An Algebraic Multigrid Solver for Analytical with Layout Based Clustering Placement

2 ABSTRACT efficient matrix solver is critical to the analytical placement. As the size of the matrix becomes huge, the multilevel methods tum out to be more efficient and more scalable. Algebraic Multigrid (AMG) is a multilevel technique to speedup the iterative matrix solver (lo). We apply the algebraic multigrid method to solve the linear equations that arise from the analytical placement. A layout based clustering scheme is put forward to generate coarsening levels for the multigrid method. The experimental results show that the algebraic multigrid solver is promising for analytical placement.

[1]  Igor L. Markov,et al.  Quadratic placement revisited , 1997, DAC.

[2]  Georg Sigl,et al.  GORDIAN: VLSI placement by quadratic programming and slicing optimization , 1991, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[3]  Marian Brezina,et al.  Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems , 2005, Computing.

[4]  Sani R. Nassif,et al.  Multigrid-like technique for power grid analysis , 2001, ICCAD 2001.

[5]  Igor L. Markov,et al.  Consistent placement of macro-blocks using floorplanning and standard-cell placement , 2002, ISPD '02.

[6]  Frank M. Johannes,et al.  Generic global placement and floorplanning , 1998, Proceedings 1998 Design and Automation Conference. 35th DAC. (Cat. No.98CH36175).

[7]  Vipin Kumar,et al.  Multilevel k-way hypergraph partitioning , 1999, DAC '99.

[8]  K. Stüben A review of algebraic multigrid , 2001 .

[9]  Joseph R. Shinnerl,et al.  Multilevel optimization for large-scale circuit placement , 2000, IEEE/ACM International Conference on Computer Aided Design. ICCAD - 2000. IEEE/ACM Digest of Technical Papers (Cat. No.00CH37140).

[10]  Andrew B. Kahng,et al.  Multilevel circuit partitioning , 1998, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..