### Table 2: Scalability for graph with 777488 vertices, without cycle

2001

"... In PAGE 19: ... Both algorithms perform equally well on graphs with cycles. We have accomplished yet another set of tests (see Table2 ) in order to validate the scalability of the DSP algorithm. The tests con rm that it scales well, i.... ..."

Cited by 2

### Table 2: Scalability for graph with 777488 vertices, without cycle

2001

"... In PAGE 19: ... Both algorithms perform equally well on graphs with cycles. We have accomplished yet another set of tests (see Table2 ) in order to validate the scalability of the DSP algorithm. The tests confirm that it scales well, i.... ..."

Cited by 2

### Table 2: Minimum, median, and maximum least costs found for nine di erent control schedules applied 100 times to the four test graphs.

1992

"... In PAGE 14: ...adius is small (i.e., r0 = r s). Three additional test graphs are employed: Medianus-II, a later version of Medianus-I containing 56 vertices and 110 edges; Sparse, a computer generated graph of 50 vertices and 100 edges; and Dense, a computer generated graph of 50 vertices and 359 edges. The results obtained by applying the top third control schedules in Table 1 100 times to all four graphs are displayed in Table2 . In Table 1 the... In PAGE 15: ...rom the 18th best to the 19th best schedule (i.e., the boundary between the middle and last third). By calculating the average relative deviation of the median values from the least me- dian for each control schedule in Table2 we nd that the ranking of the schedules is 5, 2, 3, 7, 1, 8, 9, 4, 6 (i.e.... In PAGE 16: ... constant small radius (schedule c) is found to be superior, although schedules a and b are not signi cantly worse. By comparing the median values in Table 3 by the least medians in Table2 we calculate the average relative deviation as above (see Figure 1). It is interesting to compare schedules a, b, c and d with schedules 3, 1, 5 and 4, respectively, as they have pairwise identical radius schedules.... In PAGE 17: ... Kj rul (1990) found a heuristic called the minimum weight heuristic to be superior. By comparing the gures from Kj rul (1990) with those of Table2 it is found that the median cost produced by annealing for the Medianus-I graph is slightly better than the median cost produced by the minimum weight heuristic, whereas a similar comparison for Medianus-II shows that the heuristic algorithm is slightly better than annealing. In both cases the di erence is insigni cant.... ..."

Cited by 20

### Table 1: Labelings of the Complete Graph on 5 vertices

2004

"... In PAGE 16: ... For K 5 , wemust have35 k 45. In Table1 we exhibit one solution for each k 40. For K 6 ,weget59 k 73.... ..."

Cited by 5

### Table 1 Number of topologically different planar graphs using a fixed amount of vertices of degree at least n

### Table 4: The worst and the average deviations from the optimum for different values of n (the number of vertices in a graph) [19].

"... In PAGE 16: ... The results of the experiments are presented in Table 4. As it can be seen in Table4 , algorithm AMU performs much bet- ter than AU and AM separately. For the considered type of graphs with random edge costs, algorithm AMU is always within very few percentage points off the optimum.... ..."

### Table 1 Area-requirements for planar grid tree drawings. not vertices of G. ? is an orthogonal drawing (see Fig. 1.c) if each edge is a chain of alternating horizontal and vertical segments. A grid drawing is such that the vertices and bends along the edges have integer coordinates. Planar drawings, where edges do not intersect, are especially important because they improve the readability of the drawing, and, in the context of VLSI layouts, they simplify the design process [2, 19, 28]. An upward drawing of a directed graph is such that every edge is a curve monotonically nondecreasing in the vertical direction (when traversed along the direction of the edge).

1996

Cited by 12

### Table 1: The number gn;m of unlabelled 2-connected planar graphs having n vertices and m edges.

2008

"... In PAGE 28: ...Thus, we extended to 14 vertices the generating function f BP (x; y) of unlabelled 2-connected planar graphs and to 12 internal vertices the generating functions f NP (x; y) and f NP (x; y) of unlabelled strongly planar networks. The coe cients of f BP (x; y) are given in Table1 . Setting y = 1, we have f BP (x) = x2 + x3 + 3x4 + 9x5 + 44x6 + 294x7 + 2893x8 + 36496x9 + 545808x10 + 9029737x11 + 159563559x12 + 2952794985x13 + 56589742050x14 + (111) f NP (x) = 1 + 2 x + 10 x2 + 72 x3 + 696 x4 + 8530 x5 + 124926 x6 +2068888 x7 + 37204942 x8 + 708076350 x9 + 14038364914 x10 +287091103062 x11 + 6016760068874 x12 + (112) and f NP (x) = 1 + 2 x + 6 x2 + 20 x3 + 96 x4 + 470 x5 + 3074 x6 + 23408 x7 + 243482 x8 +3221018 x9 + 51729286 x10 + 929983374 x11 + 17911049418 x12 + (113) Remark.... ..."

### Table 4: The number HP (n) of labelled 2-connected homeomorphically irreducible planar graphs (having n vertices).

2007

### Table 7: Results of the nal mapping of graphs with 9 vertices.

"... In PAGE 31: ... The nal mapping indicates that the initial mapping has been constrained by the structure. Table7 lists the nal mapping, and the nal semantic matrix T(f) and distance matrix D(f) is given in (19) and (20) respectively. Under- lined entries in the matrices denote the assignments returned from the hungarian... ..."