### Table 1: average time for the generation of one random point (in s)

"... In PAGE 23: ... The time for the generation of random points below the hat has shown to be almost linear in dimension n. Table1 shows the average time for the generation of a single point. For comparison we give the time for generation of n normal distributed points using the Box/Muller method [BM58] (which gives a standard multi- normal distributed point with density proportional to f(x) = exp(? Pn i=1 x2 i )).... ..."

### Table 1: Comparison of the methods for calculating bounding spheres on random points using -search and centroid-farthest-point method.

1997

"... In PAGE 6: ... EXPERIMENTAL RESULTS In this section, we give our empirical test results. First, we compare the spheres obtained from our approxi- mation algorithm and the sphere resulting from using the centroid of the data as the center and distance of this center to the farthest point as the radius ( Table1 , Figure 7). Then, we look at the similarity searches performance of the SS+-tree on uniform point data comparing the e ect of using di erent bounding envelopes for the nodes.... In PAGE 6: ... Lastly, we compare the performance of the SS+-tree on the eigenface data.22 The comparison between the -search and the centroid-farthest point method to calculate the bounding spheres of 10 and 100 random points (for 100 trials each) ( Table1 and Figure 7 respectively) suggest that the advantage of using a smaller bounding sphere will be more evident for high-dimensional space. Although the ratio between the radius of the spheres produced by the search and centroid-farthest-point method (r-ratio) is not large, the ratio between volumes (V -ratio) can be quite signi cant in a high dimensional space.... ..."

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### Table 5 Random Graph, 200 Points

### Table 4. Averages of the use percentage of recurrence relation (10), up to one million uniform random points, in evaluating all the Lagrange basis polynomials at degree n = 20 # of random points % recurr. (averages)

2004

### Table 2: Mean Aexpected-score between adjacent compared to random points

"... In PAGE 6: ...BO1 Random Walk Beam, BO1 Beam, EO1 (iA two randomly selected points in the search space. Table2 shows the relative smoothness of the two domains for the three search algorithms. For random search.... ..."

### Table 4: Ten experimentally computed values for the variancy of 10,000 random points, multiplied with 1000.

"... In PAGE 12: ... To get the expectation value of the distance, the first moment has to be computed: Z p 2 0 xp#28x#29dx = p 2 +ln#28 p 2 +1#29 3 apos; 0:7652: (20) So we get for the expectation value of the distance of a randomly selected point within a square with diagonallength 1 to one corner E#5BR= p 2#5D apos; 0:541: (21) Table 3 gives some experimentally computed values, using 20,000 random points in each case. For the variancy one gets: s 2#5BR= p 2#5D = 1 2 Z p 2 0 #28x,E#5BR#5D#29 2p#28x#29dx = 4 ,2p 2log#281 + p 2#29,log#281 + p 2#29 2 18 apos; 0:0405 (22) Table4 gives ten experimentally computed values, using 10,000 random points in each case. To summarize: equally distributed points in a unit square will have an average... ..."

### Table 4: kf ?sk1 for random interpolation points in the unit ball

"... In PAGE 12: ...1) is set to the product c = (1=n)1=d for the range of values of that has been used already, the factor (1=n)1=d being the magnitude of nearest neighbour distances between data points. A selection of the values of kf?sk1 that were found is given in Table4 . The set D was not altered during the calculations of each column of the table, and the set fxi : i=1; 2; : : : ; ng was not changed when was increased for each d and n.... ..."

### Table 2: Performance measures for a random distribution of points of interest

2003

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