2 # -*- coding: utf-8 -*-
3 ##############################################################################
5 # OpenERP, Open Source Management Solution
6 # Copyright (C) 2004-2009 Tiny SPRL (<http://tiny.be>).
8 # This program is free software: you can redistribute it and/or modify
9 # it under the terms of the GNU Affero General Public License as
10 # published by the Free Software Foundation, either version 3 of the
11 # License, or (at your option) any later version.
13 # This program is distributed in the hope that it will be useful,
14 # but WITHOUT ANY WARRANTY; without even the implied warranty of
15 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 # GNU Affero General Public License for more details.
18 # You should have received a copy of the GNU Affero General Public License
19 # along with this program. If not, see <http://www.gnu.org/licenses/>.
21 ##############################################################################
27 def __init__(self, nodes, transitions, no_ancester=None):
28 """Initailize graph's object
30 @param nodes: list of ids of nodes in the graph
31 @param transitions: list of edges in the graph in the form (source_node, destination_node)
32 @param no_ancester: list of nodes with no incoming edges
35 self.nodes = nodes or []
36 self.edges = transitions or []
37 self.no_ancester = no_ancester or {}
41 trans.setdefault(t[0], [])
42 trans[t[0]].append(t[1])
43 self.transitions = trans
48 """Computes rank of the nodes of the graph by finding initial feasible tree
51 for link in self.links:
52 self.edge_wt[link] = self.result[link[1]]['x'] - self.result[link[0]]['x']
54 tot_node = self.partial_order.__len__()
55 #do until all the nodes in the component are searched
56 while self.tight_tree()<tot_node:
60 for node in self.nodes:
61 if node not in self.reachable_nodes:
62 list_node.append(node)
64 for edge in self.edge_wt:
65 if edge not in self.tree_edges:
66 list_edge.append(edge)
70 for edge in list_edge:
71 if ((self.reachable_nodes.__contains__(edge[0]) and edge[1] not in self.reachable_nodes) or
72 (self.reachable_nodes.__contains__(edge[1]) and edge[0] not in self.reachable_nodes)):
73 if(slack>self.edge_wt[edge]-1):
74 slack = self.edge_wt[edge]-1
77 if new_edge[0] not in self.reachable_nodes:
78 delta = -(self.edge_wt[new_edge]-1)
80 delta = self.edge_wt[new_edge]-1
82 for node in self.result:
83 if node in self.reachable_nodes:
84 self.result[node]['x'] += delta
86 for edge in self.edge_wt:
87 self.edge_wt[edge] = self.result[edge[1]]['x'] - self.result[edge[0]]['x']
93 self.reachable_nodes = []
95 self.reachable_node(self.start)
96 return self.reachable_nodes.__len__()
99 def reachable_node(self, node):
100 """Find the nodes of the graph which are only 1 rank apart from each other
103 if node not in self.reachable_nodes:
104 self.reachable_nodes.append(node)
105 for edge in self.edge_wt:
107 if self.edge_wt[edge]==1:
108 self.tree_edges.append(edge)
109 if edge[1] not in self.reachable_nodes:
110 self.reachable_nodes.append(edge[1])
111 self.reachable_node(edge[1])
114 def init_cutvalues(self):
115 """Initailize cut values of edges of the feasible tree.
116 Edges with negative cut-values are removed from the tree to optimize rank assignment
122 for edge in self.tree_edges:
125 rest_edges += self.tree_edges
126 rest_edges.__delitem__(i)
127 self.head_component(self.start, rest_edges)
131 for source_node in self.transitions:
132 if source_node in self.head_nodes:
133 for dest_node in self.transitions[source_node]:
134 if dest_node not in self.head_nodes:
137 for dest_node in self.transitions[source_node]:
138 if dest_node in self.head_nodes:
141 self.cut_edges[edge] = positive - negative
144 def head_component(self, node, rest_edges):
145 """Find nodes which are reachable from the starting node, after removing an edge
147 if node not in self.head_nodes:
148 self.head_nodes.append(node)
150 for edge in rest_edges:
152 self.head_component(edge[1],rest_edges)
155 def process_ranking(self, node, level=0):
156 """Computes initial feasible ranking after making graph acyclic with depth-first search
159 if node not in self.result:
160 self.result[node] = {'y': None, 'x':level, 'mark':0}
162 if level > self.result[node]['x']:
163 self.result[node]['x'] = level
165 if self.result[node]['mark']==0:
166 self.result[node]['mark'] = 1
167 for sec_end in self.transitions.get(node, []):
168 self.process_ranking(sec_end, level+1)
171 def make_acyclic(self, parent, node, level, tree):
172 """Computes Partial-order of the nodes with depth-first search
175 if node not in self.partial_order:
176 self.partial_order[node] = {'level':level, 'mark':0}
178 tree.append((parent, node))
180 if self.partial_order[node]['mark']==0:
181 self.partial_order[node]['mark'] = 1
182 for sec_end in self.transitions.get(node, []):
183 self.links.append((node, sec_end))
184 self.make_acyclic(node, sec_end, level+1, tree)
189 def rev_edges(self, tree):
190 """reverse the direction of the edges whose source-node-partail_order> destination-node-partail_order
191 to make the graph acyclic
195 for link in self.links:
198 edge_len = self.partial_order[des]['level'] - self.partial_order[src]['level']
200 self.links.__delitem__(i)
201 self.links.insert(i, (des, src))
202 self.transitions[src].remove(des)
203 self.transitions.setdefault(des, []).append(src)
205 elif math.fabs(edge_len) > 1:
211 def exchange(self, e, f):
212 """Exchange edges to make feasible-tree optimized
213 @param edge: edge with negative cut-value
214 @param edge: new edge with minimum slack-value
216 self.tree_edges.__delitem__(self.tree_edges.index(e))
217 self.tree_edges.append(f)
218 self.init_cutvalues()
221 def enter_edge(self, edge):
222 """Finds a new_edge with minimum slack value to replace an edge with negative cut-value
224 @param edge: edge with negative cut-value
229 rest_edges += self.tree_edges
230 rest_edges.__delitem__(rest_edges.index(edge))
231 self.head_component(self.start, rest_edges)
233 if self.head_nodes.__contains__(edge[1]):
235 for node in self.result:
236 if not self.head_nodes.__contains__(node):
242 for source_node in self.transitions:
243 if source_node in self.head_nodes:
244 for dest_node in self.transitions[source_node]:
245 if dest_node not in self.head_nodes:
246 if(slack>(self.edge_wt[edge]-1)):
247 slack = self.edge_wt[edge]-1
248 new_edge = (source_node, dest_node)
253 def leave_edge(self):
254 """Returns the edge with negative cut_value(if exists)
256 if self.critical_edges:
257 for edge in self.critical_edges:
258 self.cut_edges[edge] = 0
260 for edge in self.cut_edges:
261 if self.cut_edges[edge]<0:
267 def finalize_rank(self, node, level):
268 self.result[node]['x'] = level
269 for destination in self.optimal_edges.get(node, []):
270 self.finalize_rank(destination, level+1)
274 """The ranks are normalized by setting the least rank to zero.
277 least_rank = min(map(lambda x: x['x'], self.result.values()))
280 for node in self.result:
281 self.result[node]['x']-=least_rank
284 def make_chain(self):
285 """Edges between nodes more than one rank apart are replaced by chains of unit
286 length edges between temporary nodes.
289 for edge in self.edge_wt:
290 if self.edge_wt[edge]>1:
291 self.transitions[edge[0]].remove(edge[1])
292 start = self.result[edge[0]]['x']
293 end = self.result[edge[1]]['x']
295 for rank in range(start+1, end):
296 if not self.result.get((rank, 'temp'), False):
297 self.result[(rank, 'temp')] = {'y': None, 'x': rank, 'mark': 0}
299 for rank in range(start, end):
301 self.transitions[edge[0]].append((rank+1, 'temp'))
303 self.transitions.setdefault((rank, 'temp'), []).append(edge[1])
305 self.transitions.setdefault((rank, 'temp'), []).append((rank+1, 'temp'))
308 def init_order(self, node, level):
309 """Initialize orders the nodes in each rank with depth-first search
311 if not self.result[node]['y']:
312 self.result[node]['y'] = self.order[level]
313 self.order[level] = self.order[level]+1
315 for sec_end in self.transitions.get(node, []):
316 self.init_order(sec_end, self.result[sec_end]['x'])
319 def order_heuristic(self):
325 """Applies median heuristic to find optimzed order of the nodes with in their ranks
327 for level in self.levels:
330 nodes = self.levels[level]
332 node_median.append((node, self.median_value(node, level-1)))
334 sort_list = sorted(node_median, key=operator.itemgetter(1))
336 new_list = [tuple[0] for tuple in sort_list]
338 self.levels[level] = new_list
341 self.result[node]['y'] = order
345 def median_value(self, node, adj_rank):
346 """Returns median value of a vertex , defined as the median position of the adjacent vertices
348 @param node: node to process
349 @param adj_rank: rank 1 less than the node's rank
351 adj_nodes = self.adj_position(node, adj_rank)
358 return adj_nodes[m]#median of the middle element
360 return (adj_nodes[0]+adj_nodes[1])/2
362 left = adj_nodes[m-1] - adj_nodes[0]
363 right = adj_nodes[l-1] - adj_nodes[m]
364 return ((adj_nodes[m-1]*right) + (adj_nodes[m]*left))/(left+right)
367 def adj_position(self, node, adj_rank):
368 """Returns list of the present positions of the nodes adjacent to node in the given adjacent rank.
370 @param node: node to process
371 @param adj_rank: rank 1 less than the node's rank
374 pre_level_nodes = self.levels.get(adj_rank, [])
378 for src in pre_level_nodes:
379 if (self.transitions.get(src) and self.transitions[src].__contains__(node)):
380 adj_nodes.append(self.result[src]['y'])
385 def preprocess_order(self):
388 for r in self.partial_order:
389 l = self.result[r]['x']
390 levels.setdefault(l,[])
396 def graph_order(self):
397 """Finds actual-order of the nodes with respect to maximum number of nodes in a rank in component
400 max_level = max(map(lambda x: len(x), self.levels.values()))
402 for level in self.levels:
404 no = len(self.levels[level])
405 factor = (max_level - no) * 0.10
406 list = self.levels[level]
410 first_half = list[no/2:]
413 first_half = list[no/2+1:]
414 if max_level==1:#for the case when horizontal graph is there
415 self.result[list[no/2]]['y'] = mid_pos + (self.result[list[no/2]]['x']%2 * 0.5)
417 self.result[list[no/2]]['y'] = mid_pos + factor
419 last_half = list[:no/2]
422 for node in first_half:
423 self.result[node]['y'] = mid_pos - (i + factor)
427 for node in last_half:
428 self.result[node]['y'] = mid_pos + (i + factor)
431 self.max_order += max_level+1
432 mid_pos = self.result[self.start]['y']
435 def tree_order(self, node, last=0):
436 mid_pos = self.result[node]['y']
437 l = self.transitions.get(node, [])
442 first_half = l[no/2:]
445 first_half = l[no/2+1:]
451 for child in first_half:
452 self.result[child]['y'] = mid_pos - (i - (factor * 0.5))
455 if self.transitions.get(child, False):
457 self.result[child]['y'] = last + len(self.transitions[child])/2 + 1
458 last = self.tree_order(child, last)
462 self.result[mid_node]['y'] = mid_pos
464 if self.transitions.get((mid_node), False):
466 self.result[mid_node]['y'] = last + len(self.transitions[mid_node])/2 + 1
467 last = self.tree_order(mid_node)
470 self.result[mid_node]['y'] = last + 1
471 self.result[node]['y'] = self.result[mid_node]['y']
472 mid_pos = self.result[node]['y']
476 for child in last_half:
477 self.result[child]['y'] = mid_pos + (i - (factor * 0.5))
480 if self.transitions.get(child, False):
482 self.result[child]['y'] = last + len(self.transitions[child])/2 + 1
483 last = self.tree_order(child, last)
486 last = self.result[last_child]['y']
491 def process_order(self):
492 """Finds actual-order of the nodes with respect to maximum number of nodes in a rank in component
496 max_level = max(map(lambda x: len(x), self.levels.values()))
499 self.result[self.start]['y'] = (max_level+1)/2 + self.max_order + (self.max_order and 1)
501 self.result[self.start]['y'] = (max_level)/2 + self.max_order + (self.max_order and 1)
506 self.result[self.start]['y'] = 0
507 self.tree_order(self.start, 0)
508 min_order = math.fabs(min(map(lambda x: x['y'], self.result.values())))
510 index = self.start_nodes.index(self.start)
515 for start in self.start_nodes[:index]:
517 for edge in self.tree_list[start][1:]:
518 if self.tree_list[self.start].__contains__(edge):
527 min_order += self.max_order
529 min_order += self.max_order + 1
531 for level in self.levels:
532 for node in self.levels[level]:
533 self.result[node]['y'] += min_order
536 roots.append(self.start)
537 one_level_el = self.tree_list[self.start][0][1]
538 base = self.result[one_level_el]['y']# * 2 / (index + 2)
542 first_half = roots[:no/2]
545 last_half = roots[no/2:]
547 last_half = roots[no/2+1:]
549 factor = -math.floor(no/2)
550 for start in first_half:
551 self.result[start]['y'] = base + factor
555 self.result[roots[no/2]]['y'] = base + factor
558 for start in last_half:
559 self.result[start]['y'] = base + factor
562 self.max_order = max(map(lambda x: x['y'], self.result.values()))
564 def find_starts(self):
565 """Finds other start nodes of the graph in the case when graph is disconneted
568 for node in self.nodes:
569 if not self.partial_order.get(node):
570 rem_nodes.append(node)
573 if len(rem_nodes)==1:
574 self.start_nodes.append(rem_nodes[0])
578 new_start = rem_nodes[0]
581 for node in rem_nodes:
582 self.partial_order = {}
583 tree = self.make_acyclic(None, node, 0, [])
584 if len(tree)+1 > count:
585 count = len(tree) + 1
590 new_start = rem_nodes[0]
591 rem_nodes.remove(new_start)
593 self.start_nodes.append(new_start)
596 for edge in largest_tree:
597 if rem_nodes.__contains__(edge[0]):
598 rem_nodes.remove(edge[0])
599 if rem_nodes.__contains__(edge[1]):
600 rem_nodes.remove(edge[1])
607 """Finds the optimized rank of the nodes using Network-simplex algorithm
609 @param start: starting node of the component
612 self.critical_edges = []
613 self.partial_order = {}
615 self.Is_Cyclic = False
617 self.tree_list[self.start] = self.make_acyclic(None, self.start, 0, [])
618 self.Is_Cyclic = self.rev_edges(self.tree_list[self.start])
619 self.process_ranking(self.start)
622 #make cut values of all tree edges to 0 to optimize feasible tree
623 e = self.leave_edge()
626 f = self.enter_edge(e)
628 self.critical_edges.append(e)
631 e = self.leave_edge()
633 #finalize rank using optimum feasible tree
634 # self.optimal_edges = {}
635 # for edge in self.tree_edges:
636 # source = self.optimal_edges.setdefault(edge[0], [])
637 # source.append(edge[1])
639 # self.finalize_rank(self.start, 0)
643 for edge in self.edge_wt:
644 self.edge_wt[edge] = self.result[edge[1]]['x'] - self.result[edge[0]]['x']
646 def order_in_rank(self):
647 """Finds optimized order of the nodes within their ranks using median heuristic
649 @param start: starting node of the component
653 self.preprocess_order()
655 max_rank = max(map(lambda x: x, self.levels.keys()))
657 for i in range(max_rank+1):
660 self.init_order(self.start, self.result[self.start]['x'])
662 for level in self.levels:
663 self.levels[level].sort(lambda x, y: cmp(self.result[x]['y'], self.result[y]['y']))
665 self.order_heuristic()
668 def process(self, starting_node):
669 """Process the graph to find ranks and order of the nodes
671 @param starting_node: node from where to start the graph search
674 self.start_nodes = starting_node or []
675 self.partial_order = {}
681 #add dummy edges to the nodes which does not have any incoming edges
682 tree = self.make_acyclic(None, self.start_nodes[0], 0, [])
684 for node in self.no_ancester:
685 for sec_node in self.transitions.get(node, []):
686 if sec_node in self.partial_order.keys():
687 self.transitions[self.start_nodes[0]].append(node)
690 self.partial_order = {}
691 tree = self.make_acyclic(None, self.start_nodes[0], 0, [])
694 # if graph is disconnected or no start-node is given
695 #than to find starting_node for each component of the node
696 if len(self.nodes) > len(self.partial_order):
700 #for each component of the graph find ranks and order of the nodes
701 for s in self.start_nodes:
703 self.rank() # First step:Netwoek simplex algorithm
704 self.order_in_rank() #Second step: ordering nodes within ranks
709 for l in self.levels:
710 result += 'PosY: ' + str(l) + '\n'
711 for node in self.levels[l]:
712 result += '\tPosX: '+ str(self.result[node]['y']) + ' - Node:' + node + "\n"
716 def scale(self, maxx, maxy, nwidth=0, nheight=0, margin=20):
717 """Computes actual co-ordiantes of the nodes
720 #for flat edges ie. source an destination nodes are on the same rank
721 for src in self.transitions:
722 for des in self.transitions[src]:
723 if (self.result[des]['x'] - self.result[src]['x'] == 0):
724 self.result[src]['x'] += 0.08
725 self.result[des]['x'] -= 0.08
727 factorX = maxx + nheight
728 factorY = maxy + nwidth
730 for node in self.result:
731 self.result[node]['y'] = (self.result[node]['y']) * factorX + margin
732 self.result[node]['x'] = (self.result[node]['x']) * factorY + margin
735 def result_get(self):
738 if __name__=='__main__':
739 starting_node = ['profile'] # put here nodes with flow_start=True
740 nodes = ['project','account','hr','base','product','mrp','test','profile']
744 ('project','product'),
747 ('project','account'),
750 ('account','product'),
758 g = graph(nodes, transitions)
759 g.process(starting_node)
760 g.scale(radius*3,radius*3, radius, radius)
764 img = Image.new("RGB", (800, 600), "#ffffff")
765 draw = ImageDraw.Draw(img)
767 result = g.result_get()
770 node_res[node] = result[node]
772 for name,node in node_res.items():
774 draw.arc( (int(node['y']-radius), int(node['x']-radius),int(node['y']+radius), int(node['x']+radius) ), 0, 360, (128,128,128))
775 draw.text( (int(node['y']), int(node['x'])), name, (128,128,128))
778 for t in transitions:
779 draw.line( (int(node_res[t[0]]['y']), int(node_res[t[0]]['x']),int(node_res[t[1]]['y']),int(node_res[t[1]]['x'])),(128,128,128) )
780 img.save("graph.png", "PNG")
783 # vim:expandtab:smartindent:tabstop=4:softtabstop=4:shiftwidth=4: