  Quantum annealing promises to be an effective heuristic for complex NP-hard
problems. However, clear demonstrations of quantum advantage are wanting,
primarily constrained by the difficulty of embedding the problem into the
quantum hardware. Community detection methods such as the Girvin--Newman
algorithm can provide a divide-and-conquer approach to large problems. Here, we
propose a problem-focused division for embedding, deliberately worsening
typical measures of embedding quality to improve the partial solutions we
obtain. We apply this approach first to the highly irregular graph of an
integer factorisation problem and, passing this initial test, move on to
consider more regular geometrically frustrated systems. Our results show that a
problem-focused approach to embedding can improve performance by orders of
magnitude.
