### Table 3: The effect of sparsification

2000

"... In PAGE 5: ... An efficient direct linear solver based on Cholesky fac- tors was used in all the experiments. The extracted power grids of four high performance general purpose/DSP microprocessor chips were used to benchmark the performance of macromodeling (Ta- bles 1 and 2) and sparsification ( Table3 ) techniques. Chips 1, 2 and 4 are DSP and communication chips whose power grids are imple- mented in 3 layers of metal.... ..."

Cited by 45

### Table 1: Sparsification in the standard basis.

2000

"... In PAGE 5: ... A common approach to reducing the density of coupling in the substrate conductance matrix is simply to drop entries that, in the normal basis, are small. Table1 shows a sparsity ratio and error obtained by thresholding without a change of basis, demonstrating that this more obvious approach can be quite ineffective. However, when the multiscale basis is employed, much better results can be obtained.... ..."

Cited by 9

### Table 1: Sparsification in the standard basis.

2000

"... In PAGE 5: ... A common approach to reducing the density of coupling in the substrate conductance matrix is simply to drop entries that, in the normal basis, are small. Table1 shows a sparsity ratio and error obtained by thresholding without a change of basis, demonstrating that this more obvious approach can be quite ineffective. However, when the multiscale basis is employed, much better results can be obtained.... ..."

Cited by 9

### TABLE I RESULTS OF NUMERICAL SPARSIFICATION

2003

Cited by 9

### Table 5: Spectral Graph Partitioning results for Yahoo K1

### Table 3 Relative deviation of spectral distances for Delaunay graphs

### Table 4 Relative deviation of spectral distances for random graphs

### Table 2: Results for random graphs. Graph |V | |E| Spectral Cuthill-McKee

2005

"... In PAGE 13: ... We compare a single run of our V-cycles with the results of the exact spectral method and with those of the Cuthill-McKee permutation [16] which was checked also in [14]. The results are summarized in Table2 showing a clear advantage to our multilevel approach even for those obviously unstructured random graphs. 4.... ..."

Cited by 1

### Table 5. Experiments with sparsification on top of Spanning Tree, and Spanning Tree on di erent graphs and sequences of 500 updates. For each algorithm the left column is the preprocessing and the right colum is the processing time in seconds. Each data set is the average of ten di erent samples.

1996

Cited by 24