本文整理汇总了Python中cnfformula.cnf.CNF.less_or_equal_constraint方法的典型用法代码示例。如果您正苦于以下问题：Python CNF.less_or_equal_constraint方法的具体用法？Python CNF.less_or_equal_constraint怎么用？Python CNF.less_or_equal_constraint使用的例子？那么恭喜您, 这里精选的方法代码示例或许可以为您提供帮助。您也可以进一步了解该方法所在类cnfformula.cnf.CNF的用法示例。
在下文中一共展示了CNF.less_or_equal_constraint方法的1个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: DominatingSet
# 需要导入模块: from cnfformula.cnf import CNF [as 别名]
# 或者: from cnfformula.cnf.CNF import less_or_equal_constraint [as 别名]
def DominatingSet(G,d, alternative = False):
r"""Generates the clauses for a dominating set for G of size <= d
The formula encodes the fact that the graph :math:`G` has
a dominating set of size :math:`d`. This means that it is possible
to pick at most :math:`d` vertices in :math:`V(G)` so that all remaining
vertices have distance at most one from the selected ones.
Parameters
----------
G : networkx.Graph
a simple undirected graph
d : a positive int
the size limit for the dominating set
alternative : bool
use an alternative construction that
is provably hard from resolution proofs.
Returns
-------
CNF
the CNF encoding for dominating of size :math:`\leq d` for graph :math:`G`
"""
F=CNF()
if not isinstance(d,int) or d<1:
ValueError("Parameter \"d\" is expected to be a positive integer")
# Describe the formula
name="{}-dominating set".format(d)
if hasattr(G,'name'):
F.header=name+" of graph:\n"+G.name+".\n\n"+F.header
else:
F.header=name+".\n\n"+F.header
# Fix the vertex order
V=enumerate_vertices(G)
def D(v):
return "x_{{{0}}}".format(v)
def M(v,i):
return "g_{{{0},{1}}}".format(v,i)
def N(v):
return tuple(sorted([ v ] + [ u for u in G.neighbors(v) ]))
# Create variables
for v in V:
F.add_variable(D(v))
for i,v in product(range(1,d+1),V):
F.add_variable(M(v,i))
# No two (active) vertices map to the same index
if alternative:
for u,v in combinations(V,2):
for i in range(1,d+1):
F.add_clause( [ (False,D(u)),(False,D(v)), (False,M(u,i)), (False,M(v,i)) ])
else:
for i in range(1,d+1):
for c in CNF.less_or_equal_constraint([M(v,i) for v in V],1):
F.add_clause(c)
# (Active) Vertices in the sequence are not repeated
if alternative:
for v in V:
for i,j in combinations(range(1,d+1),2):
F.add_clause([(False,D(v)),(False,M(v,i)),(False,M(v,j))])
else:
for i,j in combinations_with_replacement(range(1,d+1),2):
i,j = min(i,j),max(i,j)
for u,v in combinations(V,2):
u,v = max(u,v),min(u,v)
F.add_clause([(False,M(u,i)),(False,M(v,j))])
# D(v) = M(v,1) or M(v,2) or ... or M(v,d)
if not alternative:
for i,v in product(range(1,d+1),V):
F.add_clause([(False,M(v,i)),(True,D(v))])
for v in V:
F.add_clause([(False,D(v))] + [(True,M(v,i)) for i in range(1,d+1)])
# Every neighborhood must have a true D variable
neighborhoods = sorted( set(N(v) for v in V) )
for N in neighborhoods:
F.add_clause([ (True,D(v)) for v in N])
return F