Esempio n. 1
0
    def process_existing_clique(self, clique, timestamp):

        free_nodes = []
        satisfied = True  #new clique satisfied or not

        #1. get new_loc
        expanding_list = {}  #dict of lists
        query_list = []

        for node in clique:
            query = self.query_log.trajs[node][timestamp]
            query_list.append(query)

        for query in query_list:
            seg_list = self.map_data.compute_fixed_expanding(
                query.x, query.y, query.cur_edge_id, option.INIT_DISTANCE)
            seg_list = EdgeSegmentSet.clean_fixed_expanding(seg_list)
            expanding_list[query.obj_id] = seg_list

        #2. build graph
        degree = {}
        adj = {}
        for query in query_list:
            degree[query.obj_id] = 0

        for i in range(len(query_list)):
            for j in range(i + 1, len(query_list)):
                if EdgeSegmentSet.is_set_cover(Point(query_list[i]), expanding_list[query_list[j].obj_id]) and \
                    EdgeSegmentSet.is_set_cover(Point(query_list[j]), expanding_list[query_list[i].obj_id]):
                    adj[(query_list[i].obj_id, query_list[j].obj_id)] = 1
                    adj[(query_list[j].obj_id, query_list[i].obj_id)] = 1
        for pair in adj.iterkeys():
            degree[pair[0]] += 1
            degree[pair[1]] += 1

        for node in clique:
            if degree[node] == 0:
                free_nodes.append(node)
                del expanding_list[node]
                satisfied = False

        #3. compute union (mesh) and ...
        mesh = []
        for seg_list in expanding_list.itervalues():
            mesh = EdgeSegmentSet.union(mesh, seg_list)

        #3.2 check total_len
        if EdgeSegmentSet.length(mesh) > option.MAX_MESH_LENGTH:
            satisfied = False
            # remove (heuristically) nodes which have low degrees
            while True:
                node = min(degree, degree.get)

                free_nodes.append(node)
                del degree[node]

                for node_2 in clique:
                    if adj.has_key((node, node_2)):
                        del adj[(node, node_2)]
                        del adj[(node_2, node)]
                        degree[node_2] = degree[node_2] - 1

                #re-compute union (mesh) and check total_len
                mesh = []
                for seg_list in expanding_list.itervalues():
                    mesh = EdgeSegmentSet.union(mesh, seg_list)
                if EdgeSegmentSet.length(mesh) <= option.MAX_MESH_LENGTH:
                    break

        #4. return
        return (satisfied, free_nodes, mesh)
Esempio n. 2
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    def solve_new_queries(self, timestamp):
        start_time = time.clock()

        #        mmb_list = []       #list of lists
        #        mmb_list_index = [] #list of sets
        query_list = self.query_log.frames[timestamp]

        #1. compute SC, SD, SN, (SF)
        set_F = set([])
        new_user_set = set([])

        for query in query_list:
            new_user_set = new_user_set | set([query.obj_id])

        set_C = self.user_set & new_user_set
        set_D = self.user_set - new_user_set
        set_N = new_user_set - self.user_set

        print "set_D", set_D
        print "set_N", set_N

        #2. process set_D (disappear)
        self.remove_from_mc_set(set_D)

        #3. compute_mesh_expanding (MAX_SPEED)
        for clique in self.mc_set:
            if len(clique) < option.K_ANONYMITY:
                continue

            node = list(clique)[0]
            #print "debug", clique, node

            seg_list = self.map_data.compute_mesh_expanding(
                self.user_mesh[node], option.MAX_SPEED)
            self.mmb_mesh[node] = seg_list
            for node_2 in clique:
                if node_2 != node and self.user_mc_set[
                        node_2] == self.user_mc_set[node]:
                    self.mmb_mesh[node_2] = seg_list

        #3.1
        num_edges = 0
        list_edges = []
        for node_1 in set_C:
            for node_2 in set_C:
                if node_1 != node_2 and self.mmb_mesh.has_key(
                        node_1) and self.mmb_mesh.has_key(node_2):
                    point_1 = Point(self.query_log.trajs[node_1][timestamp])
                    point_2 = Point(self.query_log.trajs[node_2][timestamp])
                    if  EdgeSegmentSet.is_set_cover(point_1, self.mmb_mesh[node_2]) and \
                        EdgeSegmentSet.is_set_cover(point_2, self.mmb_mesh[node_1]):
                        num_edges += 1
                        list_edges.append((node_1, node_2))
        print "num_edges (set_C) = ", num_edges
        graph.add_to_mc_set(list_edges)

        #3.2
        num_edges = 0
        list_edges = []
        for node_1 in set_C:
            for node_2 in set_N:
                point_2 = Point(self.query_log.trajs[node_2][timestamp])
                if self.mmb_mesh.has_key(
                        node_1) and EdgeSegmentSet.is_set_cover(
                            point_2, self.mmb_mesh[node_1]):
                    num_edges += 1
                    list_edges.append((node_1, node_2))
        print "num_edges (set_N) = ", num_edges
        graph.add_to_mc_set(list_edges)

        #4. update self.user_mc_set, self.user_mesh, self.user_set

        #4.1 compute user_mc_set, max clique for each obj_id
        self.user_mc_set = {}
        for clique in self.mc_set:
            for obj_id in clique:
                if not self.user_mc_set.has_key(obj_id):
                    self.user_mc_set[obj_id] = clique
                elif len(self.user_mc_set[obj_id]) < len(clique):
                    self.user_mc_set[obj_id] = clique
        print "Compute user_mc_set: DONE"

        #4.2 compute MMBs (CLOAKING MESHES) and self.user_set
        max_mesh_len = 0
        min_mesh_len = 1000000
        self.user_mesh = {}
        for clique in self.mc_set:
            if len(clique) >= option.K_ANONYMITY:
                locations = []
                for node in clique:
                    locations.append(self.query_log.trajs[node][timestamp])

                mesh = self.map_data.compute_mesh_mbr(
                    locations)  #TEMPORARILY !!

                #
                temp_len = EdgeSegmentSet.length(mesh)
                if max_mesh_len < temp_len:
                    max_mesh_len = temp_len
                if min_mesh_len > temp_len:
                    min_mesh_len = temp_len

                # assign mesh to all obj_id in 'clique'
                for obj_id in clique:
                    self.user_mesh[obj_id] = mesh

                #
                for obj_id in clique:
                    self.user_set = self.user_set | set([obj_id])

        print "Compute CLOAKING MESH: DONE"
        print "max_mesh_len =", max_mesh_len
        print "min_mesh_len =", min_mesh_len

        print "elapsed : ", (time.clock() - start_time)
Esempio n. 3
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    def init_mc_set(self):
        start_time = time.clock()

        expanding_list = {}  #[[]] * option.MAX_USER   #dict of lists
        query_list = self.query_log.frames[0]  #init timestamp
        min_obj_id = option.MAX_USER
        max_obj_id = 0

        #1. compute expanding_list
        for query in query_list:
            if max_obj_id < query.obj_id:
                max_obj_id = query.obj_id
            if min_obj_id > query.obj_id:
                min_obj_id = query.obj_id
            #
            self.num_user = max(self.num_user, query.obj_id)
            seg_list = self.map_data.compute_fixed_expanding(
                query.x, query.y, query.cur_edge_id, option.INIT_DISTANCE)
            seg_list = EdgeSegmentSet.clean_fixed_expanding(seg_list)

            expanding_list[query.obj_id] = seg_list

        #1.2 check connectivity of each seg_list --> OK
#        print "Connectivity check: STARTED"
#        for query in query_list:
#            if not Map.check_connected_expanding(expanding_list[query.obj_id]):
#                print "error found at obj_id=", query.obj_id
#        print "Connectivity check: DONE"

#2. init self.mc_set
        self.reset()
        for query in query_list:
            self.mc_set.append(set([query.obj_id]))

        #3. compute mc_set
        num_edges = 0
        list_edges = []
        for i in range(len(query_list)):
            for j in range(i + 1, len(query_list)):
                if get_distance(query_list[i].x, query_list[i].y, query_list[j].x, query_list[j].y) > \
                    option.INIT_DISTANCE:
                    continue

                if EdgeSegmentSet.is_set_cover(Point(query_list[i]), expanding_list[query_list[j].obj_id]) and \
                    EdgeSegmentSet.is_set_cover(Point(query_list[j]), expanding_list[query_list[i].obj_id]):
                    num_edges += 1
                    list_edges.append(
                        (query_list[i].obj_id, query_list[j].obj_id))
        print "num_edges=", num_edges
        print "list_edges - elapsed : ", (time.clock() - start_time)

        start_time = time.clock()
        graph.add_to_mc_set(list_edges)

        print "add_to_mc_set - elapsed : ", (time.clock() - start_time)
        print "mc_set =", self.mc_set

        #4. compute user_mc_set, max clique for each obj_id
        self.user_mc_set = {}
        for clique in self.mc_set:
            if len(clique) >= option.K_ANONYMITY:
                for obj_id in clique:
                    if not self.user_mc_set.has_key(obj_id):
                        self.user_mc_set[obj_id] = clique
                    elif len(self.user_mc_set[obj_id]) < len(clique):
                        self.user_mc_set[obj_id] = clique
        print "Compute user_mc_set: DONE"
        print "user_mc_set = ", self.user_mc_set

        #5. compute MMBs (CLOAKING MESHES) and self.user_set
        max_mesh_len = 0
        min_mesh_len = 1000000
        for clique in self.mc_set:
            if len(clique) >= option.K_ANONYMITY:
                mesh = []
                for obj_id in clique:
                    mesh = EdgeSegmentSet.union(mesh, expanding_list[obj_id])

                #
                temp_len = EdgeSegmentSet.length(mesh)
                if max_mesh_len < temp_len:
                    max_mesh_len = temp_len
                if min_mesh_len > temp_len:
                    min_mesh_len = temp_len

                # assign mesh to all obj_id in 'clique'
                for obj_id in clique:
                    self.user_mesh[obj_id] = mesh

                #
                for obj_id in clique:
                    self.user_set = self.user_set | set([obj_id])

        print "self.user_set = ", self.user_set

        print "Compute CLOAKING MESH: DONE"
        print "max_mesh_len =", max_mesh_len
        print "min_mesh_len =", min_mesh_len

        #5.2 check connectivity of each user_mesh --> OK
        #        start_time = time.clock()
        #        print "MMB Connectivity check: STARTED"
        #        for clique in self.mc_set:
        #            for obj_id in clique:
        #                if not Map.check_connected_expanding(self.user_mesh[obj_id]):
        #                    print "error found at clique=", clique
        #                continue
        #        print "MMB Connectivity check: DONE"
        #        print "elapsed : ", (time.clock() - start_time)

        #DEBUG
        print "len(graph.mc_set) = ", len(graph.mc_set)
        print graph.mc_set
Esempio n. 4
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    def solve_new_queries(self, timestamp):
        start_time = time.clock()
        
        
#        mmb_list = []       #list of lists
#        mmb_list_index = [] #list of sets 
        query_list = self.query_log.frames[timestamp]
        
        #1. compute SC, SD, SN, (SF)
        set_F = set([])
        new_user_set = set([])
        
        for query in query_list:
            new_user_set = new_user_set | set([query.obj_id])
            
        set_C = self.user_set & new_user_set
        set_D = self.user_set - new_user_set
        set_N = new_user_set - self.user_set
        
        print "set_D", set_D
        print "set_N", set_N
        
        #2. process set_D (disappear)
        self.remove_from_mc_set(set_D)
        
        #3. compute_mesh_expanding (MAX_SPEED)
        for clique in self.mc_set:
            if len(clique) < option.K_ANONYMITY:
                continue
            
            node = list(clique)[0]
            #print "debug", clique, node
            
            seg_list = self.map_data.compute_mesh_expanding(self.user_mesh[node], option.MAX_SPEED)
            self.mmb_mesh[node] = seg_list
            for node_2 in clique:
                if node_2 != node and self.user_mc_set[node_2] == self.user_mc_set[node]:
                    self.mmb_mesh[node_2] = seg_list
        
        #3.1
        num_edges = 0 
        list_edges = []
        for node_1 in set_C:
            for node_2 in set_C:
                if node_1 != node_2 and self.mmb_mesh.has_key(node_1) and self.mmb_mesh.has_key(node_2):
                    point_1 = Point(self.query_log.trajs[node_1][timestamp])
                    point_2 = Point(self.query_log.trajs[node_2][timestamp])
                    if  EdgeSegmentSet.is_set_cover(point_1, self.mmb_mesh[node_2]) and \
                        EdgeSegmentSet.is_set_cover(point_2, self.mmb_mesh[node_1]):
                        num_edges += 1
                        list_edges.append((node_1, node_2))
        print "num_edges (set_C) = ", num_edges
        graph.add_to_mc_set(list_edges)
        
                    
        #3.2
        num_edges = 0 
        list_edges = []
        for node_1 in set_C:
            for node_2 in set_N:    
                point_2 = Point(self.query_log.trajs[node_2][timestamp])
                if  self.mmb_mesh.has_key(node_1) and EdgeSegmentSet.is_set_cover(point_2, self.mmb_mesh[node_1]):
                    num_edges += 1
                    list_edges.append((node_1, node_2))
        print "num_edges (set_N) = ", num_edges
        graph.add_to_mc_set(list_edges)
                    
        #4. update self.user_mc_set, self.user_mesh, self.user_set
        
        #4.1 compute user_mc_set, max clique for each obj_id
        self.user_mc_set = {}
        for clique in self.mc_set:
            for obj_id in clique:
                if not self.user_mc_set.has_key(obj_id):
                    self.user_mc_set[obj_id] = clique
                elif len(self.user_mc_set[obj_id]) < len(clique):
                    self.user_mc_set[obj_id] = clique
        print "Compute user_mc_set: DONE"
                    
        #4.2 compute MMBs (CLOAKING MESHES) and self.user_set
        max_mesh_len = 0
        min_mesh_len = 1000000
        self.user_mesh = {}
        for clique in self.mc_set:
            if len(clique) >= option.K_ANONYMITY:
                locations = []
                for node in clique:
                    locations.append(self.query_log.trajs[node][timestamp])
                
                mesh = self.map_data.compute_mesh_mbr(locations)        #TEMPORARILY !!
                
                #    
                temp_len = EdgeSegmentSet.length(mesh)
                if max_mesh_len < temp_len:
                    max_mesh_len = temp_len
                if min_mesh_len > temp_len:
                    min_mesh_len = temp_len    
                     
                # assign mesh to all obj_id in 'clique'
                for obj_id in clique:
                    self.user_mesh[obj_id] = mesh
                    
                # 
                for obj_id in clique:
                    self.user_set = self.user_set | set([obj_id])
                
                
        print "Compute CLOAKING MESH: DONE"
        print "max_mesh_len =", max_mesh_len
        print "min_mesh_len =", min_mesh_len
        
        
                    
        print "elapsed : ", (time.clock() - start_time)    
Esempio n. 5
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 def process_existing_clique(self, clique, timestamp):
     
     free_nodes = []
     satisfied = True        #new clique satisfied or not
     
     #1. get new_loc
     expanding_list = {}     #dict of lists
     query_list = []
     
     for node in clique:
         query = self.query_log.trajs[node][timestamp]
         query_list.append(query)
         
     for query in query_list:
         seg_list = self.map_data.compute_fixed_expanding(query.x, query.y, 
                                         query.cur_edge_id, option.INIT_DISTANCE)
         seg_list = EdgeSegmentSet.clean_fixed_expanding(seg_list)
         expanding_list[query.obj_id] = seg_list
         
         
     #2. build graph
     degree = {}
     adj = {}
     for query in query_list:
         degree[query.obj_id] = 0
         
     for i in range(len(query_list)):
         for j in range(i+1,len(query_list)):
             if EdgeSegmentSet.is_set_cover(Point(query_list[i]), expanding_list[query_list[j].obj_id]) and \
                 EdgeSegmentSet.is_set_cover(Point(query_list[j]), expanding_list[query_list[i].obj_id]):
                 adj[(query_list[i].obj_id, query_list[j].obj_id)] = 1
                 adj[(query_list[j].obj_id, query_list[i].obj_id)] = 1
     for pair in adj.iterkeys():
         degree[pair[0]] += 1
         degree[pair[1]] += 1            
     
     for node in clique:
         if degree[node] == 0:
             free_nodes.append(node)
             del expanding_list[node]
             satisfied = False
                 
     #3. compute union (mesh) and ...
     mesh = []
     for seg_list in expanding_list.itervalues():
         mesh = EdgeSegmentSet.union(mesh, seg_list)
     
     #3.2 check total_len
     if EdgeSegmentSet.length(mesh) > option.MAX_MESH_LENGTH:
         satisfied = False
         # remove (heuristically) nodes which have low degrees
         while True:
             node = min(degree, degree.get)
             
             free_nodes.append(node)
             del degree[node]
             
             for node_2 in clique:
                 if adj.has_key((node, node_2)):
                     del adj[(node, node_2)]
                     del adj[(node_2, node)]
                     degree[node_2] = degree[node_2] - 1 
             
             #re-compute union (mesh) and check total_len
             mesh = []
             for seg_list in expanding_list.itervalues():
                 mesh = EdgeSegmentSet.union(mesh, seg_list)
             if EdgeSegmentSet.length(mesh) <= option.MAX_MESH_LENGTH:
                 break    
      
     #4. return
     return (satisfied, free_nodes, mesh)   
Esempio n. 6
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    def init_mc_set(self):         
        start_time = time.clock()
        
        expanding_list = {} #[[]] * option.MAX_USER   #dict of lists
        query_list = self.query_log.frames[0]   #init timestamp
        min_obj_id = option.MAX_USER
        max_obj_id = 0
        
        #1. compute expanding_list
        for query in query_list:
            if max_obj_id < query.obj_id:
                max_obj_id = query.obj_id
            if min_obj_id > query.obj_id:
                min_obj_id = query.obj_id
            #        
            self.num_user = max(self.num_user, query.obj_id)
            seg_list = self.map_data.compute_fixed_expanding(query.x, query.y, 
                                            query.cur_edge_id, option.INIT_DISTANCE)
            seg_list = EdgeSegmentSet.clean_fixed_expanding(seg_list)
            
            expanding_list[query.obj_id] = seg_list
            
            
        #1.2 check connectivity of each seg_list --> OK
#        print "Connectivity check: STARTED"
#        for query in query_list:
#            if not Map.check_connected_expanding(expanding_list[query.obj_id]):   
#                print "error found at obj_id=", query.obj_id
#        print "Connectivity check: DONE"    
                
        #2. init self.mc_set
        self.reset()
        for query in query_list:
            self.mc_set.append(set([query.obj_id]))
            
        #3. compute mc_set
        num_edges = 0 
        list_edges = []
        for i in range(len(query_list)):
            for j in range(i+1,len(query_list)):
                if get_distance(query_list[i].x, query_list[i].y, query_list[j].x, query_list[j].y) > \
                    option.INIT_DISTANCE:
                    continue
                
                if EdgeSegmentSet.is_set_cover(Point(query_list[i]), expanding_list[query_list[j].obj_id]) and \
                    EdgeSegmentSet.is_set_cover(Point(query_list[j]), expanding_list[query_list[i].obj_id]):
                    num_edges += 1
                    list_edges.append((query_list[i].obj_id, query_list[j].obj_id))
        print "num_edges=", num_edges
        print "list_edges - elapsed : ", (time.clock() - start_time)               
                 
        start_time = time.clock()            
        graph.add_to_mc_set(list_edges) 
        
        print "add_to_mc_set - elapsed : ", (time.clock() - start_time)   
        print "mc_set =", self.mc_set
        
        #4. compute user_mc_set, max clique for each obj_id
        self.user_mc_set = {}
        for clique in self.mc_set:
            if len(clique) >= option.K_ANONYMITY:
                for obj_id in clique:
                    if not self.user_mc_set.has_key(obj_id):
                        self.user_mc_set[obj_id] = clique
                    elif len(self.user_mc_set[obj_id]) < len(clique):
                        self.user_mc_set[obj_id] = clique
        print "Compute user_mc_set: DONE"
        print "user_mc_set = ", self.user_mc_set
                    
        #5. compute MMBs (CLOAKING MESHES) and self.user_set
        max_mesh_len = 0
        min_mesh_len = 1000000
        for clique in self.mc_set:
            if len(clique) >= option.K_ANONYMITY:
                mesh = []
                for obj_id in clique:
                    mesh = EdgeSegmentSet.union(mesh, expanding_list[obj_id])
                
                #    
                temp_len = EdgeSegmentSet.length(mesh)
                if max_mesh_len < temp_len:
                    max_mesh_len = temp_len
                if min_mesh_len > temp_len:
                    min_mesh_len = temp_len    
                     
                # assign mesh to all obj_id in 'clique'
                for obj_id in clique:
                    self.user_mesh[obj_id] = mesh
                    
                # 
                for obj_id in clique:
                    self.user_set = self.user_set | set([obj_id])
        
        print "self.user_set = ", self.user_set        
                
        print "Compute CLOAKING MESH: DONE"
        print "max_mesh_len =", max_mesh_len
        print "min_mesh_len =", min_mesh_len
        
        
        
        #5.2 check connectivity of each user_mesh --> OK
#        start_time = time.clock()
#        print "MMB Connectivity check: STARTED"
#        for clique in self.mc_set:
#            for obj_id in clique:
#                if not Map.check_connected_expanding(self.user_mesh[obj_id]):   
#                    print "error found at clique=", clique
#                continue
#        print "MMB Connectivity check: DONE"      
#        print "elapsed : ", (time.clock() - start_time)                
                    
        
            
        #DEBUG
        print "len(graph.mc_set) = ", len(graph.mc_set)
        print graph.mc_set
Esempio n. 7
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    def solve_new_queries(self, timestamp):
        start_time = time.clock()

        expanding_list = {}  #dict of lists
        query_list = self.query_log.frames[timestamp]  # timestamp
        min_obj_id = option.MAX_USER
        max_obj_id = 0

        #1. compute expanding_list
        for query in query_list:
            if max_obj_id < query.obj_id:
                max_obj_id = query.obj_id
            if min_obj_id > query.obj_id:
                min_obj_id = query.obj_id
            #
            seg_list = self.map_data.compute_fixed_expanding(
                query.x, query.y, query.cur_edge_id, option.INIT_DISTANCE)
            seg_list = EdgeSegmentSet.clean_fixed_expanding(seg_list)

            expanding_list[query.obj_id] = seg_list

        #2. init self.mc_set
        self.reset()
        for query in query_list:
            self.mc_set.append(set([query.obj_id]))

        #3. compute mc_set
        start_time = time.clock()
        num_edges = 0
        list_edges = []
        for i in range(len(query_list)):
            for j in range(i + 1, len(query_list)):
                if get_distance(query_list[i].x, query_list[i].y, query_list[j].x, query_list[j].y) > \
                    option.INIT_DISTANCE:
                    continue

                if EdgeSegmentSet.is_set_cover(Point(query_list[i]), expanding_list[query_list[j].obj_id]) and \
                    EdgeSegmentSet.is_set_cover(Point(query_list[j]), expanding_list[query_list[i].obj_id]):
                    num_edges += 1
                    list_edges.append(
                        (query_list[i].obj_id, query_list[j].obj_id))
        print "num_edges=", num_edges
        print "list_edges - elapsed : ", (time.clock() - start_time)

        start_time = time.clock()
        graph.add_to_mc_set(list_edges)

        print "add_to_mc_set - elapsed : ", (time.clock() - start_time)
        print "mc_set =", self.mc_set

        #4. compute user_mc_set, max clique for each obj_id
        start_time = time.clock()
        self.user_mc_set = {}
        for clique in self.mc_set:
            if len(clique) >= option.K_ANONYMITY:
                for obj_id in clique:
                    if not self.user_mc_set.has_key(obj_id):
                        self.user_mc_set[obj_id] = clique
                    elif len(self.user_mc_set[obj_id]) < len(clique):
                        self.user_mc_set[obj_id] = clique
        print "Compute user_mc_set - elapsed : ", (time.clock() - start_time)
        print "user_mc_set = ", self.user_mc_set

        #5. compute MMBs (CLOAKING MESHES) and self.user_set
        start_time = time.clock()
        max_mesh_len = 0
        min_mesh_len = 1000000
        for clique in self.mc_set:
            if len(clique) >= option.K_ANONYMITY:
                mesh = []
                for obj_id in clique:
                    mesh = EdgeSegmentSet.union(mesh, expanding_list[obj_id])

                #
                temp_len = EdgeSegmentSet.length(mesh)
                if max_mesh_len < temp_len:
                    max_mesh_len = temp_len
                if min_mesh_len > temp_len:
                    min_mesh_len = temp_len

                # assign mesh to all obj_id in 'clique'
                for obj_id in clique:
                    self.user_mesh[obj_id] = mesh

                #
                for obj_id in clique:
                    self.user_set = self.user_set | set([obj_id])

        #print "self.user_set = ", self.user_set
        print "Compute CLOAKING MESH - elapsed : ", (time.clock() - start_time)

        print "max_mesh_len =", max_mesh_len
        print "min_mesh_len =", min_mesh_len