Zhiqiang Zhao
ABSTRACT
Vectorless integrity verification is becoming increasingly critical to robust design of nanoscale power delivery networks (PDNs). To dramatically improve efficiency and capability of vectorless integrity verifications, this paper introduces a scalable multilevel integrity verification framework by leveraging a hierarchy of almost linear-sized spectral power grid sparsifiers that can well retain effective resistances between nodes, as well as a recent graph-theoretic algebraic multigrid (AMG) algorithmic framework. As a result, vectorless integrity verification solution obtained on coarse level problems can effectively help find the solution of the original problem. Extensive experimental results show that the proposed vectorless verification framework can always efficiently and accurately obtain worst-case scenarios in even very large power grid designs.
- J. Batson, D. Spielman, N. Srivastava, and S. Teng. 2013. Spectral sparsiflcation of graphs: theory and algorithms. Commun. ACM 56, 8 (2013), 87--94. Google Scholar
Digital Library
- D. Kouroussis and I. Ferzli and F. Najm. 2005. Incremental partitioning-based vectorless power grid verification. In Proc. IEEE/ACM ICCAD. 358--364. Google ScholarDigital Library
- Z. Feng. 2013. Scalable Multilevel Vectorless Power Grid Voltage Integrity Verification. IEEE Trans. on VLSI Systems 21, 8 (August 2013), 1526--1539. Google ScholarDigital Library
- Z. Feng. 2013. Scalable Vectorless Power Grid Current Integrity Verification. In Proc. of IEEE/ACM DAC. 86:1--86:8. Google ScholarDigital Library
- Z. Feng. 2016. Spectral Graph Sparsification in Nearly-Linear Time Leveraging Efficient Spectral Perturbation Analysis. In Proc. IEEE/ACM DAC. Google ScholarDigital Library
- N. Ghani and F. Najm. 2009. Fast Vectorless Power Grid Verification Using an Approximate Inverse Technique. In Proc. IEEE/ACM DAC. 184--189. Google ScholarDigital Library
- A. Goyal and F. Najm. 2011. Efficient RC power grid verification using node elimination. In Proc. of IEEE/ACM DATE. 257--260.Google Scholar
- D. Kouroussis and F. Najm. 2003. A static pattern-independent technique for power grid voltage integrity verification. In Proc. IEEE/ACM DAC. 99--104. Google ScholarDigital Library
- R. Lewis and S. Nash. 2005. Model Problems for the Multigrid Optimization of Systems Governed by Differential Equations. SIAM J. Sci. Comput. 26, 6 (2005), 1811--1837. Google ScholarDigital Library
- O. Livne and A. Brandt. 2012. Lean algebraic multigrid (LAMG): Fast graph Laplacian linear solver. SIAM Journal on Scientific Computing 34, 4 (2012), B499--B522.Google ScholarDigital Library
- F. Najm. 2012. Overview of vectorless/early power grid verification. In Proc. of IEEE/ACM ICCAD. 670--677. Google ScholarDigital Library
- S. R. Nassif. 2008. IBM power grid benchmarks. {Online}. Available: http://dropzone.tamu.edu/pli/PGBench/.Google Scholar
- Gurobi Optimization. 2016. Gurobi optimizer {Online}. Available: www.gurobi.com. (2016).Google Scholar
- H. Qian, S. R. Nassif, and S. S. Sapatnekar. 2005. Early-stage power grid analysis for uncertain working modes. IEEE Trans. on Computer-Aided Design 24, 5 (2005), 676--682. Google ScholarDigital Library
- D. Spielman and N. Srivastava. 2008. Graph sparsiflcation by effective resistances. In Proc. ACM STOC. 563--568. Google ScholarDigital Library
- D. Spielman and S. Teng. 2011. Spectral sparsiflcation of graphs. SIAM J. Comput. 40,4(2011), 981--1025. Google ScholarDigital Library
- X. Xiong and J. Wang. 2010. An Efficient Dual Algorithm for Vectorless Power Grid Verification under Linear Current Constraints. In Proc. IEEE/ACM DAC. 837--842. Google ScholarDigital Library
- J. Yang and Z. Li. THU power grid benchmarks. {Online}. Available: http://tiger.cs.tsinghua.edu.cn/PGBench/.Google Scholar
- X. Zhao, Z. Feng, and C. Zhuo. 2014. An efficient spectral graph sparsiflcation approach to scalable reduction of large flip-chip power grids. In Proceedings of the 2014 IEEE/ACM International Conference on Computer-Aided Design. IEEE Press, 218--223. Google ScholarDigital Library
Index Terms
- A Spectral Graph Sparsification Approach to Scalable Vectorless Power Grid Integrity Verification
Recommendations
Scalable Multilevel Vectorless Power Grid Voltage Integrity Verification
With the current aggressive integrated circuit technology scaling, vectorless power grid voltage integrity verification becomes key to designing reliable power delivery networks. To address the challenges of existing vectorless power grid verification ...
Scalable vectorless power grid current integrity verification
DAC '13: Proceedings of the 50th Annual Design Automation ConferenceTo deal with the growing phenomenon of electromigration (EM), power grid current integrity verification becomes indispensable to designing reliable power delivery networks (PDNs). Unlike previous works that focus on vectorless voltage integrity ...
A Multilevel Spectral Framework for Scalable Vectorless Power/Thermal Integrity Verification
Vectorless integrity verification is becoming increasingly critical to the robust design of nanoscale integrated circuits. This article introduces a general vectorless integrity verification framework that allows computing the worst-case voltage drops or ...
Comments