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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)