Table 2 How to replace a non-correcting move \(\beta _i\) with a correcting move \(\beta '_i\) [29]; in all cases, \(e<f\), and x is arbitrary
From: On the parameterized complexity of the median and closest problems under some permutation metrics
Case | \(\pi \) | \(\pi '=\pi \beta _i\) | \(\pi ''=\pi \beta '_i\) |
|---|---|---|---|
1 | \(\ldots ef \ldots \) | \(\ldots fe \ldots \) | \(\ldots ef \ldots \) |
2 | \(\ldots exf \ldots \) | \(\ldots xfe \ldots \) | \(\ldots xef \ldots \) |
3 | \(\ldots exf \ldots \) | \(\ldots fex \ldots \) | \(\ldots efx \ldots \) |
4 | \(\ldots xef \ldots \) | \(\ldots fxe \ldots \) | \(\ldots exf \ldots \) |
5 | \(\ldots efx \ldots \) | \(\ldots fxe \ldots \) | \(\ldots exf \ldots \) |