Hierarchical random-walk algorithms for power grid analysis

It is found that the efficiency of the generic random walk analyzer varies for power grids with different packagings: a wire-bond power grid requires much higher runtime than one with C4’s. To address this robustness issue, this paper presents a power grid analyzer that combines a divide-and-conquer strategy with a random-walk engine. A single-level hierarchical method is first described and then extended to multi-level and “virtual-layer ” hierarchy. Experimental 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 industrial 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 wirebond power grid, for which the performance of the generic method degrades, is solved in 75.88 seconds. 1