Hierarchical random-walk algorithms for power grid analysis

Abstract — This paper presents a power grid an-alyzer that combines a divide-and-conquer strategy with a random-walk engine. A single-level hierarchi-cal method is first described and then extended to multi-level and “virtual-layer ” hierarchy. Experimen-tal results show that these algorithms not only achieve speedups over the generic random-walk method, but also are more robust in solving various types of in-dustrial circuits. For example, a 71K-node circuit is solved in 4.16 seconds, showing a more than 4 times speedup over the generic method; a 348K-node wire-bond power grid, for which the performance of the generic method degrades, is solved in 75.88 seconds. I