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homomorphism_solver.pyx
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homomorphism_solver.pyx
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#!python
#cython: language_level=3
#cython: profile=True
#cython: linetrace=True
#distutils: language=c++
from random import randint
from random import choice
import networkx as nx
from libcpp.vector cimport vector
from libcpp.set cimport set
from libcpp cimport bool
cdef class Solver:
cdef readonly int UNDEFINED
cdef readonly int FORWARD
cdef readonly int BACKTRACK
cdef object g
cdef object h
cdef int no_gnodes
cdef int no_hnodes
cdef vector[bool] adjacency_g
cdef vector[bool] adjacency_h
cdef int i
cdef int action
cdef vector[vector[int]] possibles
cdef vector[int] g_nodes
cdef vector[int] hcolor_inds
cdef vector[int] soln
# heuristics
cdef vector[int] error_g
cdef vector[int] pruned_h
cdef public int no_solns
cdef public object solution
def __init__(self, object g, object h):
self.UNDEFINED = -1
self.FORWARD = 0
self.BACKTRACK = 1
self.g = g
self.no_gnodes = len(g.nodes())
self.adjacency_g = vector[bool](self.no_gnodes ** 2, 0)
for e in g.edges():
self.adjacency_g[e[0] * self.no_gnodes + e[1]] = 1
self.adjacency_g[e[1] * self.no_gnodes + e[0]] = 1
self.h = h
self.no_hnodes = len(h.nodes())
self.adjacency_h = vector[bool](self.no_hnodes ** 2, 0)
for e in h.edges():
self.adjacency_h[e[0] * self.no_hnodes + e[1]] = 1
self.adjacency_h[e[1] * self.no_hnodes + e[0]] = 1
self.i = 0
self.possibles = vector[vector[int]](self.no_gnodes, vector[int](self.no_hnodes, 0))
for i in range(self.no_gnodes):
for j in range(self.no_hnodes):
self.possibles[i][j] = j
self.g_nodes = vector[int](self.no_gnodes, self.UNDEFINED)
for i in range(self.no_gnodes):
self.g_nodes[i] = i
self.hcolor_inds = vector[int](self.no_gnodes, self.UNDEFINED)
self.soln = vector[int](self.no_gnodes, self.UNDEFINED)
self.action = self.FORWARD
self.error_g = vector[int](self.no_gnodes, 0)
self.pruned_h = vector[int](self.no_hnodes, 0)
self.no_solns = 0
self.solution = None
cdef bool is_last_option(self) nogil:
cdef int i
cdef unsigned hcolor
i = 0 if self.i < 0 else self.i
hcolor = self.g_nodes[i]
return self.hcolor_ind() == self.possibles[hcolor].size() - 1
cdef bool is_valid_option(self, int val=-1) nogil:
cdef int i
cdef unsigned hcolor
i = 0 if self.i < 0 else self.i
hcolor = self.g_nodes[i]
if val == -1:
val = self.hcolor_ind()
return val >= 0 and val < self.possibles[hcolor].size()
cdef void forward_node(self, int mapto) nogil:
cdef int i
cdef unsigned ind
cdef unsigned hcolor
i = 0 if self.i == -1 else self.i
ind = self.g_nodes[i]
self.action = self.FORWARD
self.hcolor_inds[ind] = mapto
hcolor = self.hcolor_inds[ind]
self.soln[ind] = self.possibles[ind][hcolor]
self.i += 1
cdef void set_rollback(self) nogil:
cdef int i
cdef unsigned ind
i = max(0, self.i)
ind = self.g_nodes[i]
self.error_g[ind] += 1
self.action = self.BACKTRACK
# self.g_nodes[i] = Solver.UNDEFINED
self.hcolor_inds[ind] = self.UNDEFINED
self.soln[ind] = self.UNDEFINED
self.i -= 1
cdef int hcolor_ind(self) nogil:
cdef int i
i = max(0, self.i)
return self.hcolor_inds[self.g_nodes[i]]
cdef inline bool g_has_edge(self, int u, int v) nogil:
return self.adjacency_g[u * self.no_gnodes + v]
cdef inline bool h_has_edge(self, int u, int v) nogil:
return self.adjacency_h[u * self.no_hnodes + v]
cdef inline int find_possible_map(self) nogil:
cdef int i, ind, mapto
i = 0 if self.i < 0 else self.i
ind = self.g_nodes[i]
mapto = self.hcolor_ind() + 1
# print(self.soln)
while self.is_valid_option(mapto):
approved = True
if i > 0:
gu = ind
hu = self.possibles[gu][mapto]
for j in range(i):
gv = self.g_nodes[j]
hv = self.soln[gv]
if self.g_has_edge(gu, gv) and not self.h_has_edge(hu, hv):
approved = False
self.pruned_h[mapto] += 1
break
if approved:
break
mapto += 1
return mapto
cdef is_valid_solution(self):
assert self.i == self.soln.size()
for e in list(self.g.edges()):
u, v = e
hu, hv = self.soln[u], self.soln[v]
if not self.h_has_edge(hu, hv):
return False
return True
cdef int count_g_neighbors_in_set(self, int node, vector[int] nodes) nogil:
cdef int ret
ret = 0
for out in nodes:
if self.g_has_edge(node, out):
ret += 1
return ret
cdef int count_h_neighbors_in_set(self, int node, vector[int] nodes) nogil:
cdef int ret
ret = 0
for out in nodes:
if self.h_has_edge(node, out):
ret += 1
return ret
# heuristics
cdef choose_best_node(self):
cdef int option, rating, new_rating, ind
cdef vector[int] g_nodes_visited
cdef set[int] visited
option, rating = -1, -1
g_nodes_visited = self.g_nodes[:self.i]
visited = set[int](self.g_nodes[:self.i])
for ind in range(len(self)):
if visited.count(ind):
continue
new_rating = 0
no_nbs = self.count_g_neighbors_in_set(ind, g_nodes_visited)
new_rating += 100 * no_nbs
new_rating += 50 * (self.i - no_nbs)
if new_rating > rating:
option, rating = ind, new_rating
elif new_rating == rating and self.error_g[ind] > self.error_g[option]:
option, rating = ind, new_rating
if option != -1:
return option
return self.g_nodes[self.i]
cdef int choose_target_rating_func(self, int g_ind, int h_ind) nogil:
cdef int i, target, nb_count, rating
cdef vector[int] map_image
i = max(0, self.i)
target = self.possibles[g_ind][h_ind]
map_image = vector[int](i)
for idx in range(i):
map_image[idx] = self.soln[self.g_nodes[idx]]
# map_image = [self.soln[idx] for idx in self.g_nodes[:i]]
rating = 0
nb_count = self.count_h_neighbors_in_set(target, map_image)
rating += 10000 * nb_count
rating += 1000 * (map_image.size() - nb_count)
rating += self.pruned_h[h_ind]
return rating
# heuristics
cdef void choose_target_order(self):
cdef int i, g_ind
i = max(0, self.i)
g_ind = self.g_nodes[i]
hcolors = [x for x in self.possibles[g_ind]]
hcolors.sort(key=lambda h_ind: self.choose_target_rating_func(g_ind, h_ind), reverse=True)
self.possibles[g_ind] = hcolors
# print(self.i, [x for x in self.possibles[g_ind]])
cpdef find_solutions(self, stopfunc):
while True:
while self.i in range(len(self)):
# print(self)
if self.action == self.FORWARD:
# choose g-node
self.g_nodes[self.i] = self.choose_best_node()
# select order in which h-colors will be tested
if self.i + 5 < self.soln.size():
self.choose_target_order()
assert self.i >= -1
if self.action == self.BACKTRACK and self.hcolor_ind() != self.UNDEFINED:
pass
mapto = self.find_possible_map()
if self.is_valid_option(mapto):
self.forward_node(mapto)
else:
self.set_rollback()
if self.i < 0:
break
# print(self)
assert self.is_valid_solution()
if not stopfunc([self.soln[i] for i in range(len(self.soln))]):
return
self.i -= 1
self.action = self.BACKTRACK
if self.i != -1 and not stopfunc([self.soln[i] for i in range(len(self.soln))]):
return
def __str__(self):
s = 'backtrack' if self.action else 'forward'
s += ' ' + str(self.i) + ' soln:'
# s += str([self.hcolor_inds[x] for x in self.g_nodes])
s += str([self.soln[i] for i in range(len(self.soln))])
return s
def __len__(self):
return self.no_gnodes
def compose_solutions(psi, phi):
return [phi[x] for x in psi]
def find_homomorphisms(g, h):
s = Solver(g, h)
def stopfunc(soln):
s.no_solns += 1
return True
s.find_solutions(stopfunc)
return s.no_solns
def is_homomorphic(g, h):
s = Solver(g, h)
def func(soln):
s.no_solns = 1
s.solution = [s.soln[i] for i in range(len(s.soln))]
return False
s.find_solutions(stopfunc=func)
if s.no_solns == 1:
return s.solution
return None