Finding critical regions in a network

It is important that our vital networks (e.g., infrastructures) are robust to more than single-link failures. Failures might for instance affect a part of the network that resides in a certain geographical region. In this paper, considering networks embedded in a two-dimensional plane, we study the problem of finding a critical region - that is, a part of the network that can be enclosed by a given elementary figure (a circle, ellipse, rectangle, square, or equilateral triangle) with a predetermined size - whose removal would lead to the highest network disruption. We determine that there is a polynomial number of non-trivial positions for such a figure that need to be considered and, subsequently, we propose a polynomial-time algorithm for the problem. Simulations on realistic networks illustrate that different figures with equal area result in different critical regions in a network.