+ def __init__(self, nodes, transitions, no_ancester=None):
+ """Initailize graph's object
+
+ @param nodes: list of ids of nodes in the graph
+ @param transitions: list of edges in the graph in the form (source_node, destination_node)
+ @param no_ancester: list of nodes with no incoming edges
+ """
+
+ self.nodes = nodes or []
+ self.edges = transitions or []
+ self.no_ancester = no_ancester or {}
+ trans = {}
+
+ for t in transitions:
+ trans.setdefault(t[0], [])
+ trans[t[0]].append(t[1])
+ self.transitions = trans
+ self.result = {}
+
+
+ def init_rank(self):
+ """Computes rank of the nodes of the graph by finding initial feasible tree
+ """
+ self.edge_wt = {}
+ for link in self.links:
+ self.edge_wt[link] = self.result[link[1]]['x'] - self.result[link[0]]['x']
+
+ tot_node = self.partial_order.__len__()
+ #do until all the nodes in the component are searched
+ while self.tight_tree()<tot_node:
+ list_node = []
+ list_edge = []
+
+ for node in self.nodes:
+ if node not in self.reachable_nodes:
+ list_node.append(node)
+
+ for edge in self.edge_wt:
+ if edge not in self.tree_edges:
+ list_edge.append(edge)
+
+ slack = 100
+
+ for edge in list_edge:
+ if ((self.reachable_nodes.__contains__(edge[0]) and edge[1] not in self.reachable_nodes) or
+ (self.reachable_nodes.__contains__(edge[1]) and edge[0] not in self.reachable_nodes)):
+ if(slack>self.edge_wt[edge]-1):
+ slack = self.edge_wt[edge]-1
+ new_edge = edge
+
+ if new_edge[0] not in self.reachable_nodes:
+ delta = -(self.edge_wt[new_edge]-1)
+ else:
+ delta = self.edge_wt[new_edge]-1
+
+ for node in self.result:
+ if node in self.reachable_nodes:
+ self.result[node]['x'] += delta
+
+ for edge in self.edge_wt:
+ self.edge_wt[edge] = self.result[edge[1]]['x'] - self.result[edge[0]]['x']
+
+ self.init_cutvalues()
+
+
+ def tight_tree(self):
+ self.reachable_nodes = []
+ self.tree_edges = []
+ self.reachable_node(self.start)
+ return self.reachable_nodes.__len__()
+
+
+ def reachable_node(self, node):
+ """Find the nodes of the graph which are only 1 rank apart from each other
+ """
+
+ if node not in self.reachable_nodes:
+ self.reachable_nodes.append(node)
+ for edge in self.edge_wt:
+ if edge[0]==node:
+ if self.edge_wt[edge]==1:
+ self.tree_edges.append(edge)
+ if edge[1] not in self.reachable_nodes:
+ self.reachable_nodes.append(edge[1])
+ self.reachable_node(edge[1])
+
+
+ def init_cutvalues(self):
+ """Initailize cut values of edges of the feasible tree.
+ Edges with negative cut-values are removed from the tree to optimize rank assignment
+ """
+ self.cut_edges = {}
+ self.head_nodes = []
+ i=0;
+
+ for edge in self.tree_edges:
+ self.head_nodes = []
+ rest_edges = []
+ rest_edges += self.tree_edges
+ rest_edges.__delitem__(i)
+ self.head_component(self.start, rest_edges)
+ i+=1
+ positive = 0
+ negative = 0
+ for source_node in self.transitions:
+ if source_node in self.head_nodes:
+ for dest_node in self.transitions[source_node]:
+ if dest_node not in self.head_nodes:
+ negative+=1
+ else:
+ for dest_node in self.transitions[source_node]:
+ if dest_node in self.head_nodes:
+ positive+=1
+
+ self.cut_edges[edge] = positive - negative
+
+
+ def head_component(self, node, rest_edges):
+ """Find nodes which are reachable from the starting node, after removing an edge
+ """
+ if node not in self.head_nodes:
+ self.head_nodes.append(node)
+
+ for edge in rest_edges:
+ if edge[0]==node:
+ self.head_component(edge[1],rest_edges)
+
+
+ def process_ranking(self, node, level=0):
+ """Computes initial feasible ranking after making graph acyclic with depth-first search
+ """
+
+ if node not in self.result:
+ self.result[node] = {'y': None, 'x':level, 'mark':0}
+ else:
+ if level > self.result[node]['x']:
+ self.result[node]['x'] = level
+
+ if self.result[node]['mark']==0:
+ self.result[node]['mark'] = 1
+ for sec_end in self.transitions.get(node, []):
+ self.process_ranking(sec_end, level+1)
+
+
+ def make_acyclic(self, parent, node, level, tree):
+ """Computes Partial-order of the nodes with depth-first search
+ """
+
+ if node not in self.partial_order:
+ self.partial_order[node] = {'level':level, 'mark':0}
+ if parent:
+ tree.append((parent, node))
+
+ if self.partial_order[node]['mark']==0:
+ self.partial_order[node]['mark'] = 1
+ for sec_end in self.transitions.get(node, []):
+ self.links.append((node, sec_end))
+ self.make_acyclic(node, sec_end, level+1, tree)
+
+ return tree
+
+
+ def rev_edges(self, tree):
+ """reverse the direction of the edges whose source-node-partail_order> destination-node-partail_order
+ to make the graph acyclic
+ """
+ Is_Cyclic = False
+ i=0
+ for link in self.links:
+ src = link[0]
+ des = link[1]
+ edge_len = self.partial_order[des]['level'] - self.partial_order[src]['level']
+ if edge_len < 0:
+ self.links.__delitem__(i)
+ self.links.insert(i, (des, src))
+ self.transitions[src].remove(des)
+ self.transitions.setdefault(des, []).append(src)
+ Is_Cyclic = True
+ elif math.fabs(edge_len) > 1:
+ Is_Cyclic = True
+ i += 1
+
+ return Is_Cyclic
+
+ def exchange(self, e, f):
+ """Exchange edges to make feasible-tree optimized
+ @param edge: edge with negative cut-value
+ @param edge: new edge with minimum slack-value
+ """
+ self.tree_edges.__delitem__(self.tree_edges.index(e))
+ self.tree_edges.append(f)
+ self.init_cutvalues()
+
+
+ def enter_edge(self, edge):
+ """Finds a new_edge with minimum slack value to replace an edge with negative cut-value
+
+ @param edge: edge with negative cut-value
+ """
+
+ self.head_nodes = []
+ rest_edges = []
+ rest_edges += self.tree_edges
+ rest_edges.__delitem__(rest_edges.index(edge))
+ self.head_component(self.start, rest_edges)
+
+ if self.head_nodes.__contains__(edge[1]):
+ l = []
+ for node in self.result:
+ if not self.head_nodes.__contains__(node):
+ l.append(node)
+ self.head_nodes = l
+
+ slack = 100
+ new_edge = edge
+ for source_node in self.transitions:
+ if source_node in self.head_nodes:
+ for dest_node in self.transitions[source_node]:
+ if dest_node not in self.head_nodes:
+ if(slack>(self.edge_wt[edge]-1)):
+ slack = self.edge_wt[edge]-1
+ new_edge = (source_node, dest_node)
+
+ return new_edge
+
+
+ def leave_edge(self):
+ """Returns the edge with negative cut_value(if exists)
+ """
+ if self.critical_edges:
+ for edge in self.critical_edges:
+ self.cut_edges[edge] = 0
+
+ for edge in self.cut_edges:
+ if self.cut_edges[edge]<0:
+ return edge
+
+ return None
+
+
+ def finalize_rank(self, node, level):
+ self.result[node]['x'] = level
+ for destination in self.optimal_edges.get(node, []):
+ self.finalize_rank(destination, level+1)
+
+
+ def normalize(self):
+ """The ranks are normalized by setting the least rank to zero.
+ """
+
+ least_rank = min(map(lambda x: x['x'], self.result.values()))
+
+ if(least_rank!=0):
+ for node in self.result:
+ self.result[node]['x']-=least_rank
+
+
+ def make_chain(self):
+ """Edges between nodes more than one rank apart are replaced by chains of unit
+ length edges between temporary nodes.
+ """
+
+ for edge in self.edge_wt:
+ if self.edge_wt[edge]>1:
+ self.transitions[edge[0]].remove(edge[1])
+ start = self.result[edge[0]]['x']
+ end = self.result[edge[1]]['x']
+
+ for rank in range(start+1, end):
+ if not self.result.get((rank, 'temp'), False):
+ self.result[(rank, 'temp')] = {'y': None, 'x': rank, 'mark': 0}
+
+ for rank in range(start, end):
+ if start==rank:
+ self.transitions[edge[0]].append((rank+1, 'temp'))
+ elif rank==end-1:
+ self.transitions.setdefault((rank, 'temp'), []).append(edge[1])
+ else:
+ self.transitions.setdefault((rank, 'temp'), []).append((rank+1, 'temp'))
+
+
+ def init_order(self, node, level):
+ """Initialize orders the nodes in each rank with depth-first search
+ """
+ if not self.result[node]['y']:
+ self.result[node]['y'] = self.order[level]
+ self.order[level] = self.order[level]+1
+
+ for sec_end in self.transitions.get(node, []):
+ self.init_order(sec_end, self.result[sec_end]['x'])
+
+
+ def order_heuristic(self):
+ for i in range(12):
+ self.wmedian()
+
+
+ def wmedian(self):
+ """Applies median heuristic to find optimzed order of the nodes with in their ranks
+ """
+ for level in self.levels:
+
+ node_median = []
+ nodes = self.levels[level]
+ for node in nodes:
+ node_median.append((node, self.median_value(node, level-1)))
+
+ sort_list = sorted(node_median, key=operator.itemgetter(1))
+
+ new_list = [tuple[0] for tuple in sort_list]
+
+ self.levels[level] = new_list
+ order = 0
+ for node in nodes:
+ self.result[node]['y'] = order
+ order +=1
+
+
+ def median_value(self, node, adj_rank):
+ """Returns median value of a vertex , defined as the median position of the adjacent vertices
+
+ @param node: node to process
+ @param adj_rank: rank 1 less than the node's rank
+ """
+ adj_nodes = self.adj_position(node, adj_rank)
+ l = len(adj_nodes)
+ m = l/2
+
+ if l==0:
+ return -1.0
+ elif l%2 == 1:
+ return adj_nodes[m]#median of the middle element
+ elif l==2:
+ return (adj_nodes[0]+adj_nodes[1])/2
+ else:
+ left = adj_nodes[m-1] - adj_nodes[0]
+ right = adj_nodes[l-1] - adj_nodes[m]
+ return ((adj_nodes[m-1]*right) + (adj_nodes[m]*left))/(left+right)
+
+
+ def adj_position(self, node, adj_rank):
+ """Returns list of the present positions of the nodes adjacent to node in the given adjacent rank.
+
+ @param node: node to process
+ @param adj_rank: rank 1 less than the node's rank
+ """
+
+ pre_level_nodes = self.levels.get(adj_rank, [])
+ adj_nodes = []
+
+ if pre_level_nodes:
+ for src in pre_level_nodes:
+ if (self.transitions.get(src) and self.transitions[src].__contains__(node)):
+ adj_nodes.append(self.result[src]['y'])
+
+ return adj_nodes
+
+
+ def preprocess_order(self):
+ levels = {}
+
+ for r in self.partial_order:
+ l = self.result[r]['x']
+ levels.setdefault(l,[])
+ levels[l].append(r)
+
+ self.levels = levels
+
+
+ def graph_order(self):
+ """Finds actual-order of the nodes with respect to maximum number of nodes in a rank in component
+ """
+ mid_pos = 0.0
+ max_level = max(map(lambda x: len(x), self.levels.values()))
+
+ for level in self.levels:
+ if level:
+ no = len(self.levels[level])
+ factor = (max_level - no) * 0.10
+ list = self.levels[level]
+ list.reverse()
+
+ if no%2==0:
+ first_half = list[no/2:]
+ factor = -factor
+ else:
+ first_half = list[no/2+1:]
+ if max_level==1:#for the case when horizontal graph is there
+ self.result[list[no/2]]['y'] = mid_pos + (self.result[list[no/2]]['x']%2 * 0.5)
+ else:
+ self.result[list[no/2]]['y'] = mid_pos + factor
+
+ last_half = list[:no/2]
+
+ i=1
+ for node in first_half:
+ self.result[node]['y'] = mid_pos - (i + factor)
+ i += 1
+
+ i=1
+ for node in last_half:
+ self.result[node]['y'] = mid_pos + (i + factor)
+ i += 1
+ else:
+ self.max_order += max_level+1
+ mid_pos = self.result[self.start]['y']
+
+
+ def tree_order(self, node, last=0):
+ mid_pos = self.result[node]['y']
+ l = self.transitions.get(node, [])
+ l.reverse()
+ no = len(l)
+
+ if no%2==0:
+ first_half = l[no/2:]
+ factor = 1
+ else:
+ first_half = l[no/2+1:]
+ factor = 0
+
+ last_half = l[:no/2]
+
+ i=1
+ for child in first_half:
+ self.result[child]['y'] = mid_pos - (i - (factor * 0.5))
+ i += 1
+
+ if self.transitions.get(child, False):
+ if last:
+ self.result[child]['y'] = last + len(self.transitions[child])/2 + 1
+ last = self.tree_order(child, last)
+
+ if no%2:
+ mid_node = l[no/2]
+ self.result[mid_node]['y'] = mid_pos
+
+ if self.transitions.get((mid_node), False):
+ if last:
+ self.result[mid_node]['y'] = last + len(self.transitions[mid_node])/2 + 1
+ last = self.tree_order(mid_node)
+ else:
+ if last:
+ self.result[mid_node]['y'] = last + 1
+ self.result[node]['y'] = self.result[mid_node]['y']
+ mid_pos = self.result[node]['y']
+
+ i=1
+ last_child = None
+ for child in last_half:
+ self.result[child]['y'] = mid_pos + (i - (factor * 0.5))
+ last_child = child
+ i += 1
+ if self.transitions.get(child, False):
+ if last:
+ self.result[child]['y'] = last + len(self.transitions[child])/2 + 1
+ last = self.tree_order(child, last)
+
+ if last_child:
+ last = self.result[last_child]['y']
+
+ return last
+
+
+ def process_order(self):
+ """Finds actual-order of the nodes with respect to maximum number of nodes in a rank in component
+ """
+
+ if self.Is_Cyclic:
+ max_level = max(map(lambda x: len(x), self.levels.values()))
+
+ if max_level%2:
+ self.result[self.start]['y'] = (max_level+1)/2 + self.max_order + (self.max_order and 1)
+ else:
+ self.result[self.start]['y'] = (max_level)/2 + self.max_order + (self.max_order and 1)
+
+ self.graph_order()
+
+ else:
+ self.result[self.start]['y'] = 0
+ self.tree_order(self.start, 0)
+ min_order = math.fabs(min(map(lambda x: x['y'], self.result.values())))
+
+ index = self.start_nodes.index(self.start)
+ same = False
+
+ roots = []
+ if index>0:
+ for start in self.start_nodes[:index]:
+ same = True
+ for edge in self.tree_list[start][1:]:
+ if self.tree_list[self.start].__contains__(edge):
+ continue
+ else:
+ same = False
+ break
+ if same:
+ roots.append(start)
+
+ if roots:
+ min_order += self.max_order
+ else:
+ min_order += self.max_order + 1
+
+ for level in self.levels:
+ for node in self.levels[level]:
+ self.result[node]['y'] += min_order
+
+ if roots:
+ roots.append(self.start)
+ one_level_el = self.tree_list[self.start][0][1]
+ base = self.result[one_level_el]['y']# * 2 / (index + 2)
+
+
+ no = len(roots)
+ first_half = roots[:no/2]
+
+ if no%2==0:
+ last_half = roots[no/2:]
+ else:
+ last_half = roots[no/2+1:]
+
+ factor = -math.floor(no/2)
+ for start in first_half:
+ self.result[start]['y'] = base + factor
+ factor += 1
+
+ if no%2:
+ self.result[roots[no/2]]['y'] = base + factor
+ factor +=1
+
+ for start in last_half:
+ self.result[start]['y'] = base + factor
+ factor += 1
+
+ self.max_order = max(map(lambda x: x['y'], self.result.values()))
+
+ def find_starts(self):
+ """Finds other start nodes of the graph in the case when graph is disconneted
+ """
+ rem_nodes = []
+ for node in self.nodes:
+ if not self.partial_order.get(node):
+ rem_nodes.append(node)
+ cnt = 0
+ while True:
+ if len(rem_nodes)==1:
+ self.start_nodes.append(rem_nodes[0])
+ break
+ else:
+ count = 0
+ new_start = rem_nodes[0]
+ largest_tree = []
+
+ for node in rem_nodes:
+ self.partial_order = {}
+ tree = self.make_acyclic(None, node, 0, [])
+ if len(tree)+1 > count:
+ count = len(tree) + 1
+ new_start = node
+ largest_tree = tree
+ else:
+ if not largest_tree:
+ new_start = rem_nodes[0]
+ rem_nodes.remove(new_start)
+
+ self.start_nodes.append(new_start)
+
+
+ for edge in largest_tree:
+ if rem_nodes.__contains__(edge[0]):
+ rem_nodes.remove(edge[0])
+ if rem_nodes.__contains__(edge[1]):
+ rem_nodes.remove(edge[1])
+
+ if not rem_nodes:
+ break
+
+
+ def rank(self):
+ """Finds the optimized rank of the nodes using Network-simplex algorithm
+
+ @param start: starting node of the component
+ """
+ self.levels = {}
+ self.critical_edges = []
+ self.partial_order = {}
+ self.links = []
+ self.Is_Cyclic = False
+
+ self.tree_list[self.start] = self.make_acyclic(None, self.start, 0, [])
+ self.Is_Cyclic = self.rev_edges(self.tree_list[self.start])
+ self.process_ranking(self.start)
+ self.init_rank()
+
+ #make cut values of all tree edges to 0 to optimize feasible tree
+ e = self.leave_edge()
+
+ while e :
+ f = self.enter_edge(e)
+ if e==f:
+ self.critical_edges.append(e)
+ else:
+ self.exchange(e,f)
+ e = self.leave_edge()
+
+ #finalize rank using optimum feasible tree
+# self.optimal_edges = {}
+# for edge in self.tree_edges:
+# source = self.optimal_edges.setdefault(edge[0], [])
+# source.append(edge[1])
+
+# self.finalize_rank(self.start, 0)
+
+ #normalization
+ self.normalize()
+ for edge in self.edge_wt:
+ self.edge_wt[edge] = self.result[edge[1]]['x'] - self.result[edge[0]]['x']
+
+ def order_in_rank(self):
+ """Finds optimized order of the nodes within their ranks using median heuristic
+
+ @param start: starting node of the component
+ """
+
+ self.make_chain()
+ self.preprocess_order()
+ self.order = {}
+ max_rank = max(map(lambda x: x, self.levels.keys()))
+
+ for i in range(max_rank+1):
+ self.order[i] = 0
+
+ self.init_order(self.start, self.result[self.start]['x'])
+
+ for level in self.levels:
+ self.levels[level].sort(lambda x, y: cmp(self.result[x]['y'], self.result[y]['y']))
+
+ self.order_heuristic()
+ self.process_order()
+
+ def process(self, starting_node):
+ """Process the graph to find ranks and order of the nodes
+
+ @param starting_node: node from where to start the graph search
+ """
+
+ self.start_nodes = starting_node or []
+ self.partial_order = {}
+ self.links = []
+ self.tree_list = {}
+
+ if self.nodes:
+ if self.start_nodes:
+ #add dummy edges to the nodes which does not have any incoming edges
+ tree = self.make_acyclic(None, self.start_nodes[0], 0, [])
+
+ for node in self.no_ancester:
+ for sec_node in self.transitions.get(node, []):
+ if sec_node in self.partial_order.keys():
+ self.transitions[self.start_nodes[0]].append(node)
+ break
+
+ self.partial_order = {}
+ tree = self.make_acyclic(None, self.start_nodes[0], 0, [])
+
+
+ # if graph is disconnected or no start-node is given
+ #than to find starting_node for each component of the node
+ if len(self.nodes) > len(self.partial_order):
+ self.find_starts()
+
+ self.max_order = 0
+ #for each component of the graph find ranks and order of the nodes
+ for s in self.start_nodes:
+ self.start = s
+ self.rank() # First step:Netwoek simplex algorithm
+ self.order_in_rank() #Second step: ordering nodes within ranks
+
+
+ def __str__(self):
+ result = ''
+ for l in self.levels:
+ result += 'PosY: ' + str(l) + '\n'
+ for node in self.levels[l]:
+ result += '\tPosX: '+ str(self.result[node]['y']) + ' - Node:' + str(node) + "\n"
+ return result
+
+
+ def scale(self, maxx, maxy, nwidth=0, nheight=0, margin=20):
+ """Computes actual co-ordiantes of the nodes
+ """
+
+ #for flat edges ie. source an destination nodes are on the same rank
+ for src in self.transitions:
+ for des in self.transitions[src]:
+ if (self.result[des]['x'] - self.result[src]['x'] == 0):
+ self.result[src]['x'] += 0.08
+ self.result[des]['x'] -= 0.08
+
+ factorX = maxx + nheight
+ factorY = maxy + nwidth
+
+ for node in self.result:
+ self.result[node]['y'] = (self.result[node]['y']) * factorX + margin
+ self.result[node]['x'] = (self.result[node]['x']) * factorY + margin
+
+
+ def result_get(self):
+ return self.result