Random walks in a supply network

This paper presents a power grid analyzer based on a random walk technique. A linear-time algorithm is first demonstrated for DC analysis, and is then extended to perform transient analysis. The method has the desirable property of localizing computation, so that it shows massive benefits over conventional methods when only a small part of the grid is to be analyzed (for example, when the effects of small changes to the grid are to be examined). Even for the full analysis of the grid, experimental results show that the method is faster than existing approaches and has an acceptable error margin. This method has been applied to test circuits of up to 2.3M nodes. For example, for a circuit with 70K nodes, the solution time for a single node was 0.42 sec and the complete solution was obtained in 17.6 sec.