Map Coloring: Full Code

See Map Coloring for a description of the following code.

import networkx as nx
import matplotlib.pyplot as plt
from dimod.generators import combinations
from dimod import BinaryQuadraticModel, ExactSolver
from dwave.system import DWaveSampler, EmbeddingComposite

# Represent the map as the nodes and edges of a graph
provinces = ['AB', 'BC', 'MB', 'NB', 'NL', 'NS', 'NT', 'NU', 'ON', 'PE', 'QC', 'SK', 'YT']
neighbors = [('AB', 'BC'), ('AB', 'NT'), ('AB', 'SK'), ('BC', 'NT'), ('BC', 'YT'), ('MB', 'NU'),
             ('MB', 'ON'), ('MB', 'SK'), ('NB', 'NS'), ('NB', 'QC'), ('NL', 'QC'), ('NT', 'NU'),
             ('NT', 'SK'), ('NT', 'YT'), ('ON', 'QC')]

colors = ['y', 'g', 'r', 'b']

# Add constraint that each node (province) select a single color
bqm_one_color = BinaryQuadraticModel('BINARY')
for province in provinces:
  variables = [province + "_" + c for c in colors]
  bqm_one_color.update(combinations(variables, 1))

# Add constraint that each pair of nodes with a shared edge not both select one color
bqm_neighbors  = BinaryQuadraticModel('BINARY')
for neighbor in neighbors:
  v, u = neighbor
  interactions = [(v + "_" + c, u + "_" + c) for c in colors]
  for interaction in interactions:
    bqm_neighbors.add_quadratic(interaction[0], interaction[1], 1)

bqm = bqm_one_color + bqm_neighbors

# Set up a solver and sample 1000 times
sampler = EmbeddingComposite(DWaveSampler())
sampleset = sampler.sample(bqm, num_reads=1000, label='SDK Examples - Map Coloring BQM')

best = sampleset.first

def plot_map(sample):
  G = nx.Graph()
  # Create a {province: selected color} dict
  color_map = {}
  for province in provinces:
    for c in colors:
     if sample[province + '_' + c]:
         color_map[province] = c
  # Plot with the selected colors
  node_colors = [color_map.get(node) for node in G.nodes()]
  nx.draw_circular(G, with_labels=True, node_color=node_colors, node_size=3000,

# Plot the lowest-energy sample if it meets the constraints
sample = sampleset.first.sample
if > 0:
    print("Failed to color map")