Quantum optimization is expected to resolve many computationally hard problems, such as Radio Resource Allocation (RRA) in wireless communications and networking. However, given noisy intermediate-scale quantum (NISQ) computers that supply a very limited number of effective logical qubits after quantum error correction, computationally efficient algorithms are highly desirable to facilitate quantum advantages, particularly the required number of qubits. To achieve quantum advantageous optimization by small number of qubits, we formulate RRA as a Maximum Independent Set (MIS) on dense conflict graphs, which is challenging for the Quantum Approximate Optimization Algorithm (QAOA) using NISQ computing machines. We further propose a modified Quantum Local Search (QLS) framework that decomposes the global MIS into overlapping subgraphs defined by a tunable neighborhood radius. Hard (feasibility) constraints are enforced via partial mixers, while soft (adjacency) constraints are resolved in a classical post-processing step. Considering practical interference issues that are typically ignored in quantum computational research, we uniquely extend the method to accommodate minimal-adjacency scenarios by specifying shared boundaries causing limited interference. While complexity analysis shows polynomial scaling in the number of feasible placements, computational experiments demonstrate substantial savings on required qubits and simultaneously achieving optimal solutions across multiple adjacency configurations. Efficient quantum optimization of RRA by NISQ computers of significantly fewer qubits is therefore accomplished.