### Table 1 : Fast Algorithm

"... In PAGE 8: ...onstants c1 and c2; then, the solution of (3.4) and (3.6) needs O(n ln n) operations. The following tables give us the numerical results of the fast algorithm and the quadrature method, ( Table1 and Table 2, respectively) applied to equation (1.3) with k(x; t) de ned by (3.... ..."

### Table 2. Approximate Solution

"... In PAGE 5: ... The last two columns show the results obtained using the Lindo package, which is based on a mathematical programming method known as Branch amp;Bound method. Table2 presents the results obtained using the Threshold Accepting Algorithm. Forty runs were made for each problem.... In PAGE 7: ...This paper shows the feasibility of using the Threshold Accepting algorithm, which showed good performance for small problems and demonstrated its ability to solve large problems. However, the solution tends to grow farther as the problem size increases ( Table2 and Fig. 1).... ..."

### Table 2: Approximative Results

"... In PAGE 6: ... But previously, and because of the characteristics of this genetic algorithm, the mul- tidimensional fuzzy sets need to be projected in each domain and be approximated via a trapezoidal fuzzy set. Table2 shows the results when we consider 4 and 11 clusters and the nal results after the Genetic Al- gorithm is applied to the collection of fuzzy rules gen- erated from the fuzzy clusters: In the second approach: First, a combination of two fuzzy clustering al- gorithms is used: a substractive clustering is ap- plied to the product space of the input and out- put variable to generate the number of rules and a rst approximation to the fuzzy rules; then a classical fuzzy c-means algorithm is used to op- timise the fuzzy rules obtained. The paramet- ers considered in the substractive clustering al- gorithm were = 1 and = 2.... ..."

### Table 2: Approximate extraction by di erent algorithms

1999

"... In PAGE 17: ... In our ALPF algorithm, we use 22 = 4 and 32 = 9 DCT coe cients when chosing kb = 2 and kb = 3, respectively. In Table2 , from left to right, both the running time and SNR increase as the number of used coe cients increases. This implies that there is trade-o between the speedup and reconstructed image quality.... ..."

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### Table 1 Fast marching algorithm

"... In PAGE 3: ...eodesic active contours as well (Caselles et al., 1997). In bors which have smaller values than u. (Cohen and Kimmel, 1997) and in our Appendix A is also The algorithm is detailed in 3D in the next section in mentioned how the curvature of the minimal path is now Table1 . The Fast Marching technique selects at each controlled by the weight term w.... ..."

### Table 1. Fast Marching algorithm

"... In PAGE 4: ... This technique of considering at each step only the necessary set of grid points was originally introduced for the construction of minimum length paths in a graph between two given nodes in [7]. The algorithm is detailed in Table1 . An example is shown in Figure 2.... ..."

### Table 2 compares CPU-times spent to compute the different approximations on a 2.16GHz Intel dual core with a 2MB cache. This table shows us that computing the set median string is more than ten times as fast as computing an approximation with the greedy algorithm, which itself is more than ten times as fast as computing an approximation with the local search approaches. Also, when starting local search from the string generated by the greedy algorithm, CPU time is slightly smaller than when starting from a set median or a randomly generated string. The quality improvement is thus balanced by the CPU-time cost. However, in applications such as classification of unknown strings in already known clusters, the best representative of each cluster, e.g., the generalized median string, is computed off-line, one-for-all.

"... In PAGE 7: ...24 34.47 Table2 . Comparison of CPU-times: each line displays the length of the strings and the CPU times (in seconds) spent to compute the different approximate generalized median strings (average results for the 10 classes of the SIMPLIcity base described in 5, each class having 100 strings).... ..."

### TABLE I The FASTA, FASTS, and FASTF algorithms FASTA FASTS FASTF

2002

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