### Table 4: DL distributed subcarrier permutation (PUSC)

"... In PAGE 6: ... A permutation mechanism is designed to minimize the probability of hits between adjacent sectors/cells by reusing subcarriers, while frequency diversity minimizes the performance degradation due to fast fading characteristics of mobile environments. Table4 summarizes the parameters of DL PUSC subcarrier allocation. DL PUSC uses a cluster structure, as illustrated in Figure 3, which spans over two OFDM symbols (in time) of fourteen subcarriers, each with a total of four pilot subcarriers per cluster.... ..."

### Table 3: DL distributed subcarrier permutation (FUSC)

"... In PAGE 5: ... This mechanism is designed to minimize the probability of hits (probably of using the same physical subcarriers in adjacent cells and sectors) between adjacent sectors/cells by reusing subcarriers while frequency diversity minimizes the performance degradation due to fast fading characteristics of mobile environments. Table3 summarizes the subcarrier allocation structure parameters. In DL FUSC, there are variable and fixed sets of pilots.... ..."

### Table 1: BDD statistics for modules 97991161 and 97991162.

"... In PAGE 4: ... Nevertheless, even if the input and structural symmetries of the module function decrease the number of BDDs to be inspected, their number is still very high. Table1 shows the number of different BDDs for the module functions used in the Actel EPGAs... In PAGE 5: ... GenerateGlobalBdd( 71 ) 102 /3 create all the different BDDs 3/ for (each permutation 39105 of 115117112407141 ) 102 BDD 71 = GenerateBdd( 71, 39105 ); if (BDD 71 is isomorph to any other previously generated BDD) Free(BDD 71); 103 GBDD 71 = Reduce(Linked List of BDDs of 71); 103 In this way, although we do not reduce the number of BDDs, we decrease the computational effort and the memory used by the program. Table1 shows the total number of nodes for all the different BDDs against that of the GBDD for 97991161 and 97991162. Since the GBDD shares common subgraphs, we do not repeat the inspection of subgraphs that are isomorphic to each other, in the SubIsomorph procedure, thus improving the efficiency of the matching algorithm.... ..."

### Table 1: Comparison of BDD variable reordering for BDD size and LUT minimization

"... In PAGE 8: ... Wehave recorded the BDD size and the LUT count after the #0Crst and second reordering phase. The results are shown in Table1 . The geometric mean of the values in each column are shown at the bottom, and compared against each other.... ..."

### Table 4: Comparison of Resulting Netlists When Minimizing BDD Size Versus C8D7DB

2002

"... In PAGE 4: ... Table 3 contains the BDD size and netlist component count when this method is used. In the next set of results shown in Table4 , the technique for minimizing the sum of the switching probabilities (assuming sta- tistical independence and equally likely switching of the input variables) was used as a cost function for minimizing the BDD representing the characteristic function. These results were then... ..."

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### Table 4: Comparison of Resulting Netlists When Minimizing BDD Size Versus C8D7DB

"... In PAGE 4: ... Table 3 contains the BDD size and netlist component count when this method is used. In the next set of results shown in Table4 , the technique for minimizing the sum of the switching probabilities (assuming sta- tistical independence and equally likely switching of the input variables) was used as a cost function for minimizing the BDD representing the characteristic function. These results were then... ..."

### Table 4: Comparison of Resulting Netlists When Minimizing BDD Size Versus C8 D7DB

"... In PAGE 4: ... Table 3 contains the BDD size and netlist component count when this method is used. In the next set of results shown in Table4 , the technique for minimizing the sum of the switching probabilities (assuming sta- tistical independence and equally likely switching of the input variables) was used as a cost function for minimizing the BDD representing the characteristic function. These results were then... ..."

### Table 4: Comparison of Resulting Netlists When Minimizing BDD Size Versus C8 D7DB

### Table 1 gives a few values of the number of simple permutations, 2-permutations, and 3-permutations. The sequences for simple or 3-permutations do not appear in the OEIS.

"... In PAGE 10: ... Table1 : Number of simple permutations, 2-permutations, and 3-permutations in Sn Finally, our counting results may also be used to infer the distribution of those rearrange- ment distances based on the cycle graph. For instance, Christie [2] generalised transpositions, which exchange contiguous intervals in a permutation, to the case where the exchanged in- tervals need not be contiguous, resulting in an operation called a block-interchange.... ..."

### Table 1: Deterministic sampling using aBDD (static and dynamic)

1999

"... In PAGE 5: ...Experiment 1 ( Table1 , and Figure 2): First, we use the order computed by sampling to build the BDD statically. Except for slightly inferior orderings on c499 and c1355 (both circuits are functionally equiva- lent) we find that our methods always produce better variable orderings than those produced by DFS search based static techniques (Table 1).... In PAGE 5: ...Experiment 1 (Table 1, and Figure 2): First, we use the order computed by sampling to build the BDD statically. Except for slightly inferior orderings on c499 and c1355 (both circuits are functionally equiva- lent) we find that our methods always produce better variable orderings than those produced by DFS search based static techniques ( Table1 ). For many industrial examples we find that DFS-MIN cannot even process the circuits.... In PAGE 5: ... It is easy to see that window based sampling gives much better results than cube based methods. Interestingly, for EX3 and EX6, aBDD based methods can create a small BDD for the output function, but cube based sampling fails for some of the runs! Experiment 2 ( Table1 and Figure 3) show the utility of window based sampling in a dynamic vari- able ordering scheme. That is, we show how dynamic reordering techniques can be significantly improved if they are supplied with an initial variable ordering generated using a window based sampling technique.... In PAGE 5: ... That is, we show how dynamic reordering techniques can be significantly improved if they are supplied with an initial variable ordering generated using a window based sampling technique. In Table1 , we find that we can produce far smaller graphs than the traditional dynamic reordering meth- ods (sift, sift-convergence). Also, for most of the large circuits we take less time.... ..."

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