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The analysis of on-chip power grids requires the solution of large systems of linear algebraic equations with specific properties. Lately, a class of random walk based solvers have been developed that are capable of handling these systems: these are especially useful when only a small part of the original system must be solved. These methods build a probabilistic network that corresponds to the power grid. However, this construction does not fully exploit the properties of the problem and can result in large variances for the random walks, and consequently, large run times. This paper presents an efficient methodology, inspired by the idea of importance sampling, to improve the runtime of random walk based solvers. Experimental results show significant speedups, as compared to naive random walks used by the state-of-the-art random walk solvers.