Weakening Covert Networks by Minimizing Inverse Geodesic Length

We consider the problem of deleting nodes in a covert network to minimize its performance. The inverse geodesic length (IGL) is a well-known and widely used measure of network performance. It equals the sum of the inverse distances of all pairs of vertices. In the MINIGL problem the input is a graph G, a budget k, and a target IGL T, and the question is whether there exists a subset of vertices X with |X| = k, such that the IGL of G - X is at most T. In network analysis, the IGL is often used to evaluate how well heuristics perform in strengthening or weakening a network. In this paper, we undertake a study of the classical and parameterized complexity of the MINIGL problem. The problem is NP-complete even if T = 0 and remains both NP-complete and W[1]-hard for parameter k on bipartite and on split graphs. On the positive side, we design several multivariate algorithms for the problem. Our main result is an algorithm for MINIGL parameterized by twin cover number.

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