I'm in the search for an implementation of an ear-decomposition algorithm (http://www.ics.uci.edu/~eppstein/junkyard/euler/ear.html). I examined networkx and didn't find one. Although the algorithm layout is vaguely in my mind, I'd like to see some reference implementation, too.
I'm aware of Ulrik Brandes publication on a linear time Eager st-ordering algorithm, which results in an ear decomposition as a side product, if I understand correctly (it even includes pseudocode, which I'm trying to base my implementation on).
Side problem: First step could be an st-ordering of a graph. Are there any implementations for st-ordering algorithms you know?
Thanks for your input. I'd really like to contribute e.g. to networkx by implementing the ear-decomposi开发者_如何学Pythontion algorithm in python.
I dug this up, but the credit goes to it's author Minjae Park
# 20106911 Minjae Park
# Finding an Ear decomposition of 2(-edge)-connected graph
import networkx as nx
import matplotlib.pyplot as plt
colorList = ["orange", "blue", "red", "green", "magenta", "purple", "yellow", "black"]
global count
count=0
'''
Input Graph
'''
# Complete Graph
#G=nx.complete_graph(6)
'''
# Non 2-connected (but 2-edge-connected) Graph
G=nx.Graph()
G.add_edge(0,1)
G.add_edge(1,2)
G.add_edge(2,0)
G.add_edge(2,3)
G.add_edge(3,4)
G.add_edge(4,5)
G.add_edge(5,3)
G.add_edge(4,2)
'''
# Petersen Graph
G=nx.petersen_graph()
'''
Testing 2-edge-connectivity
'''
for e in G.edges():
H=nx.Graph(G)
G.remove_edge(*e)
if not nx.is_connected(G):
raise SystemExit("G is not 2-edge-connected. This algorithm is not valid.")
G=H
'''
Testing 2-connectivity
'''
for v in G.nodes():
H=nx.Graph(G)
G.remove_node(v)
if not nx.is_connected(G):
print "G is not 2-connected. The result is not an open ear decomposition."
G=H
'''
Algorithm for Finding an Ear Decomposition
'''
def makeSpanningTree(G,root):
T=nx.Graph()
T.add_node(root)
T.node[root]['dfsnum']=len(T.nodes())
makeSpanningTreeDFS(G,T,root)
return T
def makeSpanningTreeDFS(G,T,current):
if not 'child' in T.node[current]:
T.node[current]['child']=[]
for neighbor in G.neighbors(current):
if not neighbor in T.nodes():
T.add_node(neighbor)
T.add_edge(current,neighbor)
T.node[neighbor]['dfsnum']=len(T.nodes())
T.node[neighbor]['parent']=current
T.node[current]['child'].append(neighbor)
makeSpanningTreeDFS(G,T,neighbor)
def assignNonTreeEdgeLabel(G,T,current):
global count
subrootdfsnum=T.nodes(data=True)[current][1]['dfsnum']
for node,nodeattr in T.nodes(data=True):
if nodeattr['dfsnum']>subrootdfsnum:
if ((current,node) in G.edges() or (node,current) in G.edges()) and not ((current,node) in T.edges() or (node,current) in T.edges()):
G[current][node]['label']=count
count+=1
for neighbor in T.nodes(data=True)[current][1]['child']:
assignNonTreeEdgeLabel(G,T,neighbor)
def assignTreeEdgeLabel(G,T,current):
if not T.nodes(data=True)[current][1]['child']:
label=[]
for neighbor in G.neighbors(current):
if 'label' in G[current][neighbor]:
label.append(G[current][neighbor]['label'])
if 'parent' in T.node[current]:
parent=T.node[current]['parent']
G[current][parent]['label']=min(label)
else:
for neighbor in T.nodes(data=True)[current][1]['child']:
if not 'label' in T.node[neighbor]:
assignTreeEdgeLabel(G,T,neighbor)
if 'parent' in T.node[current]:
parent=T.node[current]['parent']
label=[]
for neighbor in G.neighbors(current):
if 'label' in G[current][neighbor]:
label.append(G[current][neighbor]['label'])
G[current][parent]['label']=min(label)
T=makeSpanningTree(G,0)
assignNonTreeEdgeLabel(G,T,0)
assignTreeEdgeLabel(G,T,0)
'''
Output
'''
pos=nx.circular_layout(G)
ear_list=[[] for i in range(count+1)]
for (x,y) in G.edges():
ear=G[x][y]['label']
ear_list[ear].append((x,y))
nx.draw_networkx_nodes(G,pos)
nx.draw_networkx_labels(G,pos)
for i in range(len(ear_list)):
nx.draw_networkx_edges(G,pos,edgelist=ear_list[i],edge_color=colorList[i%len(colorList)],alpha=0.5,width=3)
nx.draw_networkx_edge_labels(G,pos,alpha=0.5)
plt.show()
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