777 lines
26 KiB
Python
Executable File
777 lines
26 KiB
Python
Executable File
#!/usr/bin/env python
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# -*- coding: utf-8 -*-
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##############################################################################
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#
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# OpenERP, Open Source Management Solution
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# Copyright (C) 2004-2009 Tiny SPRL (<http://tiny.be>).
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#
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# This program is free software: you can redistribute it and/or modify
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# it under the terms of the GNU Affero General Public License as
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# published by the Free Software Foundation, either version 3 of the
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# License, or (at your option) any later version.
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#
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# This program is distributed in the hope that it will be useful,
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# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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# GNU Affero General Public License for more details.
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#
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# You should have received a copy of the GNU Affero General Public License
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# along with this program. If not, see <http://www.gnu.org/licenses/>.
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#
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##############################################################################
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import operator
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import math
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class graph(object):
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def __init__(self, nodes, transitions, no_ancester=None):
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"""Initialize graph's object
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@param nodes list of ids of nodes in the graph
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@param transitions list of edges in the graph in the form (source_node, destination_node)
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@param no_ancester list of nodes with no incoming edges
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"""
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self.nodes = nodes or []
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self.edges = transitions or []
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self.no_ancester = no_ancester or {}
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trans = {}
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for t in transitions:
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trans.setdefault(t[0], [])
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trans[t[0]].append(t[1])
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self.transitions = trans
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self.result = {}
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def init_rank(self):
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"""Computes rank of the nodes of the graph by finding initial feasible tree
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"""
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self.edge_wt = {}
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for link in self.links:
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self.edge_wt[link] = self.result[link[1]]['x'] - self.result[link[0]]['x']
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tot_node = len(self.partial_order)
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#do until all the nodes in the component are searched
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while self.tight_tree()<tot_node:
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list_node = []
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list_edge = []
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for node in self.nodes:
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if node not in self.reachable_nodes:
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list_node.append(node)
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for edge in self.edge_wt:
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if edge not in self.tree_edges:
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list_edge.append(edge)
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slack = 100
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for edge in list_edge:
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if ((edge[0] in self.reachable_nodes and edge[1] not in self.reachable_nodes) or
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(edge[1] in self.reachable_nodes and edge[0] not in self.reachable_nodes)):
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if slack > self.edge_wt[edge]-1:
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slack = self.edge_wt[edge]-1
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new_edge = edge
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if new_edge[0] not in self.reachable_nodes:
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delta = -(self.edge_wt[new_edge]-1)
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else:
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delta = self.edge_wt[new_edge]-1
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for node in self.result:
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if node in self.reachable_nodes:
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self.result[node]['x'] += delta
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for edge in self.edge_wt:
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self.edge_wt[edge] = self.result[edge[1]]['x'] - self.result[edge[0]]['x']
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self.init_cutvalues()
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def tight_tree(self):
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self.reachable_nodes = []
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self.tree_edges = []
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self.reachable_node(self.start)
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return len(self.reachable_nodes)
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def reachable_node(self, node):
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"""Find the nodes of the graph which are only 1 rank apart from each other
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"""
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if node not in self.reachable_nodes:
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self.reachable_nodes.append(node)
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for edge in self.edge_wt:
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if edge[0]==node:
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if self.edge_wt[edge]==1:
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self.tree_edges.append(edge)
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if edge[1] not in self.reachable_nodes:
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self.reachable_nodes.append(edge[1])
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self.reachable_node(edge[1])
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def init_cutvalues(self):
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"""Initailize cut values of edges of the feasible tree.
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Edges with negative cut-values are removed from the tree to optimize rank assignment
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"""
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self.cut_edges = {}
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self.head_nodes = []
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i=0
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for edge in self.tree_edges:
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self.head_nodes = []
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rest_edges = []
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rest_edges += self.tree_edges
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del rest_edges[i]
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self.head_component(self.start, rest_edges)
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i+=1
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positive = 0
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negative = 0
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for source_node in self.transitions:
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if source_node in self.head_nodes:
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for dest_node in self.transitions[source_node]:
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if dest_node not in self.head_nodes:
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negative+=1
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else:
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for dest_node in self.transitions[source_node]:
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if dest_node in self.head_nodes:
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positive+=1
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self.cut_edges[edge] = positive - negative
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def head_component(self, node, rest_edges):
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"""Find nodes which are reachable from the starting node, after removing an edge
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"""
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if node not in self.head_nodes:
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self.head_nodes.append(node)
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for edge in rest_edges:
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if edge[0]==node:
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self.head_component(edge[1],rest_edges)
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def process_ranking(self, node, level=0):
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"""Computes initial feasible ranking after making graph acyclic with depth-first search
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"""
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if node not in self.result:
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self.result[node] = {'y': None, 'x':level, 'mark':0}
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else:
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if level > self.result[node]['x']:
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self.result[node]['x'] = level
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if self.result[node]['mark']==0:
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self.result[node]['mark'] = 1
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for sec_end in self.transitions.get(node, []):
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self.process_ranking(sec_end, level+1)
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def make_acyclic(self, parent, node, level, tree):
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"""Computes Partial-order of the nodes with depth-first search
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"""
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if node not in self.partial_order:
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self.partial_order[node] = {'level':level, 'mark':0}
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if parent:
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tree.append((parent, node))
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if self.partial_order[node]['mark']==0:
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self.partial_order[node]['mark'] = 1
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for sec_end in self.transitions.get(node, []):
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self.links.append((node, sec_end))
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self.make_acyclic(node, sec_end, level+1, tree)
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return tree
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def rev_edges(self, tree):
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"""reverse the direction of the edges whose source-node-partail_order> destination-node-partail_order
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to make the graph acyclic
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"""
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Is_Cyclic = False
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i=0
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for link in self.links:
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src = link[0]
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des = link[1]
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edge_len = self.partial_order[des]['level'] - self.partial_order[src]['level']
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if edge_len < 0:
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del self.links[i]
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self.links.insert(i, (des, src))
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self.transitions[src].remove(des)
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self.transitions.setdefault(des, []).append(src)
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Is_Cyclic = True
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elif math.fabs(edge_len) > 1:
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Is_Cyclic = True
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i += 1
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return Is_Cyclic
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def exchange(self, e, f):
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"""Exchange edges to make feasible-tree optimized
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:param e: edge with negative cut-value
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:param f: new edge with minimum slack-value
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"""
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del self.tree_edges[self.tree_edges.index(e)]
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self.tree_edges.append(f)
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self.init_cutvalues()
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def enter_edge(self, edge):
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"""Finds a new_edge with minimum slack value to replace an edge with negative cut-value
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@param edge edge with negative cut-value
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"""
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self.head_nodes = []
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rest_edges = []
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rest_edges += self.tree_edges
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del rest_edges[rest_edges.index(edge)]
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self.head_component(self.start, rest_edges)
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if edge[1] in self.head_nodes:
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l = []
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for node in self.result:
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if node not in self.head_nodes:
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l.append(node)
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self.head_nodes = l
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slack = 100
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new_edge = edge
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for source_node in self.transitions:
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if source_node in self.head_nodes:
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for dest_node in self.transitions[source_node]:
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if dest_node not in self.head_nodes:
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if slack>(self.edge_wt[edge]-1):
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slack = self.edge_wt[edge]-1
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new_edge = (source_node, dest_node)
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return new_edge
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def leave_edge(self):
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"""Returns the edge with negative cut_value(if exists)
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"""
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if self.critical_edges:
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for edge in self.critical_edges:
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self.cut_edges[edge] = 0
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for edge in self.cut_edges:
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if self.cut_edges[edge]<0:
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return edge
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return None
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def finalize_rank(self, node, level):
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self.result[node]['x'] = level
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for destination in self.optimal_edges.get(node, []):
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self.finalize_rank(destination, level+1)
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def normalize(self):
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"""The ranks are normalized by setting the least rank to zero.
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"""
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least_rank = min(map(lambda x: x['x'], self.result.values()))
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if least_rank!=0:
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for node in self.result:
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self.result[node]['x']-=least_rank
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def make_chain(self):
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"""Edges between nodes more than one rank apart are replaced by chains of unit
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length edges between temporary nodes.
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"""
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for edge in self.edge_wt:
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if self.edge_wt[edge]>1:
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self.transitions[edge[0]].remove(edge[1])
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start = self.result[edge[0]]['x']
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end = self.result[edge[1]]['x']
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for rank in range(start+1, end):
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if not self.result.get((rank, 'temp'), False):
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self.result[(rank, 'temp')] = {'y': None, 'x': rank, 'mark': 0}
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for rank in range(start, end):
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if start==rank:
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self.transitions[edge[0]].append((rank+1, 'temp'))
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elif rank==end-1:
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self.transitions.setdefault((rank, 'temp'), []).append(edge[1])
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else:
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self.transitions.setdefault((rank, 'temp'), []).append((rank+1, 'temp'))
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def init_order(self, node, level):
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"""Initialize orders the nodes in each rank with depth-first search
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"""
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if not self.result[node]['y']:
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self.result[node]['y'] = self.order[level]
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self.order[level] += 1
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for sec_end in self.transitions.get(node, []):
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if node!=sec_end:
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self.init_order(sec_end, self.result[sec_end]['x'])
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def order_heuristic(self):
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for i in range(12):
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self.wmedian()
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def wmedian(self):
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"""Applies median heuristic to find optimzed order of the nodes with in their ranks
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"""
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for level in self.levels:
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node_median = []
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nodes = self.levels[level]
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for node in nodes:
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node_median.append((node, self.median_value(node, level-1)))
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sort_list = sorted(node_median, key=operator.itemgetter(1))
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new_list = [tuple[0] for tuple in sort_list]
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self.levels[level] = new_list
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order = 0
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for node in nodes:
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self.result[node]['y'] = order
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order +=1
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def median_value(self, node, adj_rank):
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"""Returns median value of a vertex , defined as the median position of the adjacent vertices
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@param node node to process
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@param adj_rank rank 1 less than the node's rank
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"""
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adj_nodes = self.adj_position(node, adj_rank)
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l = len(adj_nodes)
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m = l/2
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if l==0:
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return -1.0
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elif l%2 == 1:
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return adj_nodes[m]#median of the middle element
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elif l==2:
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return (adj_nodes[0]+adj_nodes[1])/2
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else:
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left = adj_nodes[m-1] - adj_nodes[0]
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right = adj_nodes[l-1] - adj_nodes[m]
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return ((adj_nodes[m-1]*right) + (adj_nodes[m]*left))/(left+right)
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def adj_position(self, node, adj_rank):
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"""Returns list of the present positions of the nodes adjacent to node in the given adjacent rank.
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@param node node to process
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@param adj_rank rank 1 less than the node's rank
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"""
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pre_level_nodes = self.levels.get(adj_rank, [])
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adj_nodes = []
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if pre_level_nodes:
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for src in pre_level_nodes:
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if self.transitions.get(src) and node in self.transitions[src]:
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adj_nodes.append(self.result[src]['y'])
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return adj_nodes
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def preprocess_order(self):
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levels = {}
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for r in self.partial_order:
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l = self.result[r]['x']
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levels.setdefault(l,[])
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levels[l].append(r)
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self.levels = levels
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def graph_order(self):
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"""Finds actual-order of the nodes with respect to maximum number of nodes in a rank in component
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"""
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mid_pos = 0.0
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max_level = max(map(lambda x: len(x), self.levels.values()))
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for level in self.levels:
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if level:
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no = len(self.levels[level])
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factor = (max_level - no) * 0.10
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list = self.levels[level]
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list.reverse()
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if no%2==0:
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first_half = list[no/2:]
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factor = -factor
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else:
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first_half = list[no/2+1:]
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if max_level==1:#for the case when horizontal graph is there
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self.result[list[no/2]]['y'] = mid_pos + (self.result[list[no/2]]['x']%2 * 0.5)
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else:
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self.result[list[no/2]]['y'] = mid_pos + factor
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last_half = list[:no/2]
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i=1
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for node in first_half:
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self.result[node]['y'] = mid_pos - (i + factor)
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i += 1
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i=1
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for node in last_half:
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self.result[node]['y'] = mid_pos + (i + factor)
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i += 1
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else:
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self.max_order += max_level+1
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mid_pos = self.result[self.start]['y']
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def tree_order(self, node, last=0):
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mid_pos = self.result[node]['y']
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l = self.transitions.get(node, [])
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l.reverse()
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no = len(l)
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rest = no%2
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first_half = l[no/2+rest:]
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last_half = l[:no/2]
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for i, child in enumerate(first_half):
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self.result[child]['y'] = mid_pos - (i+1 - (0 if rest else 0.5))
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if self.transitions.get(child, False):
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if last:
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self.result[child]['y'] = last + len(self.transitions[child])/2 + 1
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last = self.tree_order(child, last)
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if rest:
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mid_node = l[no/2]
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self.result[mid_node]['y'] = mid_pos
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if self.transitions.get(mid_node, False):
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if last:
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self.result[mid_node]['y'] = last + len(self.transitions[mid_node])/2 + 1
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if node!=mid_node:
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last = self.tree_order(mid_node)
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else:
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if last:
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self.result[mid_node]['y'] = last + 1
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self.result[node]['y'] = self.result[mid_node]['y']
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mid_pos = self.result[node]['y']
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i=1
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last_child = None
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for child in last_half:
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self.result[child]['y'] = mid_pos + (i - (0 if rest else 0.5))
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last_child = child
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i += 1
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if self.transitions.get(child, False):
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if last:
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self.result[child]['y'] = last + len(self.transitions[child])/2 + 1
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if node!=child:
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last = self.tree_order(child, last)
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if last_child:
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last = self.result[last_child]['y']
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return last
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def process_order(self):
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"""Finds actual-order of the nodes with respect to maximum number of nodes in a rank in component
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"""
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if self.Is_Cyclic:
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max_level = max(map(lambda x: len(x), self.levels.values()))
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if max_level%2:
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self.result[self.start]['y'] = (max_level+1)/2 + self.max_order + (self.max_order and 1)
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else:
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self.result[self.start]['y'] = max_level /2 + self.max_order + (self.max_order and 1)
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self.graph_order()
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else:
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self.result[self.start]['y'] = 0
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self.tree_order(self.start, 0)
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min_order = math.fabs(min(map(lambda x: x['y'], self.result.values())))
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index = self.start_nodes.index(self.start)
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same = False
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roots = []
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if index>0:
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for start in self.start_nodes[:index]:
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same = True
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for edge in self.tree_list[start][1:]:
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if edge in self.tree_list[self.start]:
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continue
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else:
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same = False
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break
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if same:
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roots.append(start)
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if roots:
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min_order += self.max_order
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else:
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min_order += self.max_order + 1
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for level in self.levels:
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for node in self.levels[level]:
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self.result[node]['y'] += min_order
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if roots:
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roots.append(self.start)
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one_level_el = self.tree_list[self.start][0][1]
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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 edge[0] in rem_nodes:
|
|
rem_nodes.remove(edge[0])
|
|
if edge[1] in rem_nodes:
|
|
rem_nodes.remove(edge[1])
|
|
|
|
if not rem_nodes:
|
|
break
|
|
|
|
|
|
def rank(self):
|
|
"""Finds the optimized rank of the nodes using Network-simplex algorithm
|
|
"""
|
|
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
|
|
"""
|
|
|
|
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
|
|
|
|
if __name__=='__main__':
|
|
starting_node = ['profile'] # put here nodes with flow_start=True
|
|
nodes = ['project','account','hr','base','product','mrp','test','profile']
|
|
transitions = [
|
|
('profile','mrp'),
|
|
('mrp','project'),
|
|
('project','product'),
|
|
('mrp','hr'),
|
|
('mrp','test'),
|
|
('project','account'),
|
|
('project','hr'),
|
|
('product','base'),
|
|
('account','product'),
|
|
('account','test'),
|
|
('account','base'),
|
|
('hr','base'),
|
|
('test','base')
|
|
]
|
|
|
|
radius = 20
|
|
g = graph(nodes, transitions)
|
|
g.process(starting_node)
|
|
g.scale(radius*3,radius*3, radius, radius)
|
|
|
|
from PIL import Image
|
|
from PIL import ImageDraw
|
|
img = Image.new("RGB", (800, 600), "#ffffff")
|
|
draw = ImageDraw.Draw(img)
|
|
|
|
result = g.result_get()
|
|
node_res = {}
|
|
for node in nodes:
|
|
node_res[node] = result[node]
|
|
|
|
for name,node in node_res.items():
|
|
|
|
draw.arc( (int(node['y']-radius), int(node['x']-radius),int(node['y']+radius), int(node['x']+radius) ), 0, 360, (128,128,128))
|
|
draw.text( (int(node['y']), int(node['x'])), str(name), (128,128,128))
|
|
|
|
|
|
for t in transitions:
|
|
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) )
|
|
img.save("graph.png", "PNG")
|
|
|
|
|
|
# vim:expandtab:smartindent:tabstop=4:softtabstop=4:shiftwidth=4:
|
|
|