def test_degree0(self):
for i in range(3):
V, E = generate_graph_of_degree(0)
Ec = complement(V, E)
expected = len(naive(V, Ec))
actual = maxset(V, E)
self.assertEqual(expected, actual)
def test_random_graph(self):
for i in range(3):
V, E = generate_random_graph()
Ec = complement(V, E)
expected = len(naive(V, Ec))
actual = maxset(V, E)
self.assertEqual(expected, actual)
def evaluate_tar_troj_time(self):
""" Computes the time for the tarjan and trojanowsi's algorithm """
start = time()
Ec = complement(self.__V, self.__E)
maxset(self.__V, Ec)
end = time()
self.__tar_troj_time = round(end - start, 4)
def test_complement(self):
Ec = fun.complement(V, E)
self.assertIn({7,8}, Ec)
self.assertNotIn({1,2}, Ec)
def maxset(V, E):
""" Retruns the cardinality of the maximum independent set in (V,E) """
# -- CASE: V={} -- #
if not V:
return 0
# -- STATEMENT 0 -- #
components = fun.connected_components(V, E)
if len(components) > 1:
temp = 0
for connected_subgraph in components:
temp += maxset(connected_subgraph, fun.induced(connected_subgraph, E))
return temp
v = fun.vertex_of_min_degree(V, E)
# -- CASE: DEG=0 -- #
if fun.degree(v, V, E) == 0:
temp = V - {v}
return 1 + maxset(temp, fun.induced(temp, E))
# -- STATEMENT 1 -- #
elif fun.degree(v, V, E) == 1:
Av = fun.adjacent(v, V, E)
w = list(Av)[0]
temp = V - {v,w}
return 1 + maxset(temp, fun.induced(temp, E))
# -- STATEMENT 2 -- #
elif fun.degree(v, V, E) == 2:
# -- STATEMENT 2.1 -- #
if fun.for_all(V, lambda w: fun.degree(w, V, E) == 2):
return floor(len(V) / 2)
else:
v_, w1 = fun.n_k_degree(2, 3, V, E)
w2 = list(fun.adjacent(v_, V, E) - {w1})[0]
# -- STATEMENT 2.2 -- #
if {w1, w2} in E:
temp = V - {v_,w1,w2}
return 1 + maxset(temp, fun.induced(temp, E))
# -- STATEMENT 2.3 -- #
elif {w1, w2} not in E:
temp1 = V - {v_,w1,w2}
# According to the paper this should be V - adj(w1) - adj(w2).
# However without the - {w1} and - {w2} the algorithm does not work correctly
temp2 = V - fun.adjacent(w1, V, E) - {w1} - fun.adjacent(w2, V, E) - {w2}
return max(1 + maxset(temp1, fun.induced(temp1, E)), 2 + maxset(temp2, fun.induced(temp2, E)))
# -- STATMENT 3 -- #
elif fun.degree(v, V, E) == 3:
Av = list(fun.adjacent(v, V, E))
w1, w2, w3 = Av[0], Av[1], Av[2]
# -- STATEMENT 3.1 -- #
if {w1,w2} in E and {w1,w3} in E and {w2,w3} in E:
temp = V - {v,w1,w2,w3}
return 1 + maxset(temp, fun.induced(temp, E))
# -- STATEMENT 3.2 Part 1 -- #
elif {w1,w2} in E and {w1,w3} in E:
temp1 = V - {v,w1,w2,w3}
E1 = fun.induced(temp1, E)
# Again, according to the paper the - {w2} and - {w3} should not be here
# and yet these additions are necessary for the algorithm to work correctly
temp2 = V - fun.adjacent(w2, V, E) - {w2} - fun.adjacent(w3, V, E) - {w3}
E2 = fun.induced(temp2, E)
return max(1 + maxset(temp1, E1), 2 + maxset(temp2, E2))
# -- STATEMENT 3.2 Part 2 -- #
elif {w1,w3} in E and {w2,w3} in E:
temp1 = V - {v,w1,w2,w3}
E1 = fun.induced(temp1, E)
# Same thing here
temp2 = V - fun.adjacent(w1, V, E) - {w1} - fun.adjacent(w2, V, E) - {w2}
E2 = fun.induced(temp2, E)
return max(1 + maxset(temp1, E1), 2 + maxset(temp2, E2))
# -- STATEMENT 3.2 Part 3 -- #
elif {w1,w2} in E and {w2,w3} in E:
temp1 = V - {v,w1,w2,w3}
E1 = fun.induced(temp1, E)
# And here
temp2 = V - fun.adjacent(w1, V, E) - {w1} - fun.adjacent(w3, V, E) - {w3}
E2 = fun.induced(temp2, E)
return max(1 + maxset(temp1, E1), 2 + maxset(temp2, E2))
# -- STATEMENT 3.3 -- #
elif {w1,w2} in E or {w1,w3} in E or {w2,w3} in E:
A1c = V - {w1,w2,w3} - fun.adjacent(w1, V, E)
A2c = V - {w1,w2,w3} - fun.adjacent(w2, V, E)
A3c = V - {w1,w2,w3} - fun.adjacent(w3, V, E)
# -- STATEMENT 3.3.1 -- #
pass
# -- STATEMENT 3.3.2 -- #
if len(A1c & A3c) <= len(V) - 7 and len(A2c & A3c) <= len(V) - 7:
temp1 = V - {v,w1,w2,w3}
E1 = fun.induced(temp1, E)
temp2 = A1c & A3c
E2 = fun.induced(temp2, E)
temp3 = A2c & A3c
E3 = fun.induced(temp3, E)
return max(1 + maxset(temp1, E1), 2 + maxset(temp2, E2), 2 + maxset(temp3, E3))
# -- STATEMENT 3.4 -- #
elif {w1,w2} not in E and {w2,w3} not in E and {w1,w3} not in E:
A1c = V - fun.adjacent(w1, V, E)
A2c = V - fun.adjacent(w2, V, E)
A3c = V - fun.adjacent(w3, V, E)
# -- STATEMENT 3.4.1 -- #
if len(A1c & A2c & A3c) >= len(V) - 7:
temp1 = V - {v,w1,w2,w3}
E1 = fun.induced(temp1, E)
temp2 = V - (A1c & A2c & A3c)
E2 = fun.induced(temp2, E)
return max(1 + maxset(temp1, E1), 3 + maxset(temp2, E2))
# -- STATEMENT 3.4.2 -- #
elif len(A1c & A2c & A3c) == len(V) - 8 or len(A1c & A2c & A3c) == len(V) - 9:
# -- STATEMENT 3.4.2.1 -- #
if cases.case_3_4_2_1(A1c, A2c, A3c):
temp1 = V - {v,w1,w2,w3}
E1 = fun.induced(temp1, E)
temp2 = A1c & A2c & A3c
E2 = fun.induced(temp2, E)
return max(1 + maxset(temp1, E1), 3 + maxset(temp2, E2))
# -- STATEMENT 3.4.2.2 -- #
elif cases.case_3_4_2_2(A1c, A2c, A3c):
Aic, Ajc = fun.three_two_domination(A1c, A2c, A3c)
temp1 = V - {v,w1,w2,w3}
E1 = fun.induced(temp1, E)
temp2 = Aic & Ajc
E2 = fun.induced(temp2, E)
temp3 = A1c & A2c & A3c
E3 = fun.induced(temp3, E)
return max(1 + maxset(temp1, E1), 2 + maxset(temp2, E2), 3 + maxset(temp3, E3))
# -- STATEMENT 3.4.3 -- #
elif len(A1c & A2c & A3c) <= len(V) - 10:
# -- STATEMENT 3.4.3.1 -- #
if cases.case_3_4_3_1(A1c, A2c, A3c):
temp1 = V - {v,w1,w2,w3}
E1 = fun.induced(temp1, E)
temp2 = A1c & A2c & A3c
E2 = fun.induced(temp2, E)
return max(1 + maxset(temp1, E1), 3 + maxset(temp2, E2))
# -- STATEMENT 3.4.3.2 -- #
elif cases.case_3_4_3_2(A1c, A2c, A3c):
Aic, Ajc = fun.three_two_domination(A1c, A2c, A3c)
temp1 = V - {v,w1,w2,w3}
E1 = fun.induced(temp1, E)
temp2 = Aic & Ajc
E2 = fun.induced(temp2, E)
temp3 = A1c & A2c & A3c
E3 = fun.induced(temp3, E)
return max(1 + maxset(temp1, E1), 2 + maxset(temp2, E2), 3 + maxset(temp3, E3))
# -- STATEMENT 3.4.3.3 -- #
pass
# -- STATEMENT 4 -- #
elif fun.degree(v, V, E) == 4:
# -- STATEMENT 4.1 -- #
if fun.for_all(V, lambda w : fun.degree(w, V, E) == 4):
pass
# -- STATEMENT 4.2 -- #
else:
v_, w = fun.n_k_degree(4, 5, V, E)
temp1 = V - {w} - fun.adjacent(w, V, E)
E1 = fun.induced(temp1, E)
temp2 = V - {w}
E2 = fun.induced(temp2, E)
return max(1 + maxset(temp1, E1), maxset(temp2, E2))
# -- STATEMENT 5 -- #
elif fun.for_all(V, lambda w : fun.degree(w, V, E) == 5):
# -- STATEMENT 5.1 -- #
if len(V) == 6:
return 1
# -- STATEMENT 5.2 -- #
elif len(V) > 6:
temp1 = V - {v} - fun.adjacent(v, V, E)
E1 = fun.induced(temp1, E)
temp2 = V - {v}
E2 = fun.induced(temp2, E)
return max(1 + maxset(temp1, E1), maxset(temp2, E2))
# -- STATEMENT 6 -- #
elif fun.degree(v, V, E) >= 6:
temp1 = V - {v} - fun.adjacent(v, V, E)
E1 = fun.induced(temp1, E)
temp2 = V - {v}
E2 = fun.induced(temp2, E)
return max(1 + maxset(temp1, E1), maxset(temp2, E2))
# Default case for non-implemented statements
return len(naive(V, fun.complement(V, E)))
def test_complement():
print("Testing complement function...")
assert isinstance(complement(test_template_strand), str)
assert complement(test_template_strand) == 'TAGACTGG'
print("All tests passed!\n")