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In this paper, we present a novel multigrid-based technique for power/ground mesh area optimization subject to reliability constraints. The multigrid-based technique is applied to reduce a large-scale mesh to a much coarser one. The reduced mesh can be efficiently optimized. The solution for the original mesh is then computed using a back-mapping process. Experimental results are very encouraging. Large-scale power/ground meshes with millions of nodes can be solved in a few minutes. The proposed technique not only speeds up the optimization process significantly without compromising the quality of solutions, but also brings up the possibility of incorporating the power/ground mesh optimization into other physical design stages such as signal routing.