def sat_time(G, CNF):
"""sat_time gives the running time of minisat on instance.cnf and whether it is
satisfiable in the appropriate form for check_graph.
"""
_verbose("running " + _SOLVER + "...")
start = tm.default_timer()
ans = run_solver(CNF)
running_time = tm.default_timer() - start
return [("Running Time", running_time), ("Satisfiable", ans)]
def make_graph(vars, clas, grps, prob):
"""Makes a CNF clause (each clause with maximum 3 variables) out of VARS
variables and CLAS clauses. Each variable can be in one of GRPS grous, which
guide the CNF formula to have a community structure based on these groups.
The Q-value of the corresponding graph is approximated by PROB. Returns
(graph, CNF formula) as a tuple.
"""
_verbose("constructing CNF and incidence graph...")
variables = [i for i in range(1, vars + 1)]
grp_size = int(round(float(vars) / grps))
G = ig.Graph()
G.add_vertices(vars)
CNF = []
for i in range(clas):
rand_var = variables[rm.randrange(vars)]
rand_grp = (rand_var - 1) % grps
var2 = var3 = 0
if _with_prob(prob):
x = - 1
while (x < 0 or x >= vars):
x = rm.randrange(grp_size + 1) * grps + rand_grp
var2 = variables[x]
else:
var2 = variables[rm.randrange(vars)]
if _with_prob(prob):
x = -1
while (x < 0 or x >= vars):
x = rm.randrange(grp_size + 1) * grps + rand_grp
var3 = variables[x]
else:
var3 = variables[rm.randrange(vars)]
clause = []
if _with_prob(.5):
clause.append(rand_var)
else:
clause.append(-rand_var)
if rand_var != var2:
if _with_prob(.5):
clause.append(var2)
else:
clause.append(-var2)
if rand_var != var3 and var2 != var3:
if _with_prob(.5):
clause.append(var3)
else:
clause.append(-var3)
G.add_edges([(rand_var - 1, var2 - 1),
(rand_var - 1, var3 - 1),
(var2 - 1, var3 - 1)])
CNF.append(clause)
G.simplify()
create_DIMACS(CNF, vars, clas)
return (G, CNF)
def mod_check(G, CNF):
"""mod_check gives the modularity of the graph G as an attribute tuple for
check graph. It is calculated by the provided library igraph.
"""
_verbose("calculating Q-value...")
return [("Q-value", G.community_fastgreedy().as_clustering().q)]