### Table 1: Comparison of Partitioning Schemes

### Table I. Comparison of the different ray partitioning schemes.

### Table 14: Comparison of Reuse Partitioning Schemes Scheme Advantages Disadvantages

1996

"... In PAGE 23: ... Although the idea is appealing it is not practical for the present systems. In Table14 , a summary of the important characteristics of channel allocation schemes based on reuse partitioning is provided. 10 Other Schemes 10.... ..."

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### Table 2. Experimental results for one design with different number of partitioning schemes

"... In PAGE 9: ...partitioning schemes. In Table2 , four different number of partitioning schemes have been given to the optimization algorithm for the same design consisting of 6 cores. The optimal solution is the same in the three cases where the total number of partitioning schemes is 7, 10, and 15, respectively.... In PAGE 9: ... In the case that the number of partitioning schemes is only 5, the total test time of the obtained solution is larger than those in the other three cases. This experiment shows that, for this design, the best solution does not correspond to the partitioning scheme found among the five alternative partitioning schemes, as indicated in the first line in Table2 . If we introduce 2 additional alternative partitioning schemes (see line 2 in Table 2), a better solution is found.... ..."

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### Table 2. Experimental results for one design with different number of partitioning schemes

"... In PAGE 8: ... Experimental results for 5 different designs Number of Cores Total Number of Partitioning Schemes Problem Size Total Test Times (# of clock cycles) CPU Times (ms) 4 7 28 2775 2141 12 8 96 8306 35359 24 20 400 9789 47500 36 20 720 10017 120219 48 20 960 10941 881766 We also did experiments to see how the optimization result is impacted by the given total number of partitioning schemes. In Table2 , four different number of partitioning schemes have been given to the optimization algorithm for the same design consisting of 6 cores. The optimal solution is the same in the three cases where the total number of partitioning schemes is 7, 10, and 15, respectively.... In PAGE 8: ... In the case that the number of partitioning schemes is only 5, the total test time of the obtained solution is larger than those in the other three cases. This experiment shows that, for this design, the best solution does not correspond to the partitioning scheme found among the five alternative partitioning schemes, as indicated in the first line in Table2 . If we introduce 2 additional alternative partitioning schemes (see line 2 in Table 2), a better solution is found.... ..."

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### Table 6-2: Comparison of two partitioning schemes.

"... In PAGE 12: ...able 5-2: Size of benchmark circuits............................................................................44 Table6 -1: Area overhead and clock rate for different schemes.... In PAGE 12: ...able 6-1: Area overhead and clock rate for different schemes. .....................................61 Table6 -2: Comparison of two partitioning schemes.... In PAGE 73: ... Detailed discussions on the choice of partitioning methods for this case study can be found in Appendix E. Table6 -1 shows the resulting area and clock frequency for simplex (single module without error detection), duplex without partitioning, duplex with nine sub- circuits, and duplex with 17 sub-circuits. Note that although the area overhead in terms of CLB utilization increases with the number of sub-circuits, the number of columns used does not change significantly in different duplex schemes.... In PAGE 73: ... Degradation of maximum clock rate because of partitioning is within 10% in this case study. Table6 -1: Area overhead and clock rate for different schemes. Scheme CLB utilization (slices) CLB columns used Max.... In PAGE 74: ...62 Table6 -2 summarizes the partitioning results for duplex schemes with 9 and 17 sub-circuits. Because there are global signals connecting the controller sub-circuit and all the other sub-circuits in the systolic array, the worst-case suspect set spans the entire used region in the FPGA.... ..."

### Table 2: Data redistribution costs of the six data partitioning schemes.

1997

"... In PAGE 6: ... In [17] we studied and tabulated the cost functions of data redistribution from one partition to another. The cost table is reproduced in Table2 . Note that the communication algorithms used to generate Table 2 may not be optimal and other algorithms for all-to-all communication could be used, e.... In PAGE 18: ... Edges incident on the starting and the end nodes were of zero weight. Costs of all other edges were tabulated in Table2 . The rst node in this reduced graph represented a histogram equalization operation, which had only a single parallel implementation based on the block partition in our library.... ..."

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### Table 2. Resource utilization for several investigated partitioning schemes

2004

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