diff --git a/deferred_planarity_test/include/mps.h b/deferred_planarity_test/include/mps.h
index b1f788c..899e624 100644
--- a/deferred_planarity_test/include/mps.h
+++ b/deferred_planarity_test/include/mps.h
@@ -12,6 +12,7 @@
 #include <climits>
 #include <random>
 #include <algorithm>
+#include <unordered_map>
 #include <unordered_set>
 #include <ogdf/fileformats/GraphIO.h>
 
@@ -60,8 +61,7 @@ public:
     void guided_DFS_visit(vector<node *> &dfsList,
                           const vector<node *> &node_list,
                           int &return_index,
-                          const vector<int> &rev_post_order,
-                          int prev_node);
+                          const unordered_map<int, int> &node_id_to_pos);
     void mutated_DFS_visit(vector<node*> &dfsList, 
                            vector<node*> &node_list, 
                            int &index, 
@@ -70,7 +70,7 @@ public:
                            int mutate_point);
     
     // custom comparator function to sort nodes according to order in given vector
-    bool sortByOrder(const std::vector<int>& vec_order, node* a, node* b); 
+    bool sortByOrder(const std::unordered_map<int, int>& node_id_to_pos, node* a, node* b); 
 
 	//PARENT-CHILDREN
 	void set_parent(node* n) ;
diff --git a/deferred_planarity_test/src/mps.cpp b/deferred_planarity_test/src/mps.cpp
index 0c07fbd..bdeba63 100644
--- a/deferred_planarity_test/src/mps.cpp
+++ b/deferred_planarity_test/src/mps.cpp
@@ -3,7 +3,6 @@
 //-----------------------------------------------------------------------------------
 
 #include "mps.h"
-#include <iterator>
 
 // #define DEBUG
 
@@ -52,30 +51,39 @@ void
 maximal_planar_subgraph_finder::guidedPostOrderTraversal(vector<int> post_order) {
 	node::init_mark();
 
-    vector<int> rev_post_order;
+    // // implementation 1: pass reversed vector
+    // vector<int> rev_post_order;
+    // for (int i = post_order.size() - 1; i >= 0; --i) {
+    //    rev_post_order.push_back(post_order[i]);
+    // }
+    // int start = rev_post_order[0];
+
+
+    unordered_map<int, int> node_id_to_pos;
+    int j = 0;
+    // we flip the post_order vector around
     for (int i = post_order.size() - 1; i >= 0; --i) {
-        rev_post_order.push_back(post_order[i]);
+        node_id_to_pos[post_order[i]] = j++;
     }
 	int postOrderID = 0;
-
     int end_condition = _node_list.size();
-    int start = rev_post_order[0];
+    // we start from the end of the post_order, which is the root node
+    int start = post_order[post_order.size() - 1];
     int i = start;
     
-    int prev_node = INT_MAX;
     while (true)
     {
         if (((start > 0) && (i == (start - 1))) || ((start == 0 ) && (i == end_condition - 1)))
         {
             if (!_node_list[i]->is_marked())
             {
-                _node_list[i]->guided_DFS_visit(_post_order_list, _node_list, postOrderID, rev_post_order, prev_node);
+                _node_list[i]->guided_DFS_visit(_post_order_list, _node_list, postOrderID, node_id_to_pos);
             }
             break;
         }
         if (!_node_list[i]->is_marked())
         {
-            _node_list[i]->guided_DFS_visit(_post_order_list, _node_list, postOrderID, rev_post_order, prev_node);
+            _node_list[i]->guided_DFS_visit(_post_order_list, _node_list, postOrderID, node_id_to_pos);
         }
         i = (i + 1) % end_condition;
     }
diff --git a/deferred_planarity_test/src/mps_test.cpp b/deferred_planarity_test/src/mps_test.cpp
index 437570d..29d1819 100644
--- a/deferred_planarity_test/src/mps_test.cpp
+++ b/deferred_planarity_test/src/mps_test.cpp
@@ -9,7 +9,7 @@
 
 // #define DEBUG
 
-// #define TIME
+#define TIME
 
 //-----------------------------------------------------------------------------------
 // Finding MPS
diff --git a/deferred_planarity_test/src/node.cpp b/deferred_planarity_test/src/node.cpp
index 412d6eb..965285b 100644
--- a/deferred_planarity_test/src/node.cpp
+++ b/deferred_planarity_test/src/node.cpp
@@ -70,19 +70,19 @@ void node::DFS_visit(vector<node*> &dfsList, int &index) {
 }
 
 
-bool node::sortByOrder(const std::vector<int>& vec_order, node* a, node* b) {
-    auto itA = std::find(vec_order.begin(), vec_order.end(), a->node_id());
-    auto itB = std::find(vec_order.begin(), vec_order.end(), b->node_id());
+bool node::sortByOrder(const std::unordered_map<int, int>& node_id_to_pos, node* a, node* b) {
+    auto iter_a = node_id_to_pos.find(a->node_id());
+    auto iter_b = node_id_to_pos.find(b->node_id());
 
-    return (std::distance(vec_order.begin(), itA) < std::distance(vec_order.begin(), itB));
+    // second yields the position
+    return iter_a->second < iter_b->second;
 }
 
 
 void node::guided_DFS_visit(vector<node *> &dfsList, 
                             const vector<node *> &node_list, 
                             int &return_index, 
-                            const vector<int> &rev_post_order,
-                            int prev_node)
+                            const unordered_map<int, int> &node_id_to_pos)
 {
 
 	mark();
@@ -112,8 +112,8 @@ void node::guided_DFS_visit(vector<node *> &dfsList,
 
     // implementation 2: sort elements of _adj_list
     vector<node*> neighbor_list = _adj_list; 
-    std::sort(neighbor_list.begin(), neighbor_list.end(), [this, &rev_post_order](node* a, node* b) {
-        return sortByOrder(rev_post_order, a, b);
+    std::sort(neighbor_list.begin(), neighbor_list.end(), [this, &node_id_to_pos](node* a, node* b) {
+        return sortByOrder(node_id_to_pos, a, b);
     });
 
 
@@ -131,7 +131,7 @@ void node::guided_DFS_visit(vector<node *> &dfsList,
 	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, return_index, rev_post_order, this->node_id());
+			neighbor_list[i]->guided_DFS_visit(dfsList, node_list, return_index, node_id_to_pos);
 		}
 	}