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Target Set Selection Parameterized by Clique-Width and Maximum Threshold

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Tim A. Hartmann

Discrete Mathematics · Submitted 2 Oct 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that Target Set Selection is in FPT when parameterized with the combined parameters clique-width of the graph and the maximum threshold value.

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arXiv ID1710.00635 (version 1)
Pith ID5ON4TGGU, Pith's permanent record of this paper and its review
CitationTim A. Hartmann. "Target Set Selection Parameterized by Clique-Width and Maximum Threshold." arXiv:1710.00635 (2017). https://pith.science/paper/5ON4TGGU
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,936 input tokens.

What the abstract itself states, as probabilities: claims first 0.30 · states limitation 0.15 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.71 · compares with prior results 0.90 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The Target Set Selection problem takes as an input a graph $G$ and a non-negative integer threshold $ \mbox{thr}(v) $ for every vertex $v$. A vertex $v$ can get active as soon as at least $ \mbox{thr}(v) $ of its neighbors have been activated. The objective is to select a smallest possible initial set of vertices, the target set, whose activation eventually leads to the activation of all vertices in the graph. We show that Target Set Selection is in FPT when parameterized with the combined parameters clique-width of the graph and the maximum threshold value. This generalizes all previous FPT-membership results for the parameterization by maximum threshold, and thereby solves an open question from the literature. We stress that the time complexity of our algorithm is surprisingly well-behaved and grows only single-exponentially in the parameters.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The Target Set Selection problem takes as an input a graph $G$ and a non-negative integer threshold $ \mbox{thr}(v) $ for every vertex $v$. background 1.00 0.07 0.02 asserted 0.98
s1 A vertex $v$ can get active as soon as at least $ \mbox{thr}(v) $ of its neighbors have been activated. background 1.00 0.06 0.01 asserted 0.88
s2 The objective is to select a smallest possible initial set of vertices, the target set, whose activation eventually leads to the activation of all vertices in the graph. background 1.00 0.06 0.03 asserted 0.97
s3 We show that Target Set Selection is in FPT when parameterized with the combined parameters clique-width of the graph and the maximum threshold value. result 0.78 0.96 0.93 asserted 1.00
s4 This generalizes all previous FPT-membership results for the parameterization by maximum threshold, and thereby solves an open question from the literature. interpretation 0.85 0.81 0.19 asserted 1.00
s5 We stress that the time complexity of our algorithm is surprisingly well-behaved and grows only single-exponentially in the parameters. result 0.65 0.91 0.06 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The Target Set Selection problem takes as an input a graph $G$ and a non-negative integer threshold $ \mbox{thr}(v) $ for every vertex $v$. A vertex $v$ can get active as soon as at least $ \mbox{thr}(v) $ of its neighbors have been activated. The objective is to select a smallest possible initial set of vertices, the target set, whose activation eventually leads to the activation of all vertices in the graph. We show that Target Set Selection is in FPT when parameterized with the combined parameters clique-width of the graph and the maximum threshold value. This generalizes all previous FPT-membership results for the parameterization by maximum threshold, and thereby solves an open question from the literature. We stress that the time complexity of our algorithm is surprisingly well-behaved and grows only single-exponentially in the parameters.

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