Inapproximability and parameterized results for the target set selection problem

4 Dec 2018Suman BanerjeeRogers MathewFahad Panolan

Given an undirected graph $G$ with a threshold function $\tau:V(G) \rightarrow \mathbb{N}$, the \emph{Target Set Selection (TSS) Problem} is about choosing a minimum cardinality set, say $S \subseteq V(G)$, such that starting a diffusion process with $S$ as its seed set will eventually result in activating all the nodes in $G$. Under the non-progressive diffusion model, we have the following results on the TSS Problem: We show that the TSS Problem on bipartite graphs does not admit an approximation algorithm with a performance guarantee asymptotically better than $O(\log n_{min})$, where $n_{min}$ is the cardinality of the smaller bipartition, unless $P=NP$... (read more)

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