Random walks in a supply network

Abstract

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.

IGS: The Novel Fast IC Power Ground Network Optimization Flow Based on Improved Gauss-Seidel Method

“…Previous work refers to the Random Walk algorithm in [13], which is widely used to calculate the voltage distribution. And the Representative Random Walk algorithm presented in [14] establishes a relatively simple conductance model according to the width and density of the real PGN, then calculates the IR-drop distribution of the model, which is efficient to estimate the IR-drop distribution.…”

Incremental power network analysis using backward random walks

“…In this section, we qualitatively review the similarities and differences of backward random walks of Section II.A and the forward random walks described in [1]. The forward game captures the effect of all of the RHS elements (i.e., the current loads in power network analysis context) on the solution of a single node, while the backward game captures the effect of a single source on the solution of the entire system, as indicated by Eq.…”

“…Mainstream methods for solving such systems include direct methods such as LU/Cholesky factorization and iterative methods. Lately, there has been an upsurge of interest in the use of random walk-based solvers for solving systems with diagonally dominant LHS matrices, and these solvers are competitive with conventional solvers [1]- [4].…”

“…1 Identifying the RoI is nontrivial. The work of [11] uses the bookkeeping information of the random walk solver of [1] (which we will refer to as forward random walks), obtained as part of a preprocessing phase, to identify the RoI for any perturbation. This approach has two drawbacks: (1) it uses approximations that neglect second-order terms, leading to some errors, and (2) it neglects the fact that the bookkeeping information changes due to these perturbations, making this method increasingly inaccurate as more consecutive perturbations are made.…”

Power grid simulation via efficient sampling-based sensitivity analysis and hierarchical symbolic relaxation

“…In the past several years, power distribution networks have been an active topic of research. Both the power grid analysis [1][2][3][4][5][7][8] and optimization issues [10,[12][13][14][15] are being addressed by the EDA community. In terms of analysis, given the fact that the conventional direct solution methods do not scale with the problem size, it does not only make sense, but also becomes imperative to develop specific simulation techniques that can offer a good tradeoff between accuracy and efficiency.…”