### Table 12: Speed of Parallel FPA Using PVM Note that there is an almost linear decrease in the run time as the number of the slave processes is increased.

### Table 1: Results for FIFO Example. This example shows time and size behavior of our construction as we scale the number of vertices and edges in an assertion graph. The Depth column indicates the depth of the FIFO. (It is 8 bits wide.) Vertices and Edges indicate the size of the assertion graph. Gates and Latches indicate the size of the monitor circuit. Time is how many seconds it took to generate the monitor circuit. Size is clearly linear; run time is almost linear.

2003

"... In PAGE 5: ... Indeed, the assertion graph itself is generated via a script. Table1 shows the results as we scale the assertion graph size for different buffer depths. The size of the generated monitor circuits is clearly growing linearly in the size of the assertion graph.... ..."

Cited by 1

### Table 1: Results for FIFO Example. This example shows time and size behavior of our construction as we scale the number of vertices and edges in an assertion graph. The Depth column indicates the depth of the FIFO. (It is 8 bits wide.) Vertices and Edges indicate the size of the assertion graph. Gates and Latches indicate the size of the monitor circuit. Time is how many seconds it took to generate the monitor circuit. Size is clearly linear; run time is almost linear.

"... In PAGE 5: ... Indeed, the assertion graph itself is generated via a script. Table1 shows the results as we scale the assertion graph size for different buffer depths. The size of the generated monitor circuits is clearly growing linearly in the size of the assertion graph.... ..."

### Table VI: Time required for each step of sorting 8M integers with respect to the number of nodes using 1 and 4 threads. The graphs in Figure 4 examine the scalability of our sorting algorithm as a function of problem size, for di ering numbers of nodes and for 1 and 4 threads. For one thread, they show that for a xed number of nodes there is an almost linear dependence between the execution time and the total 16

1998

Cited by 9

### Table 2. Exec. times, speedup and e ciency. The speedups are almost linear with 4 and 8 pro- cessors. With more than 8 processors, the speedups still continue to increase, but asymptotically. A max- imum speedup of 17.18 can be achieved with 64 and 78 processors, the latter case representing a simple

"... In PAGE 8: ... Figure 6 shows the ex- ecution time for the sequential version and for 6 map- pings of the distributed simulation. Table2 presents the speedup and the e ciency (speedup/nproc) as the number of processors nproc is varied. 0 20 40 60 80 100 120 0 50000 100000 150000 200000 Real Time (secs) Virtual Time (time slots) sequential 4 nodes 8 nodes 16 nodes 32 nodes 64 nodes 78 nodes Figure 6.... ..."

### Table 5: Office with different types of rays. This shows that the performance is very close to linear in the number of rays shot and almost independent of the type of the ray. is slightly cheaper than linear: 4 times more rays cost only 3.6 times more, due to a better cache hit-rate. See Table 6 for a detailed look on the cache.

"... In PAGE 9: ....5. Lights, Reflections, and Anti-Aliasing One of the main advantages of ray tracing is its ability to ren- der physically correct shadows, reflections, and refractions. In this section we analyse the impact of these different types of rays on the overall performance by rendering the Office scene in different conditions, as listed in Table5 and shown in Figure 7 (in the color section): (a) eye rays (er) only, (b) er and reflections up to 3 levels (r3), (c) er and 3 lights (3l), (d) er, reflections and 3 lights, (e) er with a simple four times oversampling (4 os), i.e.... In PAGE 9: ... Please note that in (b) 20% of all rays are reflected. Table5 shows that the performance degrades linearly with the number of rays shot, independently of the type of rays. This is also true for refracted rays used to simulate glass- effects (not shown here).... ..."

### Table 3 and Figure 4 show how the processing time and the message size vary with the initial group size. The horizontal axis in Figure 4 is in log scale. When extrapolated, this implies that the CKMSS scheme is scalable to large groups because the processing time per request increases almost linearly with the logarithm of the group size. The reduction of the problem from O(n) to O(log(n)) leads to substantial economy in commercial applications.

1983

"... In PAGE 8: ... Table3 . Message size versus initial group size 0 5 10 15 20 25 32 64 128 256 512 1024 2048 4096 8192 16384 Initial group size Processing time (msec) Server processing time per join Server processing time per leave Server processing time per request... ..."

Cited by 1

### Table 3 and Figure 4 show how the processing time and the message size vary with the initial group size. The horizontal axis in Figure 4 is in log scale. When extrapolated, this implies that the CKMSS scheme is scalable to large groups because the processing time per request increases almost linearly with the logarithm of the group size. The reduction of the problem from O(n) to O(log(n)) leads to substantial economy in commercial applications.

1983

"... In PAGE 8: ... Table3 . Message size versus initial group size 0 5 10 15 20 25 32 64 128 256 512 1024 2048 4096 8192 16384 Initial group size Processing time (msec) Server processing time per join Server processing time per leave Server processing time per request... ..."

Cited by 1

### TABLE 3 Running times and pointwise errors for the SVD-based sparsi cation. We report results for the geometry depicted in Figure 4(c) (64 circles) for a Stokeslet ow; for two different values of the numerical rank tolerance and for an eight-fold increase in problem size. Observe the almost linear scaling in setup and solve running times with the problem size. For this example about 10,000 Nystrcurrency1 om points give single precision machine accuracy. L=N setup(s) solve(s)

2002

### Table 2: Timings for the solution phase. We observe a super linear speed-up from 16 to 32 processors, but this is probably due to a cache e ect. The speed-up from 32 to 64 processors is almost linear. This indicates that the

1995

"... In PAGE 7: ...MRES-iterations. The Jacobi-Davidson algorithm converges rapidly for our problem. Only 17 iterations are needed to reduce the norm of the residual corresponding to the smallest eigenvalue ?2:596 + 42:00i to 10?8. Table2 gives the timings for the solution phase. Number of processors Elapsed time... ..."

Cited by 3