### Table 1 shows that the a5 -input AND discrete version is

"... In PAGE 4: ... For example, an a32 -input TLFF with a63 a18 a32 is with a8a2a8a47a8 slower than a the TLFF with a63 a18 a32 . With regard to Table1 , an ETDRDFF with embedded a5 -input AND is with between a1 a4a5 a8 and a18 a7a6a9a8 faster than the same flip-flop having embedded a a8 -input and a32 -input AND respectively. Table 2 shows that an ETDRDFF hav- ing incorporated a a5 -input OR has between a8 a0 a8 and a18 a4a5 a8 less total latency than the same flip-flop having embed- ded a a8 -input and a32 -input OR respectively.... In PAGE 4: ... Since a TLFF implementing an a32 -input AND has a63 a18 a32 , more current is drawn by the nMOS transistors from the threshold map- ping bank and therefore a TLFF with a32 -input AND is faster than a TLFF with a5 -input AND. Indeed, the simulation results from Table1 show that an a32 -input AND TLFF is with a32 a3 a4a8 faster than a a5 -input TLFF and with a0 a8 faster than the a8 -input TLFF. In contrast, a a5 -input OR TLFF is marginally faster than the a8 -input OR and a32 -input OR re- spectively since the same amount of current is drawn from the power supply ( a63 a18 a32 ).... ..."

Cited by 1

### Tables 2 and 3 present the results obtained for both problems (the 10 bars and 25 bars structures), for both the benchmark continuous problem and a discretized version, where only 36 values were allowed for the areas of the bars. These 36 values included the optimal values found by the gradient-like method in [22].

1996

Cited by 162

### Table 3.1: E ects of w on convergence time and solution quality from 20 randomly generated starting points for the discretized version of Problem 2.6 in [14]. Fixed w Avg. Conv. Time Fraction Converged Avg Sol. Best Sol.

1998

Cited by 7

### Table 3.2: E ects of dynamic weighting on convergence time and solution quality from 20 randomly generated starting points for the discretized version of Problem 2.6 in [14]. Initial w Avg. Conv. Time Fraction Converged Avg. Sol. Best Sol.

1998

Cited by 7

### Table 1.1. Timing results on evaluating various combinations of strategies in CSAID, CGAID and CSAGAID with P = 3 to nd solutions that deviate by 1% and 10% from the best-known solution of a discretized version of G2. All CPU times in seconds were averaged over 10 runs and were collected on a Pentinum III 500-MHz computer with Solaris 7. apos;? apos; means that no solution with desired quality can be found.

### Table I: Description of temporal modi cations for the test phrases. For each phrase, the following information is given: (i) Total duration of the OC version in ms. (ii) Total duration of the OE version in ms. (iii) Range of shortening/lengthening of acoustic segments, expressed as the ratio of the modi ed duration in the TCC version to the original duration in the OC version. (iv) Description of \discrete quot; changes in segmental content.

1997

Cited by 5

### Table I: Description of temporal modi cations for the test phrases. For each phrase, the following information is given: (i) Total duration of the OC version in ms. (ii) Total duration of the OE version in ms. (iii) Range of shortening/lengthening of acoustic segments, expressed as the ratio of the modi ed duration in the TCC version to the original duration in the OC version. (iv) Description of \discrete quot; changes in segmental content.

1997

Cited by 5

### Table 5.1 summarizes key characteristics of the representative benchmarks selected among those used for experimental validation of our algorithms. These include an Elliptic Wave Filter (EWF), an Auto Regression Filter (ARF), a version of a Fast Fourier Transform (FFT) algorithm which is the main kernel in the RASTA benchmark from MediaBench [27], var- ious Discrete Cosine Transform (DCT) algorithms [24] and the DCT-DIT-2, an unrolled version of the DCT-DIT algorithm.

### Table 1: Running times for the continuous ASG algorithm and the discretized version The number of parameter functions that are discountinous at the same time was varied, however this was found to make relatively little di erence to the running time. 5 Concluding Remarks We have presented an active-set method which, under mild assumptions on the problem apos;s parameters, is capable of nding the exact solution to the continuous-time quadratic cost network ow problem e ciently. Although only a relatively simple example is included here for illustration purpose, the algorithm has been tested extensively on many other large and highly non-trivial problems, and has consistently return the same e ciency. Other extensions of the algorithm are possible, such as relaxing the strong convexity of the problem to a weakly convex one, or relaxing the network structure of the problem to look at a more general continuous-time monotropic programming problem (Rockafellar 1984). We are also conducting research into using this kind of model for water distribution networks and tra c ow problems.

"... In PAGE 17: ...2 Comparison with Discretization To show that the continuous ASG algorithm is more e ective in practice than just discretizing the problem, we solved a range of randomly generated problems using the two di erent approaches. The running times in CPU seconds on a DEC alpha workstation are summarized in Table1 . Problems are class ed according to the number of nodes, arcs and atomic intervals.... ..."

### Table 3: Basic properties of Discrete and Continuous Curvature Space

"... In PAGE 21: ...he area of the facet. Thus, small areas move fast, while large areas nearly do not move. When one accepts that the movement depends on the area of the facets, it is possible to de ne a more or less \continuous quot; version of the curvature space, where there is no threshold needed any more. Table3 presents basic properties of the \discrete quot; and the so-called \continuous curvature space quot; in 3D. Figure 29 shows how the facets move in the continuous curvature space.... In PAGE 21: ...urvature space quot; in 3D. Figure 29 shows how the facets move in the continuous curvature space. As no thresholding is done, there is no clearcut decision any more how to move the facets for steps. But as Table3 shows, by using a weighting function which is, e.g.... ..."