### Table 1 Performance results on nCUBE 2 and Paragon multiprocessors.

"... In PAGE 4: ... The Chaco runs were performed on an SGI Onyx with a 125 MHz clock. Table1 presents the results for 64 and 1024 partitions for both grids while Fig. 2 plots the parallel run times for the CVD grid for 64 through 1024 partitions.... ..."

### Table 11: Distribution Amount Speedup Results

1998

"... In PAGE 23: ... If too much work is donated, the granting processor will soon be in danger of becoming idle. Table11 lists the results of this experiment, demonstrating once again that the learning system is capable of e ectively selecting load balancing strategies, except when the un ltered test cases from the fteen puzzle are used (on the nCUBE and on the distributed network of workstations). The combined results are generated using training cases from the fteen puzzle and robot arm motion planning nCUBE examples.... ..."

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### Table 3 gives a breakup of the times among the various steps. These timings were taken on the nCUBE/2, with

1993

"... In PAGE 4: ... For 1024 processors, k = 8 was observed to be optimal. Table3 : Breakup of timings for sorting 223 integers on the nCUBE/2. Hist and Move are the times for histogramming and data movement, respectively.... ..."

Cited by 4

### Table 2: Calling conventions for nCUBE2, iPSC860, RS6000 machines

1993

"... In PAGE 4: ... This issue is related to machine architecture and calling conventions in the compiler. In the Table2 , we list the calling conventions for the nCUBE2, iPSC860, and RS6000 machines. Details can be found in [5, 6, 11].... ..."

Cited by 5

### Table 1: Timings in seconds for problem (16) in the nCUBE and Paragon computers.

"... In PAGE 31: ... A Fortran implementation of BLAS from Netlib [14] was compiled on the nCUBE. Table1 compares actual running times in seconds for our test case on both computers. The di erent curves are due to di erent granularities.... In PAGE 32: ... The positive root, which indicates that the maximum number of processors to be allocated is N = 5 for a matrix of order 961, N = 10 for order 3969, and N = 20 for a matrix order of 16129. The data in Figure 4 and Table1 show that our timings for the mesh architecture (Paragon in our case) followed the theoretical estimates. Preconditioning is another relevant issue concerning performance [30].... ..."

### Table 2 The timings of the PMC-3D with SOR and MG solvers on the 32-node nCUBE multiprocessor.

"... In PAGE 7: ... Table2 shows the timing results of parallel SOR and multigrid PMC-3D codes on a 32-processor nCUBE multiprocessor. The PMC-3D code is again run for 100 time steps on the same grid with 20,000 particles.... In PAGE 7: ... The PMC-3D code is again run for 100 time steps on the same grid with 20,000 particles. As can be seen from Table2 , the parallel multigrid PMC-3D code is 3#7B9 times faster than the parallel SOR PMC-3D. In this case, the multigrid solver is found to be 5#7B9 times faster than the SOR solver.... ..."

### Table 1. Balanced colorings of the n-cube for n = 3; 4; 5 and 6. 8

"... In PAGE 7: ...16) we nd N4;4 = 8(8) ? 12(1) = 52 and N5;4 = 8(52) ? 12(8) = 320. We emphasize that most of the entries in Table1 for Nn;2k were computed using formula (3.... In PAGE 7: ...ormula (3.3) of Theorem 3.1. The condition n gt; m in the hypothesis of Corollary 1 requires n gt; 7 when 2k = 8. Even if 2k = 6, there are m = 4 di erent values for N(hji) and so in Table1 only N5;6 and N6;6 can be obtained from the recurrence relation for Nn;6. The theorem can also be used to determine the number An;2k of balanced color- ings with 2k black vertices but no antipodal pair of black vertices, i.... In PAGE 7: ... On selecting k ? i of these pairs and coloring their 2(k ? i) vertices black, we obtain a balanced coloring with 2i + 2(k ? i) = 2k black vertices. Therefore the number of these for each i is 0 @ 2n?1 ? 2i k ? i 1 A An;2i: 2 The numbers Nn;2k and An;2k are displayed in Table1 for n = 3; 4; 5 and 6 and 2k 2n?1. If the colors of any 2-coloring of two vertices of the n-cube are switched, we obtain the complementary coloring or the complement.... In PAGE 9: ... Since this is true for all i with 1 i lt; n and since u; v 2 Fn we conclude that u = v, which is a contradiction. 2 We also observe in Table1 that A4;8 = N3;4 = 8, A5;16 = N4;8 = 222 and A6;32 = N5;16 = 807980. This turns out to be the case in general.... In PAGE 11: ...ence T N3;4 = 8(3)?12(1) = 12. Continuing to use (4.3) we nd T N4;4 = 8(12)? 13(3) = 60, T N5;4 = 8(60) ? 12(12) = 336 and T N6;4 = 8(336) ? 12(60) = 1968. Thus to the results given in Table1 , we can add those in Table 2, which gives the corresponding numbers of weighted, balanced n-cubes, where non-negative integer weights are allowed for the vertices. It can be shown quickly by combinatorial means that T N2;2k = k + 1 and so these values have been omitted from the table.... In PAGE 17: ...26)which is, by (4.23), equal to N3;4 (see Table1 ). Furthermore, it is easy to see from (4.... ..."

### Table 1: Times (in seconds) and Speedups for 3 applications on the nCUBE/2.

1993

Cited by 122

### Table 2. Execution times (in seconds) for matrices of type 1 through 12 on an nCUBE-2 21

1993

Cited by 11

### Table 1. A comparison of k-ary n-cubes versus de Bruijn graphs

2005

Cited by 1