int> generate_post_order(string input_file) {
@@ -26,13 +34,18 @@ vector<int> generate_post_order(string input_file) {
     return m.generate_post_order(input_file);
 }
 
-vector<int> generate_mutated_post_order(string input_file, vector<int> post_order) {
+vector<int> generate_guided_post_order(string input_file, vector<int> post_order) {
     maximal_planar_subgraph_finder m;
-    return m.generate_mutated_post_order(input_file, post_order);
+    return m.generate_guided_post_order(input_file, post_order);
+}
+
+vector<int> generate_mutated_post_order_at_x(string input_file, vector<int> post_order, int mutate_point) {
+    maximal_planar_subgraph_finder m;
+    return m.generate_mutated_post_order(input_file, post_order, mutate_point);
 }
 
 
-// ---------
+// immediate functions called by functions called from main
 
 int maximal_planar_subgraph_finder::find_mps(string input_file) {
 	read_from_gml(input_file);
@@ -40,45 +53,59 @@ int maximal_planar_subgraph_finder::find_mps(string input_file) {
 	sort_adj_list();
 	determine_edges();
 	back_edge_traversal();
-	return output_removed_edge_size();
+	return output_int_removed_edge_size();
 }
 
 vector<int> maximal_planar_subgraph_finder::generate_post_order(string input_file) {
     read_from_gml(input_file);
-    return postOrderTraversal();
+    set_mutate_point(INT_MAX); // essentially removed mutate_point
+    postOrderTraversal();
+    return return_post_order();
 }
 
-vector<int> maximal_planar_subgraph_finder::generate_mutated_post_order(string input_file, vector<int> post_order) {
-    read_from_gml(input_file);
-    return mutatedPostOrderTraversal(post_order);
-}
-
-
-int maximal_planar_subgraph_finder::compute_removed_edge_size(string input_file, vector<int> post_order) {
+vector<int> maximal_planar_subgraph_finder::generate_guided_post_order(string input_file, vector<int> post_order) {
     read_from_gml(input_file);
+    set_mutate_point(INT_MAX); // essentially remove mutate point
     guidedPostOrderTraversal(post_order);
-
-    // let's reverse the order
-    std::reverse(_post_order_list.begin(), _post_order_list.end());
-    // then set post_order_index
-    for (int i = 0; i < _post_order_list.size(); ++i) {
-        _node_list[_post_order_list[i]->node_id()]->set_post_order_index(i);
+    return return_post_order();
 }
 
-    // std::cout << "check order of duplicated traversal" << std::endl;
-    // for (int i = 0; i < _post_order_list.size(); ++i) {
-    //     std::cout << _post_order_list[i]->node_id() << " ";
-    // }
-    // std::cout << std::endl;
+
+vector<int> maximal_planar_subgraph_finder::generate_mutated_post_order(string input_file, vector<int> post_order, int mutate_point) {
+    read_from_gml(input_file);
+    set_mutate_point(INT_MAX);
+    mutatedPostOrderTraversal(post_order, mutate_point);
+    return return_post_order();
+}
+
+
+int maximal_planar_subgraph_finder::compute_removed_edge_size(string input_file, vector<int> post_order, int mutate_point) {
+	read_from_gml(input_file);
+    set_mutate_point(mutate_point);
+    guidedPostOrderTraversal(post_order);
 
 	sort_adj_list();
 	determine_edges();
 	back_edge_traversal();
-	return output_removed_edge_size();
+	return output_int_removed_edge_size();
 }
 
+void maximal_planar_subgraph_finder::print_removed_edge_stats(string input_file, vector<int> post_order, int mutate_point) {
+	read_from_gml(input_file);
+    set_mutate_point(mutate_point);
+    guidedPostOrderTraversal(post_order);
+
+	sort_adj_list();
+	determine_edges();
+	back_edge_traversal();
+	output_print_removed_edge_stats();
+}
+
+
+
+
 //-----------------------------------------------------------------------------------
-// Imput, output
+// Input, output
 //-----------------------------------------------------------------------------------
 
 
@@ -97,6 +124,14 @@ void maximal_planar_subgraph_finder::read_from_gml(string input_file) {
 		_node_list[i]->set_id(i);
 	}
 
+    // vector<ogdf::edge> unique_edges;
+    // // we want to get unique edge only
+    // for (ogdf::edge e : G.edges) {
+    //     // Check if the edge is already in the array
+    //     if (std::find(unique_edges.begin(), unique_edges.end(), e) == unique_edges.end())
+    //         unique_edges.push_back(e);
+    // }
+
     // create edges
     for (ogdf::edge e : G.edges) {
         ogdf::node source = e->source();
@@ -109,10 +144,47 @@ void maximal_planar_subgraph_finder::read_from_gml(string input_file) {
 
 
 // count the number of removed edges
-int maximal_planar_subgraph_finder::output_removed_edge_size() {
+void maximal_planar_subgraph_finder::output_print_removed_edge_stats() {
+    int mutated_sum = 0;
+    int preserved_sum = 0;
+
+    vector<pair<node*, node*>> mutated_removed_edges;
+    vector<pair<node*, node*>> preserved_removed_edges;
+    
+    for (int i = 0; i < _back_edge_list.size(); ++i) {
+		if (_is_back_edge_eliminate[i] == MUTATED_REMOVE) {
+            mutated_removed_edges.push_back(_back_edge_list[i]);
+            ++mutated_sum; 
+        }
+		if (_is_back_edge_eliminate[i] == NON_MUTATED_REMOVE) {
+            preserved_removed_edges.push_back(_back_edge_list[i]);
+            ++preserved_sum; 
+        }
+    }
+
+    // print the edges
+    // std::cout << "mutated removed edges: " << std::endl;
+    // for (int i = 0; i < mutated_removed_edges.size(); ++i) {
+    //     std::cout << mutated_removed_edges[i].first->node_id() << ", " <<
+    //     mutated_removed_edges[i].second->node_id() << std::endl;
+    // }
+
+    // std::cout << "preserved removed edges: " << std::endl;
+    // for (int i = 0; i < preserved_removed_edges.size(); ++i) {
+    //     std::cout << preserved_removed_edges[i].first->node_id() << ", " <<
+    //     preserved_removed_edges[i].second->node_id() << std::endl;
+    // }
+
+    std::cout << "<- sum of removed edges -> " << std::endl;
+    std::cout << "mutated portion: " << mutated_sum << std::endl;
+    std::cout << "preserved portion: " << preserved_sum << std::endl;
+}
+
+int maximal_planar_subgraph_finder::output_int_removed_edge_size() {
     int sum = 0;
     for (int i = 0; i < _back_edge_list.size(); ++i) {
-		if (_is_back_edge_eliminate[i]) ++sum; 
+		if (_is_back_edge_eliminate[i] != RETAINED) ++sum; 
     }
+
     return sum;
 }

deferred_planarity_test/src/node.cpp

@@ -53,6 +53,8 @@ node* node::adj(int i) {return _adj_list[i];}
 
 void node::set_adj_list(vector<node*> vec) {_adj_list = vec;}
 
+// original DFS visit implementation
+// it just uses _adj_list directly as list of neighbors
 void node::DFS_visit(vector<node*> &dfsList, int &index) {
 	mark();
 	for (int i = 0; i < _adj_list.size(); ++i) {
@@ -61,104 +63,107 @@ void node::DFS_visit(vector<node*> &dfsList, int &index) {
 			_adj_list[i]->DFS_visit(dfsList, index);
 		}
 	}
+    // head recursion: function call before returning result
 	set_post_order_index(index);
 	dfsList.push_back(this);
 	++index;
 }
 
-
-void node::guided_DFS_visit(vector<node*> &dfsList, vector<node*> &node_list, int &index, vector<int> rev_post_order) {
+void node::guided_DFS_visit(vector<node *> &dfsList, 
+                            vector<node *> &node_list, 
+                            int &return_index, 
+                            vector<int> rev_post_order)
+{
     mark();
-    // you will want to sort the neighbor nodes by the order they appear in the rev_post_order
-    vector<node *> neighbor_list;
-    std::unordered_set<int> neighbor_set; 
+
+    // purpose of this block: create list of neighbors ordered in the order they appear in rev_post_order
+    // we want to select neighbors that match the rev_post_order at the specific traversal_index
 
     // create an unordered set to efficiently check for presence of an element
+    std::unordered_set<int> neighbor_set; 
     for (int i = 0; i < _adj_list.size(); ++i) {
         neighbor_set.insert(_adj_list[i]->node_id());
     }
-
     // when an element in rev_post_order is found in neighbor_set, we add that to neighbor_list
+    // this produces a neighbor_list that follows the order by which they occur in the rev_post_order
+    // it is ok if the neighbor was already visited before, 
+    // it would've been marked and will be subsequently ignored
+    vector<node *> neighbor_list;
     for (int i = 0; i < rev_post_order.size(); ++i) {
         if (neighbor_set.find(rev_post_order[i]) != neighbor_set.end()) {
             neighbor_list.push_back(node_list[rev_post_order[i]]);
         }
     }
 
-    // print the neighbors
-    // std::cout << "current index: " << this->node_id() << std::endl;
-    // for (int i = 0; i < neighbor_list.size(); ++i) {
-    //     std::cout << neighbor_list[i]->node_id() << " ";
-    // }
-    // std::cout << std::endl;
-
-	set_post_order_index(index);
-	dfsList.push_back(this);
-	++index;
-
 	for (int i = 0; i < neighbor_list.size(); ++i) {
 		if (!neighbor_list[i]->is_marked()) {
 			neighbor_list[i]->_parent = this;
-			neighbor_list[i]->guided_DFS_visit(dfsList, node_list, index, rev_post_order);
-		}
+			neighbor_list[i]->guided_DFS_visit(dfsList, node_list, return_index, rev_post_order);
 		}
 	}
 
+    // head recursion
+	set_post_order_index(return_index);
+	dfsList.push_back(this);
+	++return_index;
+}
 
-void node::mutated_DFS_visit(vector<node*> &dfsList, vector<node*> &node_list, int &index, vector<int> rev_post_order, int &mutate_point) {
+void node::mutated_DFS_visit(vector<node*> &dfsList, 
+                             vector<node*> &node_list, 
+                             int &return_index, 
+                             int &traversal_index, 
+                             vector<int> rev_post_order, 
+                             int mutate_point) {
 	mark();
-    // you will want to sort the neighbor nodes by the order they appear in the rev_post_order
-    vector<node *> neighbor_list;
-    std::unordered_set<int> neighbor_set; 
+
+    // purpose of this block: create list of neighbors ordered in the order they appear in rev_post_order
+    // we want to select neighbors that match the rev_post_order at the specific traversal_index
 
     // create an unordered set to efficiently check for presence of an element
+    std::unordered_set<int> neighbor_set; 
     for (int i = 0; i < _adj_list.size(); ++i) {
         neighbor_set.insert(_adj_list[i]->node_id());
     }
-
     // when an element in rev_post_order is found in neighbor_set, we add that to neighbor_list
+    // this produces a neighbor_list that follows the order by which they occur in the rev_post_order
+    // it is ok if the neighbor was already visited before, 
+    // it would've been marked and will be subsequently ignored
+    vector<node *> neighbor_list;
     for (int i = 0; i < rev_post_order.size(); ++i) {
         if (neighbor_set.find(rev_post_order[i]) != neighbor_set.end()) {
             neighbor_list.push_back(node_list[rev_post_order[i]]);
         }
     }
     
-    // print the neighbors
-    // std::cout << "current index: " << this->node_id() << std::endl;
-    // for (int i = 0; i < neighbor_list.size(); ++i) {
-    //     std::cout << neighbor_list[i]->node_id() << " ";
-    // }
-    // std::cout << std::endl;
 
-	set_post_order_index(index);
-	dfsList.push_back(this);
-	++index;
-
-    if (index - 1 == mutate_point) {
+    // introduce mutation at mutate_point
+    if (traversal_index == mutate_point) {
         // Create a random number generator and seed it
         // std::cout << "mutated at index: " << index - 1<< "and at mutate point: " << mutate_point << std::endl;
         std::random_device rd;
         std::mt19937 rng(rd());
+
         // Use std::shuffle to shuffle the elements in the vector
         std::shuffle(neighbor_list.begin(), neighbor_list.end(), rng);
-        // // print the neighbors
-        // std::cout << "order after mutation: " << std::endl;
-        // std::cout << "current index: " << this->node_id() << std::endl;
-        // for (int i = 0; i < neighbor_list.size(); ++i)
-        // {
-        //     std::cout << neighbor_list[i]->node_id() << " ";
-        // }
-        // std::cout << std::endl;
     }
 
+    // increment traversal index after checking
+    // next node will receive incremented index
+    traversal_index++;
+    
     for (int i = 0; i < neighbor_list.size(); ++i)
     {
         if (!neighbor_list[i]->is_marked())
         {
             neighbor_list[i]->_parent = this;
-            neighbor_list[i]->mutated_DFS_visit(dfsList, node_list, index, rev_post_order, mutate_point);
+            neighbor_list[i]->mutated_DFS_visit(dfsList, node_list, return_index, traversal_index, rev_post_order, mutate_point);
         }
     }
+
+    // head recursion like the initial dfs visit implementation
+    set_post_order_index(return_index);
+	dfsList.push_back(this);
+	++return_index;
 }