### Table 1. The entities and their dual representations in CGA. Entity Representation G. Dual representation G.

2004

"... In PAGE 8: ... But since we only work with the entities in their dual representation, we neglect the - sign in the further formulas. The entities and their dual representation are summarized in Table1 . This table is taken from Rosenhahn (2003) and Li et al.... In PAGE 14: ...Notethat O x formalizes the reconstructed ray in projective geometry (Perwass and Hildenbrand, 2003). The expression e O x represents the reconstructed ray in conformal geometry (see Table1 ) and is therefore given in the same language as we use for our entities and mtwist generated curves. To express the incidence of a transformed point with a reconstructed ray we can apply the commutator product, which expresses collinearity and directly transforms the constraint equation in an equation given in the Euclidean space (see e.... ..."

### Table 1: Relationship between a constraint network and its dual representation.

1998

"... In PAGE 3: ... An instantiation of tuples of adjacent nodes is only valid, if the value of the shared variable is the same in all tuples. Table1 summarizes the relationship between a constraint network and its dual representation. In general, nding a solution of a CSP is NP-complete [12].... ..."

Cited by 3

### Table 1: Sizes of the message tables for each of the methods. (a) Unlabeled Partitions (these are the Bell numbers). (b) Binary labeled partitions (c) Binary labeled edge-dual representation. (d) Binary labeled

2005

"... In PAGE 6: ...5 COMPLEXITY The dominant factor in the complexity of the mes- sage passing algorithm is the time taken to process all possible partitions of the largest clique. Table1 lists the number of possible configurations for the various cases. It can be seen from the table that the method described in Section 3 offers a considerable improve-... ..."

Cited by 1

### Table 1: Sizes of the message tables for each of the methods. (a) Unlabeled Partitions (these are the Bell numbers). (b) Binary labeled partitions (c) Binary labeled edge-dual representation. (d) Binary labeled

2005

"... In PAGE 6: ...5 COMPLEXITY The dominant factor in the complexity of the mes- sage passing algorithm is the time taken to process all possible partitions of the largest clique. Table1 lists the number of possible configurations for the various cases. It can be seen from the table that the method described in Section 3 offers a considerable improve-... ..."

Cited by 1

### Table 1: Effect of the ratio of clauses to variables (m/n) on the ratio of the average number of consistency checks performed to solve the dual representation over the average number of consistency checks performed to solve the non- binary representation (cost rat.), when finding first solution to random 3-SAT problems with 100 Boolean variables.

1998

"... In PAGE 5: ... We now consider two classes of problems, random 3-SAT and crossword puzzles, and show that the maps constructed from our experimental results over the space of random non- binary problems have predictive power and so provide guid- ance for selecting between the non-binary and dual CSP models of a problem. The results for random 3-SAT are shown in Table1 . It can be seen that the cost ratios for solv- ing the original CSP and its dual representation fit well with the predictions of the order of magnitude curves (see Fig- ure 3, k =3, at the point 7/8 on the x-axis (each of the con- straints has 7 out of the 8 possible tuples)).... ..."

Cited by 76

### Table 1: Effect of the ratio of clauses to variables (m/n) on the ratio of the average number of consistency checks performed to solve the dual representation over the average number of consistency checks performed to solve the non- binary representation (cost rat.), when finding first solution to random 3-SAT problems with 100 Boolean variables.

1998

"... In PAGE 5: ... We now consider two classes of problems, random 3-SAT and crossword puzzles, and show that the maps constructed from our experimental results over the space of random non- binary problems have predictive power and so provide guid- ance for selecting between the non-binary and dual CSP models of a problem. The results for random 3-SAT are shown in Table1 . It can be seen that the cost ratios for solv- ing the original CSP and its dual representation fit well with the predictions of the order of magnitude curves (see Fig- ure 3, k = 3, at the point 7/8 on the x-axis (each of the con- straints has 7 out of the 8 possible tuples)).... ..."

Cited by 76

### Table 1: Effect of the ratio of clauses to variables (m/n) on the ratio of the average number of consistency checks performed to solve the dual representation over the average number of consistency checks performed to solve the non- binary representation (cost rat.), when finding first solution to random 3-SAT problems with 100 Boolean variables.

1998

"... In PAGE 5: ... We now consider two classes of problems, random 3-SAT and crossword puzzles, and show that the maps constructed from our experimental results over the space of random non- binary problems have predictive power and so provide guid- ance for selecting between the non-binary and dual CSP models of a problem. The results for random 3-SAT are shown in Table1 . It can be seen that the cost ratios for solv- ing the original CSP and its dual representation fit well with the predictions of the order of magnitude curves (see Fig- ure 3, k =3, at the point 7/8 on the x-axis (each of the con- straints has 7 out of the 8 possible tuples)).... ..."

Cited by 76

### Table 1 shows the number of vertices, halfedges, and faces of the six planar maps that comprise the CGM of our squashed dioctagonal pyramid. The number of faces of each planar map include the unbounded face. Table 2 shows the number of features in the primal and dual representations of a small subset of our polytopes col- lection. The number of planar features is the total number of features of the six planar maps.

2006

"... In PAGE 10: ...Constructing the CGM of a model given in the Indexed face set representation is done indirectly. Planar map V HE F 0, (x = 1) 12 32 6 1, (y = 1) 36 104 18 2, (z = 1) 12 32 6 3, (x = 1) 12 32 6 4, (y = 1) 21 72 17 5, (z = 1) 12 32 6 Total 105 304 59 Table1 : The number of features of the six planar maps of the CGM of the dioc- tagonal pyramid object. First, the Cgal Polyhedron 3 data structure that rep- resents the model is constructed [23].... ..."

Cited by 11

### Tables 2(a)-2(d) show the comparison of K-DualFM/SF and K-DualFM/DF with the K-FM algorithm for K ranging from 2 to 5. For each example, the K-FM algorithm was run 20 times, each on a random initial module partitioning. In order to obtain a fair comparison, we make sure that the runtimes of K-DualFM/SF and K-DualFM/DF are comparable with that of the K-FM algorithm. As a result, the K-DualFM algorithms were run once with the greedy net partition, and then approximately 10 times4, each on a random initial net partitioning of the dual netlist representation (HDN). The area slack parameter quot; was set to be 10% in both K-FM and K-DualFM algorithms.

1994

Cited by 15

### Table 1: Different threshold and errors introduced by rendering the coarse representation. The frame rate is measured for a 512x512 view-port on one dual-core processor.

"... In PAGE 3: ... The well- known engine data set consists of 8 Bit integer scalar values allowing for a threshold range t = [0, 255]. As Figure 2 illustrates choosing a thresh- old of 64 has only a negligible impact on the ren- dering quality while tripling the performance (see Table1 . Choosing t = 128 produces some artifacts but many details are still visible.... ..."