On Stable Instances of MINCUT

A combinatorial optimization problem is called stable if its solution is preserved under perturbation of the input parameters that do not exceed a certain threshold — the stability radius. In [1–3] exact polynomial algorithms have been built for some NP-hard problems on cuts in the assumption of the entrance stability. In this paper we show how to accelerate some algorithms for sufficiently stable polynomial problems. The approach is illustrated by the well-known problem of the minimum cut (MINCUT). We built an $ O(n^2)$ exact algorithm for solving $n$-stable instance of the MINCUT problem. Moreover, we present a polynomial algorithm for calculating the stability radius and a simple criterion for checking $n$-stability of the MINCUT problem.