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Table 2 Average percentage excess over the lower bound β; the first number denotes our algorithm, while the second one (in brackets) represents the algorithm by Pereira Zanetti et al [23]

From: On the rank-distance median of 3 permutations

n,r

0.05

0.1

0.15

0.2

0.25

0.3

12

0 (0)

3.3 (1.7)

0 (0)

2 (2.9)

3.64 (1.8)

9.3 (5.1)

16

0 (0)

0 (0)

0 (0)

0 (0)

3 (2.3)

0.7 (1.4)

20

0 (0)

0 (0)

0 (0)

2.3 (1.5)

2.1 (2.8)

6.4 (2.9)

30

3.3 (1.1)

2.2 (1.1)

2 (0.7)

1.9 (1)

1.1 (0.9)

3.7 (2.3)

50

0 (0)

0 (0)

1.1 (0.4)

0.9 (0.3)

1.6 (1)

1.8 (1.5)

100

0 (0)

0.8 (0.3)

0 (0)

0.8 (0.4)

0 (0.2)

0.8 (0.3)

200

0 (0)

0 (0)

0 (0)

0.3 (0.2)

0.1 (0.2)

0.2 (0.3)

300

0 (0)

0 (0)

0.1 (0.1)

0 (0.1)

0.4 (0.2)

0.1 (0.1)

500

0 (0)

0 (0)

0.1 (0.1)

0 (0)

0 (0.1)

0.1 (0.1)