### Table 3: Possible decomposition of G based on Newton polytopes and Minkowski sums.

### Table 1: Performances of the used Minkowski algorithms in milliseconds CPU-time. Np is the number of polyhedra in the equipment and Nv is the total number of vertices in the equipment. Nm is the number of Minkowski sums calculated, Ns the number of Minkowski sums that cut Z, K the average number of vertices of the Minkowski sums, and Ks the average number of vertices of the (nonempty) sections with Z.

1997

"... In PAGE 18: ... Figures 8, 9 give the sequence of placements performed. Table1 gives the per- formances of the algorithm for all stages of the layout scenario. Time is measured in milliseconds CPU-time, and both total and average times are given, the average being calculated on all Minkowski sums computed.... ..."

Cited by 5

### Table 1. Benchmarks: This table shows the performance of our algorithm on different models. The columns on the left show the statistics of the two primitives whose Minkowski sum is computed. They show the number of triangles in each primitive and the number of convex pieces generated by convex decomposition. The column, Num Convex Prims, shows the number of convex Minkowski sums generated. The right three columns show the time taken to generate the convex Minkowski sums, sampling (grid generation) and isosurface reconstruction.

2004

"... In PAGE 8: ...2 Performance We tested our algorithm on a number of complex models. The model complexity ( Table1 ) varied from several hun- dred to few thousand triangles. Figures 1 and 4 show the offset of three models: Bunny, Cup and Gear.... In PAGE 8: ...omplex features. Fig. 3 shows an application to motion planning. Table1 shows the model complexity and perfor- mance of our algorithm on these benchmarks. Sampling is the most time consuming step in the algorithm.... ..."

Cited by 8

### Table 2. Selected Results for Weighted Sums

2006

"... In PAGE 4: ... Bold entries show results superior to either heuristic alone. 4 Heuristic Combinations Based on Weighted Sums Table2 gives results, in terms of nodes searched, for six individual heuristics and for combinations of these heuristics using the technique of weighted sums described in Section 2. For these tests, heuristics were given equal weights.... In PAGE 6: ...00,6,0.054,0.2a108 ). For these problems min do- main/forward degree gave a mean of 3886 search nodes, while the combination of five heuristics given in Table2... In PAGE 11: ... This rule is also consistent with the two cases of synergy among the products and quotients (cf. Table2 ). However, for quotients there appears to be a further (reason- able) condition: that both the numerator and denominator favor selections consistent with those favored by the original heuristic.... In PAGE 13: ... This anal- ysis involved max forward degree, min domain and the weighted sum of the two (with equal weights; cf. Table2 ). These data indicate that this heuristic combination shows better adherence to both the fail-first and promise policies than the component heuristics acting alone.... ..."

Cited by 2

### Table 1. The Minkowski valuations used in this paper.

2005

"... In PAGE 3: ...9) In the following we will concentrate on these tensors. They are listed together with their names in Table1 . The nu- merics for calculating the Minkowski valuations for pix- elized data sets is described in [31].... ..."

### Table 3: Finding an initial selection of primary e ects.

1994

"... In PAGE 17: ... Here we use these two results to guide the design of our learning algorithm. The procedure Initial-Choice ( Table3 ) performs a preliminary selection of primary e ects. After this is done, the learning algorithm (Tables 4 to 5) is used to select additional primary e ects in order to ensure the completeness and near-optimality.... In PAGE 17: ... Therefore, the completeness of planning requires that every achievable literal l be a primary e ect of some operator. The algorithm for initial choice, presented in Table3 , makes sure that this condition is satis ed. Initially, the algorithm asks the user to select primary e ects of operators.... ..."

Cited by 4

### Table 3: Finding the optimal algorithm

"... In PAGE 10: ...lgorithm (i.e. plan derived from the algorithm) could be selected by the ISP operator. Table3 gives an overview of different possible optimization goals for capacity planning and the appropriate optimization algorithms . ... ..."

### Table 1. Selected Studies on Asymmetrical Effects Author Area Findings

"... In PAGE 4: ..., 2001; Colgate and Danaher, 2000; Kahneman and Tversky, 1979). Table1 pre- sents a summary of prior studies indicating positive-negative asymmetry effect. Prior literature in psychology suggested that events that are negatively valenced will have longer lasting and more intense consequences than positively valenced events of the same type.... ..."

### Table 1. The outline of our algorithm for gene selection.

2005

"... In PAGE 3: ... To address this problem, we propose a resampling procedure as the outer loop of our algorithm. The outline of our algorithm is given in Table1 . We found this algorithm to be robust both to overfitting and local minima problems.... In PAGE 4: ...ative genes. The significance level was fixed at p=0.01, and the p-values were calculated using all the samples.5 We then generated 10 folds of the whole data set for the resampling step in Table1 . The detailed results on these three datasets are reported in the following.... ..."

### Table 3: Time consumption (in seconds) of the Minkowski-sum computation. DP | Dioctagonal Pyramid, ODP | Orthogonal Dioctagonal Pyramid, PH | Pentagonal Hexecontahedron, TI | Truncated Icosidodecahedron, GS4 | Geodesic Sphere level 4, RGD4 | Rotated Geodesic Sphere level 4, CH | the Convex Hull algorithm, CGMO | the Cubical Gaussian Map Overlay algorithm.

2006

"... In PAGE 3: ... We are unaware of the existence of implementations of methods other than the method above to compute exact Minkowski sums. Our method exhibits much better performance than the na ve method in all cases, as demonstrated by the experiments listed in Table3 . Our methods well handles degenerate cases that require special treatment when alternative representations are used.... In PAGE 10: ... We compared the time it took to compute the exact Minkowski sum using both methods. The results listed in Table3 were produced by experiments conducted on a Pentium PC clocked at 1.8 GHz.... ..."

Cited by 11