def refineColors(self, g1, g2):
"""
Refines the colors with the graphs
:param g1: graph1
:param g2: graph2
:return: Nothing, this function acts on the current object
"""
if self.refined:
print("Warning! Refining a ColorCombination that is already flagged as refined!")
self.applyToGraphs(g1, g2)
g = disjointUnionMulti([g1, g2], True)
p = generatePartitions(g, True)
newColoring = dict()
for c in range(len(p)):
for v in p[c]:
newColoring[v] = c
# newColoring = refineColorsv2(g, True)
newColoringG1 = dict()
gV = g.V()
g1V = g1.V()
for i in range(len(g1V)):
newColoringG1[g1V[i]] = newColoring[gV[i]]
newColoringG2 = dict()
g2V = g2.V()
for i in range(len(g2V)):
newColoringG2[g2V[i]] = newColoring[gV[i + len(g1V)]]
self.generateCoreValues(newColoringG1, newColoringG2, True)
def countTreeAutomorphismsRS(G, visualize=False):
p = generatePartitions(G)
n = generateNeighbourList(G)
degrees = dict()
for v in G.V():
degree = len(n[v])
degreeSet = degrees.get(degree, 0)
if degreeSet:
degreeSet.add(v)
else:
degrees[degree] = {v}
colorOf = dict()
for color in p:
for v in color:
colorOf[v] = color
queue = []
done = set()
automorphisms = 1
for c in p:
if len(c) == 1:
queue.append((pickFromSet(c), None))
break
if not queue:
for c in p:
if len(c) == 2:
r, l = c
if True or l in n[r]:
queue.append((r, None))
break
while queue:
vertex, parent = queue[-1]
color = colorOf[vertex]
del queue[-1]
for v in n[vertex] - done:
if v not in done:
queue.append((v, vertex))
done |= colorOf[v]
if parent:
automorphisms *= math.factorial(len(n[parent] & color))**(len(colorOf[parent]))
else:
automorphisms *= math.factorial(len(color))
if visualize:
drawProgress(G, vertex, color, done, queue)
done |= color
if visualize:
drawProgress(G, None, set(), done, queue)
return automorphisms
from utilities.graphIO import writeDOT
from utilities.graphUtil import createGraph
from week1.colorRefinement import refineColorsv2
from week3.gSnellerPartitioning import generatePartitions, writeColors
def generateTree(length):
G = graph(length)
done = {G.V()[0]}
c = 0
for i in range(1, len(G.V())):
G.addedge(G.V()[i], G.V()[int((10000.0*time.time()+c)%i)])
c += 1
done.add(G.V()[i])
return G
def createSimpleExample():
return createGraph(11, [(0,4), (1,4), (4,6), (2, 5 ), (3,5), (5,6), (6,7), (7,8), (8,9), (8,10)])
# g = createGraph(22, [(0,2), (1,2), (2,9), (3,5), (4,5), (5,9), (6,8), (7,8), (8,9),
# (9, 10), (10, 11), (11, 12), (11, 13), (11,14), (13, 15), (10, 16), (10, 17), (17, 18), (17, 19), (17,20), (20,21)])
#g = createGraph(10, [(0,1), (1,2), (2,3), (3,4), (4,5), (0,6), (0,7), (5,8), (5,9)])
g = generateTree(3000)
# writeDOT(g, "testTree.dot")
# g.V()[2] = None
p = generatePartitions(g)
# refineColorsv2(g)5
print(countTreeAutomorphismsLS(g, True))
print(countTreeAutomorphismsRS(g, True))
writeColors(p)
writeDOT(g, "testTree.dot")
def countTreeAutomorphismsLS(G, visualize=False):
p = generatePartitions(G)
n = generateNeighbourList(G)
degrees = dict()
for v in G.V():
degree = len(n[v])
degreeSet = degrees.get(degree, 0)
if degreeSet:
degreeSet.add(v)
else:
degrees[degree] = {v}
colorOf = dict()
for color in p:
for v in color:
colorOf[v] = color
queue = []
done = set()
for color in p:
if len(color) > 1 and color <= degrees[1]:
queue.append(color)
done = done | color
automorphisms = 1
while queue: # is not empty
newQueue = []
for color in queue:
v = pickFromSet(color)
if visualize:
drawProgress(G, v, color, done, queue)
parent = None
for neighbour in n[v]:
if len(n[neighbour] & color) > 1 :
parent = neighbour
break
if parent is None:
unvisitedNeighbours = n[v] - done
if len(unvisitedNeighbours) == 1:
parent = unvisitedNeighbours.pop()
elif len(unvisitedNeighbours) > 1:
newQueue.append(color)
continue
if parent:
if len(colorOf[parent]) > 1 and parent not in done:
newQueue.append(colorOf[parent])
automorphisms *= math.factorial(len(n[parent] & color))**(len(colorOf[parent]))
done |= color
else:
if len(color) == 2 and len(color&n[v]) == 1:
automorphisms *= 2
queue = newQueue
for c in queue:
done |= c
if visualize:
drawProgress(G, None, set(), done, queue)
return automorphisms
