Effective Resistance Estimation for Large Circuits Using Random Walk Algorithm

We propose a method for estimating the effective resistance of large circuits using a random walk algorithm. In this method, a particle randomly hops among circuit nodes based on the circuit's topology, and the hopping probabilities are determined accordingly. We introduce two effective resistance estimation (ERE) algorithms for different scenarios: ERE between any two nodes and ERE between all nodes and a reference node. To reduce the statistical error of ERE, we repeat the random walk processes multiple times. Additionally, we compare the results obtained from this method with those obtained from a rigid solving method to evaluate its effectiveness.