We show that for any given muting fraction, a more constrained version of the problem of interest can be optimally solved in an efficient manner. In addition, the obtained solution is also a near-optimal solution for the original problem (for the given muting ratio). This allows us provide an algorithm that offers a good solution to the original problem with a tractable complexity. We also derive a lower complexity greedy that offers good performance and a certain worst-case performance guarantee. Simulations over an example LTE HetNet topology reveal the superior performance of the proposed algorithms and underscore the benefits of jointly exploiting partial muting of the macro and load balancing.