Parameterized Approximability of Maximizing the Spread of Influence in Networks
In this paper, we consider the problem of maximizing the spread of influence through a social network. Here, we are given a graph G = (V,E), a positive integer k and a threshold value thr(v) attached to each vertex v ∈ V. The objective is then to find a subset of k vertices to “activate” such that the number of activated vertices at the end of a propagation process is maximum. A vertex v gets activated if at least thr(v) of its neighbors are. We show that this problem is strongly inapproximable in fpt-time with respect to (w.r.t.) parameter k even for very restrictive thresholds. For unanimity thresholds, we prove that the problem is inapproximable in polynomial time and the decision version is W-hard w.r.t. parameter k. On the positive side, it becomes r(n)-approximable in fpt-time w.r.t. parameter k for any strictly increasing function r. Moreover, we give an fpt-time algorithm to solve the decision version for bounded degree graphs.
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