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Source code for qiskit_optimization.applications.graph_partition

# 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 graph partitioning."""

from typing import Dict, List, Optional, Union

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 GraphPartition(GraphOptimizationApplication): """Optimization application for the "graph partition" [1] problem based on a NetworkX graph. References: [1]: "Graph partition", https://en.wikipedia.org/wiki/Graph_partition """
[docs] def to_quadratic_program(self) -> QuadraticProgram: """Convert a graph partition instance into a :class:`~qiskit_optimization.problems.QuadraticProgram` Returns: The :class:`~qiskit_optimization.problems.QuadraticProgram` created from the graph partition instance. """ mdl = Model(name="Graph partition") n = self._graph.number_of_nodes() x = {i: mdl.binary_var(name=f"x_{i}") for i in range(n)} for w, v in self._graph.edges: self._graph.edges[w, v].setdefault("weight", 1) objective = mdl.sum( self._graph.edges[i, j]["weight"] * (x[i] + x[j] - 2 * x[i] * x[j]) for i, j in self._graph.edges ) mdl.minimize(objective) mdl.add_constraint(mdl.sum([x[i] for i in x]) == n // 2) op = from_docplex_mp(mdl) return op
[docs] def interpret(self, result: Union[OptimizationResult, np.ndarray]) -> List[List[int]]: """Interpret a result as a list of node indices Args: result : The calculated result of the problem Returns: A list of node indices divided into two groups. """ x = self._result_to_x(result) partition = [[], []] # type: List[List[int]] for i, value in enumerate(x): if value == 0: partition[0].append(i) else: partition[1].append(i) return partition
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 blue. return ["r" if x[node] else "b" for node in self._graph.nodes]

© Copyright 2018, 2021, Qiskit Optimization Development Team.

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