### Table 8: Experimental results for a simple non-planar graph

"... In PAGE 10: ...u3 u4 u0 u1 2 3 4 u0 u 1 2 u3 u4 Figure 5: Three good layouts obtained for graph K5 by genetic search: B1(left), B2(center) and B3(right). The experimental results are in Table8 . It must remarked that in experiments B3 the optimum value is unknown so we don apos;t know when it apos;s found.... ..."

### Table 10: The three energies E0;1;2 in the Non-Planar geometry. Wrt B de ned in table 8.

### Table 1: The number fn,m of labelled non-planar projective-planar 2-connected graphs without a K3,3-subdivision (having n vertices and m edges).

2007

### Table 2: The number fn of labelled non-planar projective-planar 2-connected graphs without a K3,3-subdivision (having n vertices).

2007

### Table 5: The number hn,m of labelled non-planar projective-planar 2-connected K3,3-free homeomorphically irreducible graphs (having n vertices and m edges).

2007

### Table 4.3: Landmark noise on the non-planar, non-white surface shown in Figure 4.6. This environment was constructed to be similar to the primary intended application, that of ultrasound-guided needle biopsy. Land- marks 2, 4, 5, 8, and 10 imaged inside the medical model; the other landmarks imaged on the curtain.

1998

### Table 1 shows the curvature and interaction check results. Only region (1,1) (lower left) was non-planar. Therefore 8 of the 9 additional patterns were selected randomly from this region. Since the ranges for both the interaction and curvature checks for region (1,2) (upper left) were wider than those of regions (2,1) and (2,2), 1 additional pattern was selected randomly from region (1,2) (upper left).

### Table 2: Comparison of Elmore-Planar-DME with other algorithms in terms of total wirelength, using the same

1994

"... In PAGE 5: ... In the last column, we also show the ZST heightasamultipleof the minimumpossible tree height, lgn. Table2 compares our algorithms with two lead- ing non-planar ZST algorithms in the literature #7B Greedy-DME #5B8#5DandKCR+DME #5B12#5D #7B as well as the previous planar routing method of Zhu and Dai #5B16#5D. Our new planar ZST solutions are competitive with the best non-planar ZST solutions of Greedy- DME #28having 10#25 greater wiring cost#29, and are su- perior to KCR+DME solutions in all cases.... ..."

Cited by 12

### Table 1. The running times of functions related to planarity: The rst column shows the type of the input graph, the second column shows the time for the call BL PLANAR(G), the third column shows the time for the call BL PLANAR(G; K), the fourth column shows the time required to check the result of the computation in the third column, i.e, the time for the call Genus(G) == 0, if G is planar, and the call CHECK KURATOWSKI(G; K) if G is non-planar, the fth column shows the time for the call HT PLANAR(G), and the last column shows the time for the call HT PLANAR(G; K). The last call is only made when G is planar, since there there is no e cient Kuratowski nder implemented for the Hopcroft-Tarjan planarity test. The meaning of the rst column is as follows: P stands for a random planar map with n nodes and m uedges, P + K3;3 stands for a random planar map with n nodes and m uedges plus a K3;3 on six randomly chosen nodes, P + K5 stands for a random planar mao with n nodes and m uedges plus a K5 on ve randomly chosen nodes, MP stands for a maximal planar map with n nodes, and MP + e stands for a maximal planar graph plus one additional edge between two random nodes that are not connected in G. In all cases the edges of the graph were permuted before the tests were started. For each type of graph we used n = 2i 1000, m = 2i 2000 for i = 0, 1, and 2.

1998

"... In PAGE 3: ... The implementation of the former function is shown in Figure 1, the imple- mentation of the latter function is equally simple. Table1 shows the running times of several functions related to planarity. In this table BL PLANAR stands for the planarity test of Lempel, Even, and Cederbaum with PQ-tree data structure of Booth and Luecker, the embedding algorithm of Chiba et al.... ..."

Cited by 4

### Table 4: Classification accuracy for different levels of intermedi- ate structure estimation. Main is the classification among the three main classes. Sub is the subclassification of the vertical structures class. The column labels are defined in Section 4.2.

2005

"... In PAGE 4: ... Tables 2 and 3 give the confusion ma- trices of the main geometric classes (ground plane, vertical things, sky) and the vertical subclasses (left-facing plane, front-facing plane, right-facing plane, porous non-planar, solid non-planar). The overall accuracy of the classifica- tion is 86% and 52% for the main geometric classes and vertical subclasses, respectively (see Table4 for baseline comparisons with simpler methods). The processing time for a 640x480 image is about 30 seconds using a 2.... In PAGE 5: ... superpixel level (SPixel), a single (nr = 9) segmentation hypothesis (OneH), and using our full multiple-hypothesis framework (MultiH). Our results ( Table4 ) show that each increase in the complexity of the algorithm offers a signifi- cant gain in classification accuracy. We also tested the accuracy of the classifier when the intermediate scene structure is determined by partitioning the superpixels according the ground truth labels.... ..."

Cited by 21