Mapping graph coloring to quantum annealing

Graph coloring using the reduced quantum genetic algorithm

“…Thus, we first consider a comparison that focuses on the forms of graph coloring problem that are solved, the ability to determine the chromatic number, and metrics used in order to determine the algorithm’s performance. Additionally, we provide a comparison that focuses on the solution count between RQGA and the algorithms presented in Silva et al (2020) ; we also compare our approach with the algorithms presented in Silva et al (2020) , Tabi et al (2020) , and Aragón Artacho & Campoy (2018) from the perspective of the number of iterations required to find a solution that colors a 5-node graph.…”

“…15 we present the comparison between our approach and the algorithms presented in Silva et al (2020) that focus on the ratio between the number of solutions (optimal, possible, and none) and the number of repetitions. RQGA performed 4 iterations 8,192 times while the algorithms presented in Silva et al (2020) performed 5,000 iterations 10,000 times. For all algorithms, we divided the number of solutions found by the number of iterations multiplied with the number of repetitions.…”

“… We use the notations from Silva et al (2020) to denote best, valid, and invalid solutions. As such, optimal represents best solutions, valid solutions are called possible, and the invalid ones are called none.…”

“…In Fig. 16 we present a comparison between RQGA and the algorithms presented in Silva et al (2020) , Tabi et al (2020) , and Aragón Artacho & Campoy (2018) , from the perspective of the number of iterations required to find the solutions that color a 5-node graph. As presented in subsection Complexity analysis and confirmed experimentally, RQGA requires 4 iterations for finding the solutions while the mentioned heuristic algorithms require 44, 5,000, and 100 iterations, respectively.…”

“…In Silva et al (2020) , the authors start by formulating the Quadratic Unconstrained Binary Optimization Problem (QUBO)—a powerful mathematical tool that can map any problem to a quantum annealing computer. Silva et al (2020) solve the problem using different approaches: QUBO with classical simulated annealing in a simulated quantum environment, using a D-Wave quantum machine, and reducing polynomial degree using both the D-Wave library and their implementation. The results show that both Simulated Annealing and QA produce good heuristics for the graph coloring problem, although more solutions can be found using the quantum approach.…”