Solving Target Set Selection with Bounded Thresholds Faster than 2n

Ivan Bliznets, Danil Sagunov*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)

Abstract

In this paper we consider the Target Set Selection problem. The problem naturally arises in many fields like economy, sociology, medicine. In the Target Set Selection problem one is given a graph G with a function thr:V(G)→N∪{0} and two integers k, ℓ. The goal of the problem is to activate at most k vertices initially so that at the end of the activation process there are at least ℓ activated vertices. The activation process occurs in the following way: (i) once activated, a vertex stays activated forever; (ii) a vertex v becomes activated if at least thr(v) of its neighbours are activated. The problem and its different special cases were extensively studied from the approximation and parameterized points of view. For example, parameterizations by the following parameters were studied: treewidth, feedback vertex set, diameter, size of target set, vertex cover, cluster editing number and others. Despite the extensive study of the problem it is still unknown whether the problem can be solved in O∗((2 - ϵ) n) time for some ϵ> 0. We partially answer this question by presenting several faster-than-trivial algorithms that work in cases of constant thresholds, constant dual thresholds or when the threshold value of each vertex is bounded by one-third of its degree. Also, we show that the problem parameterized by ℓ is W[1]-hard even when all thresholds are constant.
Original languageEnglish
Pages (from-to)384–405
Number of pages22
JournalAlgorithmica
Volume85
DOIs
Publication statusPublished - Feb-2023
Externally publishedYes

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