This code was taken from the webinar, Quantum Programming with the Ocean Tools Suite [2].

The graph below represents antenna coverage. Each of the seven nodes below represents an antenna with some amount of coverage. Note that the coverage provided by each antenna is identical. The edges between each node represent antennas with overlapping coverage.

Problem: Given the above set of antennas, which antennas should you choose such that you maximize antenna coverage without any overlaps?

Solution: One possible solution is indicated by the red nodes below.

This problem is an example of an optimization problem known as the maximum independent set problem. Our objective is to maximize the number of nodes in a set, with the constraint that no edges be contained in the set. To solve on a D-Wave system, we can reformulate this problem as a quadratic unconstrained binary optimization problem (QUBO). There are a wide variety of applications for this problem, such as scheduling and error correcting codes (as shown in [1]).

To run the demo:

python antennas.py

After running, the largest independent set found in the graph will be printed to the command line and two images (.png files) will be created. An image of the original graph can be found in the file antenna_plot_original.png, and an image of the graph with the nodes in the independent set highlighted in a different color can be found in the file antenna_plot_solution.png.

To run the program on a different problem, modify graph G to represent a different antenna network.

The program antennas.py creates a graph using the Python package networkx, and then uses the Ocean software tools to run the maximum_independent_set function from within the dwave_networkx package.

[1] Sergiy Butenko and Panagote M. Pardalos. "Maximum independent set and related problems, with applications." PhD dissertation, University of Florida, 2003.

[2] Victoria Goliber, "Quantum Programming with the Ocean Tools Suite", https://www.youtube.com/watch?v=ckJ59gsFllU

[3] Andrew Lucas, "Ising formulations of many NP problems", doi: 10.3389/fphy.2014.00005

Released under the Apache License 2.0. See LICENSE file.