Table 1 Summary of the approximation factor of the approximation algorithms presented in this manuscript for general permutations (GP), permutations with \(n\ell\) inversions for some \(\ell \ge 1\) (\(\ell\)IP), permutations with at least n inversions (1IP), and permutations with at least 2n inversions (2IP)

SbSSR

3

\(1+\frac{1}{\ell }\)

2

1.5

SbSST

3

\(1+\frac{1}{\ell }\)

2

1.5

SbSSO

3

\(1+\frac{1}{\ell }\)

2

1.5

SbSigSSR

5

\(1+\frac{2}{\ell }\)

3

2

SbSigSSO

5

\(1+\frac{2}{\ell }\)

3

2