Abstract
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 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.