  Rydberg atom arrays are among the most promising quantum simulating platforms
due to their scalability and long coherence time. From the perspective of
combinatorial optimization, they are intrinsic solver for the maximum
independent set problem because of the resemblance between the Rydberg
Hamiltonian and the cost function of the maximum independent set problem. In
this paper, we suggest a strategy to approximate maximum independent sets by
adjusting local detunings on the Rydberg Hamiltonian according to each vertex's
vertex support, which is a quantity that represents connectivity between
vertices. By doing so, we explicitly reflect on the Rydberg Hamiltonian the
potential probability that each vertex will be included in maximum independent
sets. Our strategy reduces an error rate three times for the checkerboard
graphs with defects when the adiabaticity is enough. Our strategy also
decreases the error rate for random graphs of density 3.0, even when the
adiabaticity is relatively insufficient. Moreover, we harness our strategy to
raise the fidelity between the evolved quantum state and a 2D cat state on a
square lattice, showing that our strategy helps to prepare a quantum many-body
ground state.
