def test_3prism(self):
N = 6
G = Graph(N, False)
edges = [
Edge(0, 1),
Edge(1, 2),
Edge(2, 3),
Edge(3, 4),
Edge(4, 5),
Edge(0, 5),
Edge(1, 4),
Edge(2, 0),
Edge(3, 5)
]
for node in range(N):
G.add_node(node)
for edge in edges:
G.add_edge(edge)
#print "3prism"
algorithm = HalinNodeColoring(G, outer=set([0, 2, 3, 5]))
#algorithm = HalinNodeColoring(G, outer=set([0, 1, 4, 5]))
#algorithm = HalinNodeColoring(G, outer=set([1, 2, 3, 4]))
algorithm.run()
#print "3prism outer", algorithm.outer
parent = {0: 1, 1: None, 2: 1, 3: 4, 4: 1, 5: 4}
self.assertEqual(algorithm.parent, parent)
for node in G.iternodes():
self.assertNotEqual(algorithm.color[node], None)
for edge in G.iteredges():
self.assertNotEqual(algorithm.color[edge.source],
algorithm.color[edge.target])
all_colors = set(algorithm.color[node] for node in G.iternodes())
self.assertEqual(len(all_colors), 3)
def test_wheel5(self):
N = 5
G = Graph(N, False)
edges = [
Edge(0, 1),
Edge(0, 2),
Edge(0, 3),
Edge(0, 4),
Edge(1, 2),
Edge(2, 3),
Edge(3, 4),
Edge(4, 1)
]
for node in range(N):
G.add_node(node)
for edge in edges:
G.add_edge(edge)
algorithm = HalinNodeColoring(G, outer=set([1, 2, 3, 4]))
algorithm.run()
#print "wheel5 outer", algorithm.outer
#print "wheel5 cycle", algorithm.cycle
parent = {0: None, 1: 0, 2: 0, 3: 0, 4: 0}
self.assertEqual(algorithm.parent, parent)
for node in G.iternodes():
self.assertNotEqual(algorithm.color[node], None)
for edge in G.iteredges():
self.assertNotEqual(algorithm.color[edge.source],
algorithm.color[edge.target])
all_colors = set(algorithm.color[node] for node in G.iternodes())
self.assertEqual(len(all_colors), 3)
def test_halin16(self):
N = 16
G = Graph(N, False)
edges = [Edge(0, 1), Edge(0, 2), Edge(0, 15), Edge(1, 2),
Edge(1, 6), Edge(2, 3), Edge(3, 4), Edge(3, 5),
Edge(4, 5), Edge(4, 10), Edge(5, 6), Edge(6, 7),
Edge(7, 8), Edge(7, 15), Edge(8, 9), Edge(8, 13),
Edge(9, 10), Edge(9, 11), Edge(10, 11), Edge(11, 12),
Edge(12, 13), Edge(12, 14), Edge(13, 14), Edge(14, 15)]
for node in range(N):
G.add_node(node)
for edge in edges:
G.add_edge(edge)
#print "halin16"
algorithm = HalinNodeColoring(G, outer=set([0, 2, 3, 4, 10, 11, 12, 14, 15]))
algorithm.run()
#print "halin16 outer", algorithm.outer
parent = {0: 1, 1: None, 2: 1, 3: 5, 4: 5, 5: 6, 6: 1, 7: 6,
8: 7, 9: 8, 10: 9, 11: 9, 12: 13, 13: 8, 14: 13, 15: 7}
self.assertEqual(algorithm.parent, parent)
for node in G.iternodes():
self.assertNotEqual(algorithm.color[node], None)
for edge in G.iteredges():
self.assertNotEqual(algorithm.color[edge.source],
algorithm.color[edge.target])
all_colors = set(algorithm.color[node] for node in G.iternodes())
self.assertEqual(len(all_colors), 3)
def test_halin8c(self):
N = 8
G = Graph(N, False)
edges = [
Edge(0, 1),
Edge(0, 5),
Edge(0, 7),
Edge(1, 2),
Edge(1, 7),
Edge(2, 3),
Edge(2, 6),
Edge(3, 4),
Edge(3, 6),
Edge(4, 5),
Edge(4, 6),
Edge(5, 6),
Edge(6, 7)
]
for node in range(N):
G.add_node(node)
for edge in edges:
G.add_edge(edge)
algorithm = HalinNodeColoring(G, outer=set([0, 1, 2, 3, 4, 5]))
algorithm.run()
#print "halin8c outer", algorithm.outer
parent = {0: 7, 1: 7, 2: 6, 3: 6, 4: 6, 5: 6, 6: None, 7: 6}
self.assertEqual(algorithm.parent, parent)
for node in G.iternodes():
self.assertNotEqual(algorithm.color[node], None)
for edge in G.iteredges():
self.assertNotEqual(algorithm.color[edge.source],
algorithm.color[edge.target])
all_colors = set(algorithm.color[node] for node in G.iternodes())
self.assertEqual(len(all_colors), 3)
def test_frucht12(self):
N = 10
G = Graph(N, False)
edges = [Edge(0, 1), Edge(0, 4), Edge(0, 11), Edge(1, 2),
Edge(1, 10), Edge(2, 3), Edge(2, 7), Edge(3, 4),
Edge(3, 5), Edge(4, 5), Edge(5, 6), Edge(6, 7),
Edge(6, 8), Edge(7, 8), Edge(8, 9), Edge(9, 10),
Edge(9, 11), Edge(10, 11)]
for node in range(N):
G.add_node(node)
for edge in edges:
G.add_edge(edge)
#print "frucht12"
algorithm = HalinNodeColoring(G, outer=set([0, 4, 5, 6, 8, 9, 11]))
algorithm.run()
#print "frucht12 outer", algorithm.outer
parent = {0: 1, 1: None, 2: 1, 3: 2, 4: 3, 5: 3, 6: 7, 7: 2, 8: 7, 9: 10, 10: 1, 11: 10}
self.assertEqual(algorithm.parent, parent)
for node in G.iternodes():
self.assertNotEqual(algorithm.color[node], None)
for edge in G.iteredges():
self.assertNotEqual(algorithm.color[edge.source],
algorithm.color[edge.target])
all_colors = set(algorithm.color[node] for node in G.iternodes())
self.assertEqual(len(all_colors), 3)
def test_frucht12(self):
N = 10
G = Graph(N, False)
edges = [
Edge(0, 1),
Edge(0, 4),
Edge(0, 11),
Edge(1, 2),
Edge(1, 10),
Edge(2, 3),
Edge(2, 7),
Edge(3, 4),
Edge(3, 5),
Edge(4, 5),
Edge(5, 6),
Edge(6, 7),
Edge(6, 8),
Edge(7, 8),
Edge(8, 9),
Edge(9, 10),
Edge(9, 11),
Edge(10, 11)
]
for node in range(N):
G.add_node(node)
for edge in edges:
G.add_edge(edge)
#print "frucht12"
algorithm = HalinNodeColoring(G, outer=set([0, 4, 5, 6, 8, 9, 11]))
algorithm.run()
#print "frucht12 outer", algorithm.outer
parent = {
0: 1,
1: None,
2: 1,
3: 2,
4: 3,
5: 3,
6: 7,
7: 2,
8: 7,
9: 10,
10: 1,
11: 10
}
self.assertEqual(algorithm.parent, parent)
for node in G.iternodes():
self.assertNotEqual(algorithm.color[node], None)
for edge in G.iteredges():
self.assertNotEqual(algorithm.color[edge.source],
algorithm.color[edge.target])
all_colors = set(algorithm.color[node] for node in G.iternodes())
self.assertEqual(len(all_colors), 3)
def test_halin11(self):
N = 11
G = Graph(N, False)
edges = [
Edge(0, 1),
Edge(0, 2),
Edge(0, 10),
Edge(1, 2),
Edge(1, 5),
Edge(2, 3),
Edge(3, 4),
Edge(3, 9),
Edge(4, 5),
Edge(4, 6),
Edge(5, 6),
Edge(6, 7),
Edge(7, 8),
Edge(7, 9),
Edge(8, 9),
Edge(8, 10),
Edge(9, 10)
] # E=17
for node in range(N):
G.add_node(node)
for edge in edges:
G.add_edge(edge)
algorithm = HalinNodeColoring(G, outer=set([0, 1, 5, 6, 7, 8, 10]))
algorithm.run()
#print "halin11 outer", algorithm.outer
parent = {
0: 2,
1: 2,
2: None,
3: 2,
4: 3,
5: 4,
6: 4,
7: 9,
8: 9,
9: 3,
10: 9
}
self.assertEqual(algorithm.parent, parent)
for node in G.iternodes():
self.assertNotEqual(algorithm.color[node], None)
for edge in G.iteredges():
self.assertNotEqual(algorithm.color[edge.source],
algorithm.color[edge.target])
all_colors = set(algorithm.color[node] for node in G.iternodes())
self.assertEqual(len(all_colors), 3)
def test_k4(self): # graf K4 = W4
G = self.graph_factory.make_complete(n=4, directed=False)
# Sa 4 mozliwosci narysowania K4 na plaszczyznie bez przeciec.
algorithm = HalinNodeColoring(G, outer=set([1, 2, 3]))
algorithm.run()
parent = {0: None, 1: 0, 2: 0, 3: 0}
self.assertEqual(algorithm.parent, parent)
for node in G.iternodes():
self.assertNotEqual(algorithm.color[node], None)
for edge in G.iteredges():
self.assertNotEqual(algorithm.color[edge.source],
algorithm.color[edge.target])
all_colors = set(algorithm.color[node] for node in G.iternodes())
self.assertEqual(len(all_colors), 4)
def test_k4(self): # graf K4 = W4
G = self.graph_factory.make_complete(n=4, directed=False)
# Sa 4 mozliwosci narysowania K4 na plaszczyznie bez przeciec.
algorithm = HalinNodeColoring(G, outer=set([1, 2, 3]))
algorithm.run()
parent = {0: None, 1: 0, 2: 0, 3: 0}
self.assertEqual(algorithm.parent, parent)
for node in G.iternodes():
self.assertNotEqual(algorithm.color[node], None)
for edge in G.iteredges():
self.assertNotEqual(algorithm.color[edge.source],
algorithm.color[edge.target])
all_colors = set(algorithm.color[node] for node in G.iternodes())
self.assertEqual(len(all_colors), 4)
def test_halin7(self):
N = 7
G = Graph(N, False)
edges = [Edge(0, 1), Edge(0, 2), Edge(0, 6), Edge(1, 2),
Edge(1, 4), Edge(2, 3), Edge(3, 4), Edge(3, 5),
Edge(4, 5), Edge(4, 6), Edge(5, 6)]
for node in range(N):
G.add_node(node)
for edge in edges:
G.add_edge(edge)
algorithm = HalinNodeColoring(G, outer=set([0, 2, 3, 5, 6]))
algorithm.run()
#print "halin7 outer", algorithm.outer
parent = {0: 1, 1: None, 2: 1, 3: 4, 4: 1, 5: 4, 6: 4}
self.assertEqual(algorithm.parent, parent)
for node in G.iternodes():
self.assertNotEqual(algorithm.color[node], None)
for edge in G.iteredges():
self.assertNotEqual(algorithm.color[edge.source],
algorithm.color[edge.target])
all_colors = set(algorithm.color[node] for node in G.iternodes())
self.assertEqual(len(all_colors), 3)
def test_wheel5(self):
N = 5
G = Graph(N, False)
edges = [Edge(0, 1), Edge(0, 2), Edge(0, 3), Edge(0, 4),
Edge(1, 2), Edge(2, 3), Edge(3, 4), Edge(4, 1)]
for node in range(N):
G.add_node(node)
for edge in edges:
G.add_edge(edge)
algorithm = HalinNodeColoring(G, outer=set([1, 2, 3, 4]))
algorithm.run()
#print "wheel5 outer", algorithm.outer
#print "wheel5 cycle", algorithm.cycle
parent = {0: None, 1: 0, 2: 0, 3: 0, 4: 0}
self.assertEqual(algorithm.parent, parent)
for node in G.iternodes():
self.assertNotEqual(algorithm.color[node], None)
for edge in G.iteredges():
self.assertNotEqual(algorithm.color[edge.source],
algorithm.color[edge.target])
all_colors = set(algorithm.color[node] for node in G.iternodes())
self.assertEqual(len(all_colors), 3)
def test_halin8c(self):
N = 8
G = Graph(N, False)
edges = [Edge(0, 1), Edge(0, 5), Edge(0, 7), Edge(1, 2),
Edge(1, 7), Edge(2, 3), Edge(2, 6), Edge(3, 4), Edge(3, 6),
Edge(4, 5), Edge(4, 6), Edge(5, 6), Edge(6, 7)]
for node in range(N):
G.add_node(node)
for edge in edges:
G.add_edge(edge)
algorithm = HalinNodeColoring(G, outer=set([0, 1, 2, 3, 4, 5]))
algorithm.run()
#print "halin8c outer", algorithm.outer
parent = {0: 7, 1: 7, 2: 6, 3: 6, 4: 6, 5: 6, 6: None, 7: 6}
self.assertEqual(algorithm.parent, parent)
for node in G.iternodes():
self.assertNotEqual(algorithm.color[node], None)
for edge in G.iteredges():
self.assertNotEqual(algorithm.color[edge.source],
algorithm.color[edge.target])
all_colors = set(algorithm.color[node] for node in G.iternodes())
self.assertEqual(len(all_colors), 3)
def test_halin10k(self):
N = 10
G = Graph(N, False)
edges = [Edge(0, 1), Edge(0, 2), Edge(0, 9), Edge(1, 2),
Edge(1, 4), Edge(2, 3), Edge(3, 4), Edge(3, 8),
Edge(4, 5), Edge(5, 6), Edge(5, 7), Edge(6, 7),
Edge(6, 9), Edge(7, 8), Edge(8, 9)]
for node in range(N):
G.add_node(node)
for edge in edges:
G.add_edge(edge)
algorithm = HalinNodeColoring(G, outer=set([0, 1, 4, 5, 6, 9]))
algorithm.run()
#print "halin10k outer", algorithm.outer
parent = {0: 2, 1: 2, 2: None, 3: 2, 4: 3, 5: 7, 6: 7, 7: 8, 8: 3, 9: 8}
self.assertEqual(algorithm.parent, parent)
for node in G.iternodes():
self.assertNotEqual(algorithm.color[node], None)
for edge in G.iteredges():
self.assertNotEqual(algorithm.color[edge.source],
algorithm.color[edge.target])
all_colors = set(algorithm.color[node] for node in G.iternodes())
self.assertEqual(len(all_colors), 3)
def test_halin16(self):
N = 16
G = Graph(N, False)
edges = [
Edge(0, 1),
Edge(0, 2),
Edge(0, 15),
Edge(1, 2),
Edge(1, 6),
Edge(2, 3),
Edge(3, 4),
Edge(3, 5),
Edge(4, 5),
Edge(4, 10),
Edge(5, 6),
Edge(6, 7),
Edge(7, 8),
Edge(7, 15),
Edge(8, 9),
Edge(8, 13),
Edge(9, 10),
Edge(9, 11),
Edge(10, 11),
Edge(11, 12),
Edge(12, 13),
Edge(12, 14),
Edge(13, 14),
Edge(14, 15)
]
for node in range(N):
G.add_node(node)
for edge in edges:
G.add_edge(edge)
#print "halin16"
algorithm = HalinNodeColoring(G,
outer=set(
[0, 2, 3, 4, 10, 11, 12, 14, 15]))
algorithm.run()
#print "halin16 outer", algorithm.outer
parent = {
0: 1,
1: None,
2: 1,
3: 5,
4: 5,
5: 6,
6: 1,
7: 6,
8: 7,
9: 8,
10: 9,
11: 9,
12: 13,
13: 8,
14: 13,
15: 7
}
self.assertEqual(algorithm.parent, parent)
for node in G.iternodes():
self.assertNotEqual(algorithm.color[node], None)
for edge in G.iteredges():
self.assertNotEqual(algorithm.color[edge.source],
algorithm.color[edge.target])
all_colors = set(algorithm.color[node] for node in G.iternodes())
self.assertEqual(len(all_colors), 3)
#!/usr/bin/python
import timeit
import random
from graphtheory.structures.edges import Edge
from graphtheory.structures.graphs import Graph
from graphtheory.structures.factory import GraphFactory
from graphtheory.planarity.halinnodecolor import HalinNodeColoring
from graphtheory.planarity.halintools import make_halin_outer
from graphtheory.planarity.halintools import make_halin_cubic_outer
V = 10
graph_factory = GraphFactory(Graph)
G = graph_factory.make_necklace(n=V) # V even
outer = set(range(0, V, 2)) | set([V - 1]) # necklace
#G, outer = make_halin_outer(V)
#G, outer = make_halin_cubic_outer(V)
E = G.e()
#G.show()
print("Testing HalinNodeColoring ...")
t1 = timeit.Timer(lambda: HalinNodeColoring(G, outer).run())
print("{} {} {}".format(V, E, t1.timeit(1))) # single run
# EOF
#G = graph_factory.make_complete(n=4) # V=4
#G = graph_factory.make_wheel(n=5) # V > 3
G = graph_factory.make_necklace(n=6) # V even
#G = make_halin(n=7) # V > 3
#G = make_halin_cubic(n=8) # V even
G.show()
print("Recognition ...")
print("is_wheel {}".format(is_wheel(G)))
algorithm = HalinGraph(G)
algorithm.run()
print("outer {}".format(algorithm.outer))
outer = algorithm.outer
print("Vertex coloring ...")
algorithm = HalinNodeColoring(G, outer)
algorithm.run()
print("parent {}".format(algorithm.parent))
assert len(algorithm.parent) == G.v()
print("color {}".format(algorithm.color))
all_colors = set(algorithm.color[node] for node in G.iternodes())
print("len(all_colors) {}".format(len(all_colors)))
assert len(algorithm.color) == G.v()
print("Finding PEO for chordal completion ...")
algorithm = HalinGraphPEO(G, outer)
algorithm.run()
print("parent {}".format(algorithm.parent))
assert len(algorithm.parent) == G.v()
print("order {}".format(algorithm.order))
assert len(algorithm.order) == G.v()