# Copyright 2019 D-Wave Systems Inc.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# ================================================================================================
from dwave_networkx.generators.pegasus import pegasus_graph
import networkx as nx
from minorminer.busclique import busgraph_cache
__all__ = ['find_clique_embedding', 'find_biclique_embedding']
def _get_target_graph(m=None, target_graph=None):
if target_graph is None:
if m is None:
raise TypeError("m and target_graph cannot both be None.")
target_graph = pegasus_graph(m)
return target_graph
[docs]
@nx.utils.decorators.nodes_or_number(0)
def find_clique_embedding(k, m=None, target_graph=None):
"""Find an embedding for a clique in a Pegasus graph.
Given a clique (fully connected graph) and target Pegasus graph, attempts
to find an embedding by transforming the Pegasus graph into a :math:`K_{2,2}`
Chimera graph and then applying a Chimera clique-finding algorithm. Results
are converted back to Pegasus coordinates.
Args:
k (int/iterable/:obj:`networkx.Graph`): A complete graph to embed,
formatted as a number of nodes, node labels, or a NetworkX graph.
m (int): Number of tiles in a row of a square Pegasus graph. Required to
generate an m-by-m Pegasus graph when `target_graph` is None.
target_graph (:obj:`networkx.Graph`): A Pegasus graph. Required when `m`
is None.
Returns:
dict: An embedding as a dict, where keys represent the clique's nodes and
values, formatted as lists, represent chains of pegasus coordinates.
Examples:
This example finds an embedding for a :math:`K_3` complete graph in a
2-by-2 Pegaus graph.
>>> from dwave.embedding.pegasus import find_clique_embedding
...
>>> print(find_clique_embedding(3, 2)) # doctest: +SKIP
{0: [10, 34], 1: [35, 11], 2: [32, 12]}
"""
_, nodes = k
g = _get_target_graph(m, target_graph)
embedding = busgraph_cache(g).find_clique_embedding(nodes)
if len(embedding) != len(nodes):
raise ValueError("No clique embedding found")
return embedding
[docs]
@nx.utils.decorators.nodes_or_number(0)
@nx.utils.decorators.nodes_or_number(1)
def find_biclique_embedding(a, b, m=None, target_graph=None):
"""Find an embedding for a biclique in a Pegasus graph.
Given a biclique (a bipartite graph where every vertex in a set in connected
to all vertices in the other set) and a target :term:`Pegasus` graph size or
edges, attempts to find an embedding.
Args:
a (int/iterable):
Left shore of the biclique to embed. If a is an integer, generates
an embedding for a biclique with the left shore of size a labelled
[0,a-1]. If a is an iterable of nodes, generates an embedding for a
biclique with the left shore of size len(a) labelled for the given
nodes.
b (int/iterable):
Right shore of the biclique to embed.If b is an integer, generates
an embedding for a biclique with the right shore of size b labelled
[0,b-1]. If b is an iterable of nodes, generates an embedding for a
biclique with the right shore of size len(b) labelled for the given
nodes.
m (int): Number of tiles in a row of a square Pegasus graph. Required to
generate an m-by-m Pegasus graph when `target_graph` is None.
target_graph (:obj:`networkx.Graph`): A Pegasus graph. Required when `m`
is None.
Returns:
tuple: A 2-tuple containing:
dict: An embedding mapping the left shore of the biclique to
the Pegasus lattice.
dict: An embedding mapping the right shore of the biclique to
the Pegasus lattice.
Examples:
This example finds an embedding for an alphanumerically labeled biclique in a small
Pegasus graph
>>> from dwave.embedding.pegasus import find_biclique_embedding
...
>>> left, right = find_biclique_embedding(['a', 'b', 'c'], ['d', 'e'], 2)
>>> print(left, right) # doctest: +SKIP
{'a': [40], 'b': [41], 'c': [42]} {'d': [4], 'e': [5]}
"""
_a, anodes = a
_b, bnodes = b
if isinstance(_a, int) and isinstance(_b, int):
bnodes = [len(anodes) + x for x in bnodes]
if set(anodes).intersection(set(bnodes)):
raise ValueError("a and b overlap")
g = _get_target_graph(m, target_graph)
embedding = busgraph_cache(g).find_biclique_embedding(len(anodes), len(bnodes))
if not embedding:
raise ValueError("No biclique embedding found")
return ({x: embedding[anodes.index(x)] for x in anodes},
{y: embedding[bnodes.index(y) + len(anodes)] for y in bnodes})