Speedup Factor

Table 13.3 shows the performance comparison of LEAP1 method vs. the exhaustive search. The speedup factor is the ratio between search times required by the exhaustive search and LEAP1. It is seen that in exchange for a 6% false-negative rate we can get more than a 27,000-fold speedup. If we assume that... 

Another speedup factor is for barrierless processes. Consider a reaction in which the system diffuses freely for a length L. The time to reach the end of the line using straightforward trajectories is proportional to L . In milestoning, we chop the complete length L to (say) N pieces. The time to diffuse through one piece is (L/Ny. There are N pieces and therefore the time to reach the destination in milestoning is (L/Nf N = L N. We obtain a speedup proportional to the number of milestones. 

The first experimental results reveal that with an operand bit width of p = 4, at most 16 additions can be carried out in parallel by a 64-bit adder, and 2.7 in average. Another experiment performed by a static code analysis of SPECint2006 base benchmarks gave an average speedup factor of 3.19, showing the potential of PAMOS and PAROS. 

An average speedup factor of 3.19 is reached. Through reorganization of code, the compiler can take additional care that more cases of additions with two redundant operands occur, e.g. (big 4- smalll) + small2 could be reorganized to (smalll + smaU2) + big. 

Fig. 20 Top Measured speedup factor using one to eight remote similar computers in parallel, for 2 different algorithms MGold with 7 iterations and MLE with 50 iterations. Computation was achieved using 120 stacks of 1.4 Mb each, and computers connected via a 1 Gb/s LAN. Bottom Simulation of the speedup factor as a function of the ratio TJTp for two to ten remote servers...

A Stack of 500x400 pixels x 9 planes was acquired every second over a 2-niin period with only 50 ms exposure time per plane. The acquisition of each stack in z-streaming mode took less than 500 ms, allowing more than 500 ms for fluorescence relaxation. Figure 20 shows the measured speedup factor as a fimction of the number of remote servers. The speedup factor is defined as the time required to restore all the stacks in sequential mode, divided by the time measured to restore all the stacks in parallel mode. The only difference between the algorithms is the computing time per stack. 

In the fastest case, it took only 1 min 45 s to process all the data using eight remote servers plus the chent computer, rather than about 9 min in sequential mode, giving a speedup factor greater than 5. 

In addition to the finite element simulation, other structural numerical simulations also can be greatly accelerated by the use of GPUs. For example, Durand et al. (2012) simulated rock impact on a concrete slab using the discrete element method (DEM), and the use of a GPU (Tesla C2050) reportedly showed a speedup factor of 30. 

The rationale of using hybrid simulation here is that a classic diffusion-adsorption type of model, Eq. (2), can efficiently handle large distances between steps by a finite difference coarse discretization in space. As often happens in hybrid simulations, an explicit, forward discretization in time was employed. On the other hand, KMC can properly handle thermal fluctuations at the steps, i.e., provide suitable boundary conditions to the continuum model. Initial simulations were done in (1 + 1) dimensions [a pseudo-2D KMC and a ID version of Eq. (2)] and subsequently extended to (2 + 1) dimensions [a pseudo-3D KMC and a 2D version of Eq. (2)] (Schulze, 2004 Schulze et al., 2003). Again, the term pseudo is used as above to imply the SOS approximation. Speedup up to a factor of 5 was reported in comparison with KMC (Schulze, 2004), which while important, is not as dramatic, at least for the conditions studied. As pointed out by Schulze, one would expect improved speedup, as the separation between steps increases while the KMC region remains relatively fixed in size. At the same time, implementation is definitely complex because it involves swapping a microscopic KMC cell with continuum model cells as the steps move on the surface of a growing film. 

One possibility to speedup the search is preliminary sorting of the data sets. Here, the methods of unsupervised pattern recognition are used, for example, principal component and factor analysis, cluster analysis, or neural networks (cf. Sections 5.2 and 8.2). The unknown spectrum is then compared with every class separately. 

In practice, ideal speedups are difficult to achieve, especially if the number of processes is large. One factor that reduces the speedup is the existence in an algorithm of inherently sequential parts of code that cannot benefit from a parallel implementation. An upper bound on the speedup was formulated by Amdahl, who expressed the maximum attainable speedup for a parallel algorithm in terms of the serial fraction, f, of the algorithm... 

We have used expressions involving the latency, a, and inverse bandwidth, /3, to model the communication time. An alternative model, the Hockney model, is sometimes used for the communication time in a parallel algorithm. The Hockney model expresses the time required to send a message between two processes in terms of the parameters Too and ni, which represent the asymptotic bandwidth and the message length for which half of the asymptotic bandwidth is attained, respectively. Metrics other than the speedup and efficiency are used in parallel computing. One such metric is the Karp-Flatt metric, also referred to as the experimentally determined serial fraction. This metric is intended to be used in addition to the speedup and efficiency, and it is easily computed. The Karp-Flatt metric can provide information on parallel performance characteristics that caimot be obtained from the speedup and efficiency, for instance, whether degrading parallel performance is caused by incomplete parallelization or by other factors such as load imbalance and communication overhead. ... 

Looking at the parallel performance for the iterative procedure, the speedups are significantly lower than for the integral transformation, and for the uracil dimer the iterative procedure achieves a speedup of 52 for 100 processes. The nonscalable collective communication step required in each iteration is the primary factor contributing to lowering the speedup, but a... 

Another way to speed up convergence is to use localized SCF MOs (Section 15.9) instead of canonical SCF MOs in the CSFs. Cl calculations on 1,3-butadiene using this localized correlation method showed speedups by factors of 20 to 40, since fewer CSFs needed to be included [S. Saeb0 and P. Pulay, Chem. Phys. Lett., 113,13 (1985)]. 

Maximum cardinality EFMA was implemented as a minimal invasive extension to Efmtool and fully utilizes the computational advantages of the binary null space implementation of the DD method. Both factors, the maximum cardinality EFMA strategy and the binary implementation, result in a major speedup that outperforms other, MlLP-based approaches by orders of magnitude. 

There are several criteria for successful microwave and dielectric drying systems. Cost is reduced. This is often a major factor. Cost savings may be realized through energy savings, increased throughput, labor reduction, reduction in heat load in the plant, speedup of the process, operational efficiencies, and reduced maintenance costs. 

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