On the Complexity of Calculating Sensitivity Parameters in Boolean Programming Problems - Mikhailyuk, V. A.; Lishchuk, N. V. (Cybernetics and systems analysis, 2015)
This article shows that, for NP-hard problems, the calculation of even the stability ball of radius 1 for an optimal solution is computationally intensive (i.e., a suitable polynomial algorithm is absent when P ≠ NP). In using greedy algorithms for solving the set covering problem (knapsack problem) with the stability radius r = O(1) , there are polynomial algorithms for calculating the stability ball of radius r for an ln m-approximate solution (1-approximate solution).