The hardness results for the bounded movement variant of the problem indicate that determining the existence of a repair under movement constraints is NP-complete, even for simplified cases such as a single attribute with uniform constraints. This suggests that, in general, the bounded movement variant is computationally intractable, which poses significant challenges for practical applications where movement restrictions are critical, such as in scenarios involving physical locations or sensitive data.
However, there are special cases where efficient algorithms can still be developed. For instance, in the case of a line metric, the problem remains tractable, allowing for polynomial-time algorithms to find optimal repairs while respecting the movement bounds. This suggests that while the general problem is hard, specific structures or constraints can lead to efficient solutions. Future research could explore other structured metrics or additional constraints that might allow for polynomial-time algorithms, potentially broadening the applicability of efficient repair strategies in bounded movement scenarios.