diff --git a/gklearn/ged/median/median_graph_estimator.py b/gklearn/ged/median/median_graph_estimator.py
index 228c323..7cce7dd 100644
--- a/gklearn/ged/median/median_graph_estimator.py
+++ b/gklearn/ged/median/median_graph_estimator.py
@@ -15,7 +15,7 @@ import sys
 import networkx as nx
 
 
-class MedianGraphEstimator(object):
+class MedianGraphEstimator(object): # @todo: differ dummy_node from undifined node?
 	
 	def __init__(self, ged_env, constant_node_costs):
 		"""Constructor.
@@ -377,7 +377,7 @@ class MedianGraphEstimator(object):
 					
 			self.__best_init_sum_of_distances = min(self.__best_init_sum_of_distances, self.__sum_of_distances)
 			self.__ged_env.load_nx_graph(median, set_median_id)
-			print(self.__best_init_sum_of_distances)
+# 			print(self.__best_init_sum_of_distances)
 			
 			# Print information about current iteration.
 			if self.__print_to_stdout == 2:
@@ -400,7 +400,7 @@ class MedianGraphEstimator(object):
 				decreased_order = False
 				increased_order = False
 				
-				# Update the median. # @todo!!!!!!!!!!!!!!!!!!!!!!
+				# Update the median.
 				median_modified = self.__update_median(graphs, median)
 				if self.__update_order:
 					if not median_modified or self.__itrs[median_pos] == 0:
@@ -434,6 +434,7 @@ class MedianGraphEstimator(object):
 				# Compute induced costs of the old node maps w.r.t. the updated median.
 				for graph_id in graph_ids:
 # 					print(self.__node_maps_from_median[graph_id].induced_cost())
+# 					xxx = self.__node_maps_from_median[graph_id]					   
 					self.__ged_env.compute_induced_cost(gen_median_id, graph_id, self.__node_maps_from_median[graph_id])
 #					print('---------------------------------------')
 # 					print(self.__node_maps_from_median[graph_id].induced_cost())
@@ -444,7 +445,7 @@ class MedianGraphEstimator(object):
 					print('done.')					
 					
 				# Update the node maps.
-				node_maps_modified = self.__update_node_maps() # @todo
+				node_maps_modified = self.__update_node_maps()
 
 				# Update the order of the median if no improvement can be found with the current order.
 				
@@ -592,6 +593,44 @@ class MedianGraphEstimator(object):
 		if state == 'converged':
 			return self.__converged_sum_of_distances
 		return self.__sum_of_distances
+
+
+	def get_runtime(self, state):
+		if not self.__median_available():
+			raise Exception('No median has been computed. Call run() before calling get_runtime().')
+		if state == AlgorithmState.INITIALIZED:
+			return self.__runtime_initialized
+		if state == AlgorithmState.CONVERGED:
+			return self.__runtime_converged
+		return self.__runtime
+	
+
+	def get_num_itrs(self):
+		if not self.__median_available():
+			raise Exception('No median has been computed. Call run() before calling get_num_itrs().')
+		return self.__itrs
+
+
+	def get_num_times_order_decreased(self):
+		if not self.__median_available():
+			raise Exception('No median has been computed. Call run() before calling get_num_times_order_decreased().')
+		return self.__num_decrease_order		
+	
+	
+	def get_num_times_order_increased(self):
+		if not self.__median_available():
+			raise Exception('No median has been computed. Call run() before calling get_num_times_order_increased().')
+		return self.__num_increase_order		
+	
+	
+	def get_num_converged_descents(self):
+		if not self.__median_available():
+			raise Exception('No median has been computed. Call run() before calling get_num_converged_descents().')
+		return self.__num_converged_descents
+	
+	
+	def get_ged_env(self):
+		return self.__ged_env
 	
 	
 	def __set_default_options(self):
@@ -814,7 +853,7 @@ class MedianGraphEstimator(object):
 		decreased_order = False
 		
 		# Decrease the order as long as the best deletion delta is negative.
-		while self.__compute_best_deletion_delta(graphs, median, id_deleted_node) < -self.__epsilon: # @todo
+		while self.__compute_best_deletion_delta(graphs, median, id_deleted_node) < -self.__epsilon:
 			decreased_order = True
 			median = self.__delete_node_from_median(id_deleted_node[0], median)
 			
@@ -896,7 +935,7 @@ class MedianGraphEstimator(object):
 		increased_order = False
 		
 		# Increase the order as long as the best insertion delta is negative.
-		while self.__compute_best_insertion_delta(graphs, best_config, best_label) > - self.__epsilon:
+		while self.__compute_best_insertion_delta(graphs, best_config, best_label) < - self.__epsilon: # @todo
 			increased_order = True
 			self.__add_node_to_median(best_config, best_label, median)
 			
diff --git a/gklearn/ged/median/test_median_graph_estimator.py b/gklearn/ged/median/test_median_graph_estimator.py
index 48304a8..cbfeefb 100644
--- a/gklearn/ged/median/test_median_graph_estimator.py
+++ b/gklearn/ged/median/test_median_graph_estimator.py
@@ -155,5 +155,5 @@ def test_median_graph_estimator_symb():
 
 
 if __name__ == '__main__':
- 	set_median, gen_median = test_median_graph_estimator()
-# 	set_median, gen_median = test_median_graph_estimator_symb()
\ No newline at end of file
+ 	# set_median, gen_median = test_median_graph_estimator()
+ 	set_median, gen_median = test_median_graph_estimator_symb()
\ No newline at end of file
diff --git a/gklearn/gedlib/gedlibpy.cpp b/gklearn/gedlib/gedlibpy.cpp
index c755bf2..58aa1fd 100644
--- a/gklearn/gedlib/gedlibpy.cpp
+++ b/gklearn/gedlib/gedlibpy.cpp
@@ -1542,6 +1542,14 @@ static CYTHON_INLINE PyObject* __Pyx_dict_iterator(PyObject* dict, int is_dict,
 static CYTHON_INLINE int __Pyx_dict_iter_next(PyObject* dict_or_iter, Py_ssize_t orig_length, Py_ssize_t* ppos,
                                               PyObject** pkey, PyObject** pvalue, PyObject** pitem, int is_dict);
 
+/* PyIntBinop.proto */
+#if !CYTHON_COMPILING_IN_PYPY
+static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check);
+#else
+#define __Pyx_PyInt_AddObjC(op1, op2, intval, inplace, zerodivision_check)\
+    (inplace ? PyNumber_InPlaceAdd(op1, op2) : PyNumber_Add(op1, op2))
+#endif
+
 /* PyObjectSetAttrStr.proto */
 #if CYTHON_USE_TYPE_SLOTS
 #define __Pyx_PyObject_DelAttrStr(o,n) __Pyx_PyObject_SetAttrStr(o, n, NULL)
@@ -2173,6 +2181,8 @@ static std::vector<std::vector<double> >  __pyx_convert_vector_from_py_std_3a__3
 static PyObject *__pyx_convert_vector_to_py_double(const std::vector<double>  &); /*proto*/
 static PyObject *__pyx_convert_vector_to_py_std_3a__3a_vector_3c_double_3e___(const std::vector<std::vector<double> >  &); /*proto*/
 static std::vector<std::map<std::string,std::string> >  __pyx_convert_vector_from_py_std_3a__3a_map_3c_std_3a__3a_string_2c_std_3a__3a_string_3e___(PyObject *); /*proto*/
+static std::pair<size_t,size_t>  __pyx_convert_pair_from_py_size_t__and_size_t(PyObject *); /*proto*/
+static std::vector<std::pair<size_t,size_t> >  __pyx_convert_vector_from_py_std_3a__3a_pair_3c_size_t_2c_size_t_3e___(PyObject *); /*proto*/
 #define __Pyx_MODULE_NAME "gedlibpy"
 extern int __pyx_module_is_main_gedlibpy;
 int __pyx_module_is_main_gedlibpy = 0;
@@ -2180,6 +2190,7 @@ int __pyx_module_is_main_gedlibpy = 0;
 /* Implementation of 'gedlibpy' */
 static PyObject *__pyx_builtin_range;
 static PyObject *__pyx_builtin_print;
+static PyObject *__pyx_builtin_enumerate;
 static PyObject *__pyx_builtin_TypeError;
 static PyObject *__pyx_builtin_ValueError;
 static PyObject *__pyx_builtin_RuntimeError;
@@ -2267,6 +2278,7 @@ static const char __pyx_k_adj_lists[] = "adj_lists";
 static const char __pyx_k_edge_list[] = "edge_list";
 static const char __pyx_k_edge_type[] = "edge_type";
 static const char __pyx_k_edit_cost[] = "edit_cost";
+static const char __pyx_k_enumerate[] = "enumerate";
 static const char __pyx_k_graph_ids[] = "graph_ids";
 static const char __pyx_k_iteritems[] = "iteritems";
 static const char __pyx_k_map_edges[] = "map_edges";
@@ -2285,6 +2297,7 @@ static const char __pyx_k_ImportError[] = "ImportError";
 static const char __pyx_k_LoadLibrary[] = "LoadLibrary";
 static const char __pyx_k_MemoryError[] = "MemoryError";
 static const char __pyx_k_MethodError[] = "MethodError";
+static const char __pyx_k_as_relation[] = "as_relation";
 static const char __pyx_k_clear_graph[] = "clear_graph";
 static const char __pyx_k_graph_class[] = "graph_class";
 static const char __pyx_k_init_method[] = "init_method";
@@ -2412,6 +2425,7 @@ static PyObject *__pyx_n_s_add_node;
 static PyObject *__pyx_n_s_add_nx_graph;
 static PyObject *__pyx_n_s_adj_lists;
 static PyObject *__pyx_n_s_adj_matrix;
+static PyObject *__pyx_n_s_as_relation;
 static PyObject *__pyx_n_s_cdll;
 static PyObject *__pyx_n_s_classe;
 static PyObject *__pyx_n_s_classes;
@@ -2435,6 +2449,7 @@ static PyObject *__pyx_n_s_edit_cost;
 static PyObject *__pyx_n_s_edit_cost_constant;
 static PyObject *__pyx_n_s_encode;
 static PyObject *__pyx_n_s_encode_your_map;
+static PyObject *__pyx_n_s_enumerate;
 static PyObject *__pyx_n_s_file;
 static PyObject *__pyx_n_s_g;
 static PyObject *__pyx_n_s_g1;
@@ -2630,6 +2645,7 @@ static int __pyx_pf_7cpython_5array_5array___getbuffer__(arrayobject *__pyx_v_se
 static void __pyx_pf_7cpython_5array_5array_2__releasebuffer__(CYTHON_UNUSED arrayobject *__pyx_v_self, Py_buffer *__pyx_v_info); /* proto */
 static PyObject *__pyx_tp_new_8gedlibpy_GEDEnv(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
 static PyObject *__pyx_int_0;
+static PyObject *__pyx_int_1;
 static PyObject *__pyx_k__2;
 static PyObject *__pyx_k__3;
 static PyObject *__pyx_tuple__4;
@@ -14317,63 +14333,259 @@ static PyObject *__pyx_pw_8gedlibpy_6GEDEnv_127compute_induced_cost(PyObject *__
 }
 
 static PyObject *__pyx_pf_8gedlibpy_6GEDEnv_126compute_induced_cost(struct __pyx_obj_8gedlibpy_GEDEnv *__pyx_v_self, PyObject *__pyx_v_g_id, PyObject *__pyx_v_h_id, PyObject *__pyx_v_node_map) {
+  PyObject *__pyx_v_relation = NULL;
+  PyObject *__pyx_v_dummy_node = NULL;
+  PyObject *__pyx_v_i = NULL;
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+  PyObject *__pyx_v_val1 = NULL;
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   double __pyx_v_induced_cost;
   PyObject *__pyx_r = NULL;
   __Pyx_RefNannyDeclarations
-  size_t __pyx_t_1;
-  size_t __pyx_t_2;
-  double __pyx_t_3;
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   __Pyx_RefNannySetupContext("compute_induced_cost", 0);
 
   /* "gedlibpy.pyx":1359
  * 		None.
  * 		"""
- * 		induced_cost = self.c_env.computeInducedCost(g_id, h_id)             # <<<<<<<<<<<<<<
+ * 		relation = []             # <<<<<<<<<<<<<<
+ * 		node_map.as_relation(relation)
+ * # 		print(relation)
+ */
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+  /* "gedlibpy.pyx":1360
+ * 		"""
+ * 		relation = []
+ * 		node_map.as_relation(relation)             # <<<<<<<<<<<<<<
+ * # 		print(relation)
+ * 		dummy_node = get_dummy_node()
+ */
+  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_node_map, __pyx_n_s_as_relation); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1360, __pyx_L1_error)
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+ * 		node_map.as_relation(relation)
+ * # 		print(relation)
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+ * # 		print(dummy_node)
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+ * 		dummy_node = get_dummy_node()
+ * # 		print(dummy_node)
+ * 		for i, val in enumerate(relation):             # <<<<<<<<<<<<<<
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+ * 			val2 = dummy_node if val[1] == np.inf else val[1]
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+ * 			val2 = dummy_node if val[1] == np.inf else val[1]
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+ * 		for i, val in enumerate(relation):
+ * 			val1 = dummy_node if val[0] == np.inf else val[0]
+ * 			val2 = dummy_node if val[1] == np.inf else val[1]             # <<<<<<<<<<<<<<
+ * 			relation[i] = tuple((val1, val2))
+ * # 		print(relation)
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-  __Pyx_GetModuleGlobalName(__pyx_t_5, __pyx_n_s_Error); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 1417, __pyx_L1_error)
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-  /* "gedlibpy.pyx":1438
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  * #########################################
  * 
  * def encode_your_map(map_u):             # <<<<<<<<<<<<<<
  * 	"""
  * 		Encodes Python unicode strings in dictionnary `map` to utf-8 byte strings for C++ functions.
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-  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_8gedlibpy_9encode_your_map, NULL, __pyx_n_s_gedlibpy); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1438, __pyx_L1_error)
+  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_8gedlibpy_9encode_your_map, NULL, __pyx_n_s_gedlibpy); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1448, __pyx_L1_error)
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-  if (PyDict_SetItem(__pyx_d, __pyx_n_s_encode_your_map, __pyx_t_1) < 0) __PYX_ERR(0, 1438, __pyx_L1_error)
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-  /* "gedlibpy.pyx":1456
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  * 
  * 
  * def decode_your_map(map_b):             # <<<<<<<<<<<<<<
  * 	"""
  * 		Decodes utf-8 byte strings in `map` from C++ functions to Python unicode strings.
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+  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_8gedlibpy_11decode_your_map, NULL, __pyx_n_s_gedlibpy); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1466, __pyx_L1_error)
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-  if (PyDict_SetItem(__pyx_d, __pyx_n_s_decode_your_map, __pyx_t_1) < 0) __PYX_ERR(0, 1456, __pyx_L1_error)
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-  /* "gedlibpy.pyx":1474
+  /* "gedlibpy.pyx":1484
  * 
  * 
  * def decode_graph_edges(map_edge_b):             # <<<<<<<<<<<<<<
  * 	"""
  * 	Decode utf-8 byte strings in graph edges `map` from C++ functions to Python unicode strings.
  */
-  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_8gedlibpy_13decode_graph_edges, NULL, __pyx_n_s_gedlibpy); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1474, __pyx_L1_error)
+  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_8gedlibpy_13decode_graph_edges, NULL, __pyx_n_s_gedlibpy); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1484, __pyx_L1_error)
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-  if (PyDict_SetItem(__pyx_d, __pyx_n_s_decode_graph_edges, __pyx_t_1) < 0) __PYX_ERR(0, 1474, __pyx_L1_error)
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   /* "gedlibpy.pyx":1
@@ -21935,8 +22389,8 @@ if (!__Pyx_RefNanny) {
 
   /* "vector.from_py":45
  * 
- * @cname("__pyx_convert_vector_from_py_std_3a__3a_map_3c_std_3a__3a_string_2c_std_3a__3a_string_3e___")
- * cdef vector[X] __pyx_convert_vector_from_py_std_3a__3a_map_3c_std_3a__3a_string_2c_std_3a__3a_string_3e___(object o) except *:             # <<<<<<<<<<<<<<
+ * @cname("__pyx_convert_vector_from_py_std_3a__3a_pair_3c_size_t_2c_size_t_3e___")
+ * cdef vector[X] __pyx_convert_vector_from_py_std_3a__3a_pair_3c_size_t_2c_size_t_3e___(object o) except *:             # <<<<<<<<<<<<<<
  *     cdef vector[X] v
  *     for item in o:
  */
@@ -23210,6 +23664,130 @@ static CYTHON_INLINE int __Pyx_dict_iter_next(
     return 1;
 }
 
+/* PyIntBinop */
+#if !CYTHON_COMPILING_IN_PYPY
+static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, int inplace, int zerodivision_check) {
+    (void)inplace;
+    (void)zerodivision_check;
+    #if PY_MAJOR_VERSION < 3
+    if (likely(PyInt_CheckExact(op1))) {
+        const long b = intval;
+        long x;
+        long a = PyInt_AS_LONG(op1);
+            x = (long)((unsigned long)a + b);
+            if (likely((x^a) >= 0 || (x^b) >= 0))
+                return PyInt_FromLong(x);
+            return PyLong_Type.tp_as_number->nb_add(op1, op2);
+    }
+    #endif
+    #if CYTHON_USE_PYLONG_INTERNALS
+    if (likely(PyLong_CheckExact(op1))) {
+        const long b = intval;
+        long a, x;
+#ifdef HAVE_LONG_LONG
+        const PY_LONG_LONG llb = intval;
+        PY_LONG_LONG lla, llx;
+#endif
+        const digit* digits = ((PyLongObject*)op1)->ob_digit;
+        const Py_ssize_t size = Py_SIZE(op1);
+        if (likely(__Pyx_sst_abs(size) <= 1)) {
+            a = likely(size) ? digits[0] : 0;
+            if (size == -1) a = -a;
+        } else {
+            switch (size) {
+                case -2:
+                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
+                        a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
+                        break;
+#ifdef HAVE_LONG_LONG
+                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
+                        lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
+                        goto long_long;
+#endif
+                    }
+                    CYTHON_FALLTHROUGH;
+                case 2:
+                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
+                        a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
+                        break;
+#ifdef HAVE_LONG_LONG
+                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
+                        lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
+                        goto long_long;
+#endif
+                    }
+                    CYTHON_FALLTHROUGH;
+                case -3:
+                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
+                        a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
+                        break;
+#ifdef HAVE_LONG_LONG
+                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
+                        lla = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
+                        goto long_long;
+#endif
+                    }
+                    CYTHON_FALLTHROUGH;
+                case 3:
+                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
+                        a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
+                        break;
+#ifdef HAVE_LONG_LONG
+                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
+                        lla = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
+                        goto long_long;
+#endif
+                    }
+                    CYTHON_FALLTHROUGH;
+                case -4:
+                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
+                        a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
+                        break;
+#ifdef HAVE_LONG_LONG
+                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
+                        lla = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
+                        goto long_long;
+#endif
+                    }
+                    CYTHON_FALLTHROUGH;
+                case 4:
+                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
+                        a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
+                        break;
+#ifdef HAVE_LONG_LONG
+                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
+                        lla = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
+                        goto long_long;
+#endif
+                    }
+                    CYTHON_FALLTHROUGH;
+                default: return PyLong_Type.tp_as_number->nb_add(op1, op2);
+            }
+        }
+                x = a + b;
+            return PyLong_FromLong(x);
+#ifdef HAVE_LONG_LONG
+        long_long:
+                llx = lla + llb;
+            return PyLong_FromLongLong(llx);
+#endif
+        
+        
+    }
+    #endif
+    if (PyFloat_CheckExact(op1)) {
+        const long b = intval;
+        double a = PyFloat_AS_DOUBLE(op1);
+            double result;
+            PyFPE_START_PROTECT("add", return NULL)
+            result = ((double)a) + (double)b;
+            PyFPE_END_PROTECT(result)
+            return PyFloat_FromDouble(result);
+    }
+    return (inplace ? PyNumber_InPlaceAdd : PyNumber_Add)(op1, op2);
+}
+#endif
+
 /* PyObjectSetAttrStr */
 #if CYTHON_USE_TYPE_SLOTS
 static CYTHON_INLINE int __Pyx_PyObject_SetAttrStr(PyObject* obj, PyObject* attr_name, PyObject* value) {
diff --git a/gklearn/gedlib/gedlibpy.cpython-36m-x86_64-linux-gnu.so b/gklearn/gedlib/gedlibpy.cpython-36m-x86_64-linux-gnu.so
index eab13a8..94b9401 100644
Binary files a/gklearn/gedlib/gedlibpy.cpython-36m-x86_64-linux-gnu.so and b/gklearn/gedlib/gedlibpy.cpython-36m-x86_64-linux-gnu.so differ
diff --git a/gklearn/gedlib/gedlibpy.pyx b/gklearn/gedlib/gedlibpy.pyx
index 2b997b7..54f24b0 100644
--- a/gklearn/gedlib/gedlibpy.pyx
+++ b/gklearn/gedlib/gedlibpy.pyx
@@ -105,7 +105,7 @@ cdef extern from "src/GedLibBind.hpp" namespace "pyged":
 		map[string, string] getMedianEdgeLabel(vector[map[string, string]] & edge_labels) except +
 		string getInitType() except +
 # 		double getNodeCost(size_t label1, size_t label2) except +
-		double computeInducedCost(size_t g_id, size_t h_id) except +
+		double computeInducedCost(size_t g_id, size_t h_id, vector[pair[size_t,size_t]]) except +
 		
 		
 #############################
@@ -1356,7 +1356,17 @@ cdef class GEDEnv:
 		-------
 		None.		
 		"""
-		induced_cost = self.c_env.computeInducedCost(g_id, h_id)
+		relation = []
+		node_map.as_relation(relation)
+# 		print(relation)
+		dummy_node = get_dummy_node()
+# 		print(dummy_node)
+		for i, val in enumerate(relation):
+			val1 = dummy_node if val[0] == np.inf else val[0]
+			val2 = dummy_node if val[1] == np.inf else val[1]
+			relation[i] = tuple((val1, val2))
+# 		print(relation)
+		induced_cost = self.c_env.computeInducedCost(g_id, h_id, relation)
 		node_map.set_induced_cost(induced_cost)
 
 	
diff --git a/gklearn/gedlib/src/GedLibBind.hpp b/gklearn/gedlib/src/GedLibBind.hpp
index bccf75a..63e0db3 100644
--- a/gklearn/gedlib/src/GedLibBind.hpp
+++ b/gklearn/gedlib/src/GedLibBind.hpp
@@ -477,7 +477,7 @@ public:
 	 * @param[in] h_id ID of input graph.
      * @return Computed induced cost.
 	 */
-	double computeInducedCost(std::size_t g_id, std::size_t h_id) const;
+	double computeInducedCost(std::size_t g_id, std::size_t h_id, std::vector<pair<std::size_t, std::size_t>> relation) const;
 
     // /*!
 	//  * @brief Returns node relabeling, insertion, or deletion cost.
diff --git a/gklearn/gedlib/src/GedLibBind.ipp b/gklearn/gedlib/src/GedLibBind.ipp
index 9335869..2928e0b 100644
--- a/gklearn/gedlib/src/GedLibBind.ipp
+++ b/gklearn/gedlib/src/GedLibBind.ipp
@@ -610,13 +610,38 @@ std::string PyGEDEnv::getInitType() const {
 	return initOptionsToString(env_->get_init_type());
 }
 
-double PyGEDEnv::computeInducedCost(std::size_t g_id, std::size_t h_id) const {
-	ged::NodeMap node_map = env_->get_node_map(g_id, h_id);
+double PyGEDEnv::computeInducedCost(std::size_t g_id, std::size_t h_id, std::vector<pair<std::size_t, std::size_t>> relation) const {
+	ged::NodeMap node_map = ged::NodeMap(env_->get_num_nodes(g_id), env_->get_num_nodes(h_id));
+	for (const auto & assignment : relation) {
+		node_map.add_assignment(assignment.first, assignment.second);
+		// std::cout << assignment.first << assignment.second << endl;
+	}
+	const std::vector<ged::GEDGraph::NodeID> forward_map = node_map.get_forward_map();
+	for (std::size_t i{0}; i < node_map.num_source_nodes(); i++) {
+		if (forward_map.at(i) == ged::GEDGraph::undefined_node()) {
+			node_map.add_assignment(i, ged::GEDGraph::dummy_node());
+		}
+	}
+	const std::vector<ged::GEDGraph::NodeID> backward_map = node_map.get_backward_map();
+	for (std::size_t i{0}; i < node_map.num_target_nodes(); i++) {
+		if (backward_map.at(i) == ged::GEDGraph::undefined_node()) {
+			node_map.add_assignment(ged::GEDGraph::dummy_node(), i);
+		}
+	}
+	// for (auto & map : node_map.get_forward_map()) {
+	// 	std::cout << map << ", ";
+	// }
+	// std::cout << endl;
+	// for (auto & map : node_map.get_backward_map()) {
+	// 	std::cout << map << ", ";
+	// }
 	env_->compute_induced_cost(g_id, h_id, node_map);
 	return node_map.induced_cost();
 }
 
 
+
+
 // double PyGEDEnv::getNodeCost(std::size_t label1, std::size_t label2) const {
 // 	return env_->ged_data_node_cost(label1, label2);
 // }
diff --git a/gklearn/preimage/median_preimage_generator.py b/gklearn/preimage/median_preimage_generator.py
index 7606204..fa1f4db 100644
--- a/gklearn/preimage/median_preimage_generator.py
+++ b/gklearn/preimage/median_preimage_generator.py
@@ -187,6 +187,10 @@ class MedianPreimageGenerator(PreimageGenerator):
 		results['itrs'] = self.__itrs
 		results['converged'] = self.__converged
 		results['num_updates_ecc'] = self.__num_updates_ecc
+		results['mge'] = {}
+		results['mge']['num_decrease_order'] = self.__mge.get_num_times_order_decreased()
+		results['mge']['num_increase_order'] = self.__mge.get_num_times_order_increased()
+		results['mge']['num_converged_descents'] = self.__mge.get_num_converged_descents()
 		return results
 
 		
@@ -660,27 +664,27 @@ class MedianPreimageGenerator(PreimageGenerator):
 		ged_env.init(init_option=self.__ged_options['init_option'])
 		
 		# Set up the madian graph estimator.
-		mge = MedianGraphEstimator(ged_env, constant_node_costs(self.__ged_options['edit_cost']))
-		mge.set_refine_method(self.__ged_options['method'], ged_options_to_string(self.__ged_options))
+		self.__mge = MedianGraphEstimator(ged_env, constant_node_costs(self.__ged_options['edit_cost']))
+		self.__mge.set_refine_method(self.__ged_options['method'], ged_options_to_string(self.__ged_options))
 		options = self.__mge_options.copy()
 		if not 'seed' in options:
 			options['seed'] = int(round(time.time() * 1000)) # @todo: may not work correctly for possible parallel usage.
 		
 		# Select the GED algorithm.
-		mge.set_options(mge_options_to_string(options))
-		mge.set_label_names(node_labels=self._dataset.node_labels, 
+		self.__mge.set_options(mge_options_to_string(options))
+		self.__mge.set_label_names(node_labels=self._dataset.node_labels, 
 					  edge_labels=self._dataset.edge_labels, 
 					  node_attrs=self._dataset.node_attrs, 
 					  edge_attrs=self._dataset.edge_attrs)
-		mge.set_init_method(self.__ged_options['method'], ged_options_to_string(self.__ged_options))
-		mge.set_descent_method(self.__ged_options['method'], ged_options_to_string(self.__ged_options))
+		self.__mge.set_init_method(self.__ged_options['method'], ged_options_to_string(self.__ged_options))
+		self.__mge.set_descent_method(self.__ged_options['method'], ged_options_to_string(self.__ged_options))
 		
 		# Run the estimator.
-		mge.run(graph_ids, set_median_id, gen_median_id)
+		self.__mge.run(graph_ids, set_median_id, gen_median_id)
 		
 		# Get SODs.
-		self.__sod_set_median = mge.get_sum_of_distances('initialized')
-		self.__sod_gen_median = mge.get_sum_of_distances('converged')
+		self.__sod_set_median = self.__mge.get_sum_of_distances('initialized')
+		self.__sod_gen_median = self.__mge.get_sum_of_distances('converged')
 		
 		# Get median graphs.
 		self.__set_median = ged_env.get_nx_graph(set_median_id)
diff --git a/gklearn/preimage/utils.py b/gklearn/preimage/utils.py
index a0dc9cd..f99ab8a 100644
--- a/gklearn/preimage/utils.py
+++ b/gklearn/preimage/utils.py
@@ -58,6 +58,9 @@ def generate_median_preimages_by_class(ds_name, mpg_options, kernel_options, ged
 	itrs_list = []
 	converged_list = []
 	num_updates_ecc_list = []
+	mge_decrease_order_list = []
+	mge_increase_order_list = []
+	mge_converged_order_list = []
 	nb_sod_sm2gm = [0, 0, 0]
 	nb_dis_k_sm2gm = [0, 0, 0]
 	nb_dis_k_gi2sm = [0, 0, 0]
@@ -149,7 +152,10 @@ def generate_median_preimages_by_class(ds_name, mpg_options, kernel_options, ged
 					  results['runtime_precompute_gm'], results['runtime_optimize_ec'], 
 					  results['runtime_generate_preimage'], results['runtime_total'],
 					  results['itrs'], results['converged'],
-					  results['num_updates_ecc']])
+					  results['num_updates_ecc'],
+					  results['mge']['num_decrease_order'] > 0, # @todo: not suitable for multi-start mge
+					  results['mge']['num_increase_order'] > 0,
+					  results['mge']['num_converged_descents'] > 0])
 			f_detail.close()
 		
 			# compute result summary.
@@ -165,6 +171,9 @@ def generate_median_preimages_by_class(ds_name, mpg_options, kernel_options, ged
 			itrs_list.append(results['itrs'])
 			converged_list.append(results['converged'])
 			num_updates_ecc_list.append(results['num_updates_ecc'])
+			mge_decrease_order_list.append(results['mge']['num_decrease_order'] > 0)
+			mge_increase_order_list.append(results['mge']['num_increase_order'] > 0)
+			mge_converged_order_list.append(results['mge']['num_converged_descents'] > 0)
 			# # SOD SM -> GM
 			if results['sod_set_median'] > results['sod_gen_median']:
 				nb_sod_sm2gm[0] += 1
@@ -211,7 +220,11 @@ def generate_median_preimages_by_class(ds_name, mpg_options, kernel_options, ged
 					  results['runtime_precompute_gm'], results['runtime_optimize_ec'], 
 					  results['runtime_generate_preimage'], results['runtime_total'],
 					  results['itrs'], results['converged'],
-					  results['num_updates_ecc'], nb_sod_sm2gm, 
+					  results['num_updates_ecc'], 
+					  results['mge']['num_decrease_order'] > 0, # @todo: not suitable for multi-start mge
+					  results['mge']['num_increase_order'] > 0,
+					  results['mge']['num_converged_descents'] > 0, 
+					  nb_sod_sm2gm, 
  					  nb_dis_k_sm2gm, nb_dis_k_gi2sm, nb_dis_k_gi2gm])
 			f_summary.close()
 			 
@@ -257,6 +270,9 @@ def generate_median_preimages_by_class(ds_name, mpg_options, kernel_options, ged
 		itrs_mean = np.mean(itrs_list)
 		num_converged = np.sum(converged_list)
 		num_updates_ecc_mean = np.mean(num_updates_ecc_list)
+		num_mge_decrease_order = np.sum(mge_decrease_order_list)
+		num_mge_increase_order = np.sum(mge_increase_order_list)
+		num_mge_converged = np.sum(mge_converged_order_list)
 		sod_sm2gm_mean = get_relations(np.sign(sod_gm_mean - sod_sm_mean))
 		dis_k_sm2gm_mean = get_relations(np.sign(dis_k_gm_mean - dis_k_sm_mean))
 		dis_k_gi2sm_mean = get_relations(np.sign(dis_k_sm_mean - dis_k_gi_min_mean))
@@ -271,7 +287,9 @@ def generate_median_preimages_by_class(ds_name, mpg_options, kernel_options, ged
 				  dis_k_gi2sm_mean, dis_k_gi2gm_mean,
 				  time_precompute_gm_mean, time_optimize_ec_mean,
 				  time_generate_mean, time_total_mean, itrs_mean, 
-				  num_converged, num_updates_ecc_mean])
+				  num_converged, num_updates_ecc_mean,
+				  num_mge_decrease_order, num_mge_increase_order,
+				  num_mge_converged])
 		f_summary.close()
 		
 	# save total pairwise kernel distances.
@@ -301,7 +319,8 @@ def __init_output_file(ds_name, gkernel, fit_method, dir_output):
 			  'min dis_k gi', 'SOD SM -> GM', 'dis_k SM -> GM', 'dis_k gi -> SM', 
 			  'dis_k gi -> GM', 'edit cost constants', 'time precompute gm',
 			  'time optimize ec', 'time generate preimage', 'time total',
-			  'itrs', 'converged', 'num updates ecc'])
+			  'itrs', 'converged', 'num updates ecc', 'mge decrease order', 
+			  'mge increase order', 'mge converged'])
 	f_detail.close()
 	
 #	fn_output_summary = 'results_summary.' + ds_name + '.' + gkernel + '.' + fit_method + '.csv'
@@ -313,7 +332,8 @@ def __init_output_file(ds_name, gkernel, fit_method, dir_output):
 			  'min dis_k gi', 'SOD SM -> GM', 'dis_k SM -> GM', 'dis_k gi -> SM', 
 			  'dis_k gi -> GM', 'time precompute gm', 'time optimize ec', 
 			  'time generate preimage', 'time total', 'itrs', 'num converged', 
-			  'num updates ecc', '# SOD SM -> GM', '# dis_k SM -> GM', 
+			  'num updates ecc', 'mge num decrease order', 'mge num increase order', 
+			  'mge num converged', '# SOD SM -> GM', '# dis_k SM -> GM', 
 			  '# dis_k gi -> SM', '# dis_k gi -> GM'])
 # 			   'repeats better SOD SM -> GM', 
 # 			  'repeats better dis_k SM -> GM', 'repeats better dis_k gi -> SM',