### Table 4.3: Multiplicative partitions of 210.

2006

### Table 12. Double Partition vs. Multiple Partition n DO Method with Double Partition Multiple Partition = dpn e k = 2

"... In PAGE 16: ... Because both and k have to be integer we have to assume = l 3 pn2 m and k = lp m. A comparison between the performance of the optimal delay scheme based on double partition and the the optimal delay scheme based on mul- tiple partition is given in Table12 . The strange fact that in the case of 16 bit operands the mul- tiple partition provides a delay greater then the delay provided by the double partition is a con- sequence of the error we introduced in the opti- mization in Theorem 3 by discarding the ceiling operators.... ..."

### Table VI. Matrix Multiplication: Final Partition # Ctx. Resp. Exec.

### Table IV. Partitioning Exploration in Matrix Multiplication

### Table 1 shows the speedup ratio of matrix vec- tor multiplication with 24 partitions and ma- trix multiplication with 256 partitions. The speedup ratio for matrix multiplication is a little higher. The reason is that the ratio of computation to communication for matrix multiplication is a little higher than vector ma- trix multiplication, as illustrated by Figure 9.

2006

"... In PAGE 12: ... Table1 Speedup Ratio 2 3 4 5 6 7 8 0 20 40 60 80 100 120 140 160 180 200 Workers # Time(s) Time Decouple vs Workers# (Matrix*Vector 24) Network Traffic Computing 2 3 4 5 6 7 8 0 50 100 150 200 250 300 350 400 Workers # Time(s) Time Decouple vs Workers# (Matrix*Matrix 256) Network Traffic Computing Figure 9 Computation and Network load decouple. For each workers setting, average load decouple is shown.... ..."

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### Table V: Partitioning multiple overlapping loops. Looping Program Alternative Decision function PN partitioning

### Table 2. Generating unrestricted partitions of 75 in the multiplicity representation

1993

Cited by 1

### Table 1. Potential loop-invariants for symmetric matrix multiplication for the specific partitioning in Section 3.

"... In PAGE 6: ... Alternative algorithms. Notice that by applying Steps 3- 8 to each of the potential loop-invariants in Table1 one will either conclude that the potential loop-invariant does not re- sult in an algorithm, or one will discover an alternative al- gorithm. We leave it as an exercise for the reader to derive... ..."

### Table 6 Multiple two partitions on the Letter data set for a 10-fold cross-validation using C4.5

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### Table 2. Average accuracy and total bene- fits by complete multiple model with different number of partitions.

"... In PAGE 5: ... Each result is the av- erage of different multiple models with C3 ranging from 2 to 256. In Table2 , the results are shown in two columns under accuracy and benefit. As we compare the respective results in Tables 1 and 2, the multiple model consistently and significantly beat the accuracy of the single model for all three datasets using all three different inductive learn- ers.... ..."