### Table 4: Packing and binding efficiency

"... In PAGE 6: ...1 Packing and Binding Efficiency We first show the efficiency of our packing and binding algo- rithm. Table4 gives the experimental results. The column labeled utilization gives the percentage of fabric cells which are used.... In PAGE 6: ... Two columns labeled 2 and 3 represent two block configurations in which there are 2 or 3 available spanning wires for each type (X, Y, F)inaVCB. The results in Table4 indicate that we achieve a high fabric uti- lization for various applications which differ considerably in the... ..."

### Table 2: Classi cation of areas for the packing algorithm

1999

"... In PAGE 6: ... However, di erently from [6], in the computation of our proposed bound we use the exact height for eachmodulei in group j, instead of using the height range. Table2 shows the area, width and heightofeach module. If R 0 is the highest rectangle in the oorplan, then an upper bound of the... In PAGE 7: ...e., A 2 p r p A total , and the area of the oorplan is thus bounded by: area(F ) A total + p A total = A total + A 2 p r p A total p A total = A total + A 2 p r If groups 2;; 3;; 4;;::: ;; ; 1 are empty, our bound would then come from group , that for convenience has its largest module labeled : area(F ) A total + A r ;1 2 If wenow substitute A by the area upper bound for the modules in group (see Table2 ), we can rewrite the previous equation as: area(F ) A total + A r ;1 2 lt;A total + A total r ;1 r ;1 2 = A total + A total r ;1 2 It is not di cult to show that the two proposed bounds in Equation 3 can be derived from the generalization of the aboveformulas. 2 The proposed weaker bound demonstrates that by using the maximum area for a module in group , one can improve the quality of the nal oorplan area upper bound.... ..."

### Table 3. Comparison between different heuristics for packing up to 500 circles

"... In PAGE 14: ... 4.2 Different heuristics on small and medium problems (r0 24) Table3 reports some results obtained using BL, MHD and MinD heuristics for packing circles into a container of radius r0 24. For each heuristic, n indicates the largest number of circles which can be packed into the container.... In PAGE 14: ... These results can be compared with the results of a pure random algorithm consisting in choosing arbitrarily a corner position at each step, reported in the RANDOM column. We also give in Table3 the best known results in column BEST, denoted by n , obtained using several approaches in the literature for some small problems and by the BS approach for medium problems.... In PAGE 15: ... For MinD, we take the best results in Table 1, for RANDOM and MHD, each algorithm is executed 50 times because MHD uses here the random tie-break strategy. The last column Gap of Table3 shows the gap in percentage between the different heuristics and the best known results in Column BEST, which is calculated as Gap = 100 (n n)=n . We analyze the obtained results in terms of the solution quality and the run time.... ..."

### Table 2. Comparison for packing up to 500 circles

"... In PAGE 11: ... 5.1 Results for packing up to 500 and more than 500 circles into a circular container Table2 and Figure 6 provide some results obtained by BL, MHD, MICP and Multi-MICP heuristics for packing up to 500 circles (r0 24). Table 3 and Figure 7 display some results for packing more than 500 circles (r0 25).... In PAGE 11: ...icardie.fr/~akeb. For each heuristic, n indicates the maximal number of circles which can be packed into the container of radius r0 and time(s) is the corresponding run time (in seconds) to reach a nal con guration. For the purpose of comparison, in Table2 and Table 3, we give the maximal number of packed circles known in the literature in Column BS, denoted by n . No results were reported for packing more than 500 circles due to huge run times.... In PAGE 11: ... n represents the best result among 50 executions of the random algorithm, and the run time is the average run time of an execution. The last column Gap of Table2 shows the gap in percentage between our best heuristic... In PAGE 12: ... We analyze the obtained results in terms of solution quality and run time. We rst compare our approaches MICP and Multi-MICP with the best known results for up to 500 circles : MICP and Multi-MICP cannot reach the best known results, but a motivated phenomenon is noticed from Table2 : the gaps to the best known ones gradually decrease from 6.25% for r0 = 10 to 2.... ..."

### Table 1. Evaluation of the Frame-Packing Optimzation Algorithms

"... In PAGE 13: ... Obtaining solutions that have a higher degree of schedu- lability means obtaining tighter worst-case response times, increas- ing the chances of meeting the deadlines. Table1 presents the average percentage deviation of the degree of schedulability produced by OFP from the near-optimal values obtained with SA. Together with OFP, a straightforward approach (SF) is presented.... In PAGE 13: ... Moreover, for SF we considered a TTC bus configuration consisting of a straightforward ascending order of allocation of the nodes to the TDMA slots; the slot lengths were selected to accommodate the largest message frame sent by the respective node, and the schedul- ing has been performed by the MultiClusterScheduling algorithm in Figure 8. In Table1 we have one row for each application dimension of 80 to 400 processes, and a header for each optimization algorithm consid- ered. For each of the SF and OFP algorithms we have three columns in the table.... In PAGE 14: ... Table1 shows that when packing messages to frames, the degree of schedulability improves dramatically compared to the straightfor- ward approach. The greedy heuristic OptimizeFramePacking per- forms well for all the graph dimensions, having run-times which are under 100 seconds on average.... ..."

### Table 5-2: Results using only placement and packing modifications

2004

"... In PAGE 13: ...List of Tables Table5 -1: Statistics for benchmark logic circuits .... In PAGE 13: ...able 5-1: Statistics for benchmark logic circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Table5 -2: Results using only placement and packing modifications .... In PAGE 13: ...able 5-2: Results using only placement and packing modifications . . . . . . . . . . . . . . . . . . . . . 58 Table5 -3: Speed improvement results using the new logic synthesis transformations .... In PAGE 13: ... . . . . . .59 Table5 -4: Area change due to the new logic synthesis transformations... In PAGE 70: ...1 Mult 29 21 122.2 Table5... In PAGE 72: ... We tried to improve the placement and packing of every logic circuit for about 3 hours. Table5 -2 provides a summary of these results.... In PAGE 73: ...9 6.7 Table5... In PAGE 74: ...topping logic circuit improvement are described as a part of the stopping criterion in Section 5.6.4. The speed improvement presented in Table5 -3 was determined by calculating the per cent difference between the speed of the logic circuit in Table 5-3, column 7, and the baseline logic circuit speed in Table 5-1, column 4. The results obtained for the 10 benchmark logic circuits show that using Augur improves the speed of logic circuit of up to 25.... In PAGE 74: ...topping logic circuit improvement are described as a part of the stopping criterion in Section 5.6.4. The speed improvement presented in Table 5-3 was determined by calculating the per cent difference between the speed of the logic circuit in Table5 -3, column 7, and the baseline logic circuit speed in Table 5-1, column 4. The results obtained for the 10 benchmark logic circuits show that using Augur improves the speed of logic circuit of up to 25.... In PAGE 74: ...topping logic circuit improvement are described as a part of the stopping criterion in Section 5.6.4. The speed improvement presented in Table 5-3 was determined by calculating the per cent difference between the speed of the logic circuit in Table 5-3, column 7, and the baseline logic circuit speed in Table5 -1, column 4. The results obtained for the 10 benchmark logic circuits show that using Augur improves the speed of logic circuit of up to 25.... In PAGE 74: ...5 3.1 Table5... ..."

### Table 7. Results for Di erent Energy Optimization Techniques for the DSP Benchmark Original Packing Scheduling Swapping

1996

"... In PAGE 12: ... A scheduling algorithm that uses the measured overhead costs was developed for this processor [15]. The data in Table7 illus- trates the e ectiveness of this algorithm. This table shows the impact of di erent software en- ergy optimization techniques that are applicable for the DSP (\packing quot; and \swapping quot; will be discussed later).... In PAGE 14: ... We found that an appropriate swapping of the operands, in order to exploit this asymmetry, leads to up to 30% reduction in mul- tiplication energy costs. This can translate into appreciable energy reduction for entire programs, as shown in Column 5 of Table7 . For example, for LP FIR60, the use of operand swapping reduces the energy consumption of the packed code by an additional 16%.... ..."

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### Table 1. Some examples of packings in three dimension. The packing with radius p2 is the Kepler packing. The packing with radius 120 gives a slightly denser packing as the packing reported in [17] using Penrose tilings which have densities accumulating by 0:7341.

### Table 2. The collision profile of hash functions. Packing

"... In PAGE 3: ... After training the network, NH25 has 460 hidden nodes and NH50 has 430 hidden nodes. Table2 shows the collision profile of each hash function: the figures under the hash function column correspond to the number of hash table slots to which a certain number of records, in the first column in the same row, are hashed. As can be seen in Table 2, the Mid-square performed the worst among the hash functions; NH25 has a similar result to that of the Division; and NH50 performed the best: it has the least number of unassigned slots and most slots with only one hash value assigned.... In PAGE 3: ... Table 2 shows the collision profile of each hash function: the figures under the hash function column correspond to the number of hash table slots to which a certain number of records, in the first column in the same row, are hashed. As can be seen in Table2 , the Mid-square performed the worst among the hash functions; NH25 has a similar result to that of the Division; and NH50 performed the best: it has the least number of unassigned slots and most slots with only one hash value assigned. Another criterion for judging the performance of a hash function is degradation of the collision rate as the packing density increases.... ..."

### Table 1. Performance without message packing.

2003

"... In PAGE 5: ... 3 An Adaptive Policy for Message Packing Our first suite of experiments used a source thread that continuously generates fixed- size messages, putting JBora under stress. The results obtained with message pack- ing disabled are shown in Table1 , for three different message sizes (100,1000,10000). These results constitute the baseline for comparing the results obtained through mes- sage packing.... ..."

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