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Source code for qiskit_optimization.applications.clique

# This code is part of Qiskit.
#
# (C) Copyright IBM 2018, 2021.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.

"""An application class for the clique."""
from typing import Optional, Union, List, Dict

import networkx as nx
import numpy as np
from docplex.mp.model import Model

from qiskit_optimization.algorithms import OptimizationResult
from qiskit_optimization.problems.quadratic_program import QuadraticProgram
from qiskit_optimization.translators import from_docplex_mp
from .graph_optimization_application import GraphOptimizationApplication


[docs]class Clique(GraphOptimizationApplication): """Optimization application for the "clique" [1] problem based on a NetworkX graph. References: [1]: "Clique (graph theory)", `https://en.wikipedia.org/wiki/Clique_(graph_theory) <https://en.wikipedia.org/wiki/Clique_(graph_theory)>`_ """ def __init__( self, graph: Union[nx.Graph, np.ndarray, List], size: Optional[int] = None ) -> None: """ Args: graph: A graph representing a problem. It can be specified directly as a `NetworkX <https://networkx.org/>`_ graph, or as an array or list format suitable to build out a NetworkX graph. size: The size of the clique. When it's `None`, the default, this class makes an optimization model for a maximal clique instead of the specified size of a clique. """ super().__init__(graph) self._size = size
[docs] def to_quadratic_program(self) -> QuadraticProgram: """Convert a clique problem instance into a :class:`~qiskit_optimization.problems.QuadraticProgram`. When "size" is None, this makes an optimization model for a maximal clique instead of the specified size of a clique. Returns: The :class:`~qiskit_optimization.problems.QuadraticProgram` created from the clique problem instance. """ complement_g = nx.complement(self._graph) mdl = Model(name="Clique") n = self._graph.number_of_nodes() x = {i: mdl.binary_var(name=f"x_{i}") for i in range(n)} for w, v in complement_g.edges: mdl.add_constraint(x[w] + x[v] <= 1) if self.size is None: mdl.maximize(mdl.sum(x[i] for i in x)) else: mdl.add_constraint(mdl.sum(x[i] for i in x) == self.size) op = from_docplex_mp(mdl) return op
[docs] def interpret(self, result: Union[OptimizationResult, np.ndarray]) -> List[int]: """Interpret a result as a list of node indices Args: result : The calculated result of the problem Returns: The list of node indices whose corresponding variable is 1 """ x = self._result_to_x(result) clique = [] for i, value in enumerate(x): if value: clique.append(i) return clique
def _draw_result( self, result: Union[OptimizationResult, np.ndarray], pos: Optional[Dict[int, np.ndarray]] = None, ) -> None: """Draw the result with colors Args: result : The calculated result for the problem pos: The positions of nodes """ x = self._result_to_x(result) nx.draw(self._graph, node_color=self._node_colors(x), pos=pos, with_labels=True) def _node_colors(self, x: np.ndarray) -> List[str]: # Return a list of strings for draw. # Color a node with red when the corresponding variable is 1. # Otherwise color it with dark gray. return ["r" if x[node] else "darkgrey" for node in self._graph.nodes] @property def size(self) -> Optional[int]: """Getter of size Returns: The size of the clique, `None` when maximal clique """ return self._size @size.setter def size(self, size: Optional[int]) -> None: """Setter of size Args: size: The size of the clique, `None` for maximal clique """ self._size = size

© Copyright 2018, 2021, Qiskit Optimization Development Team.

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