Partial immunization of trees

For a graph G and a non-negative integer-valued function τ on its vertex set, a dynamic monopoly is a set of vertices of G such that iteratively adding to it vertices u of G that have at least τ(u) neighbors in it eventually yields the vertex set of G. We study the problem of maximizing the minimum...

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Veröffentlicht in:Discrete optimization 2020-02, Vol.35, p.100568, Article 100568
Hauptverfasser: Dourado, Mitre C., Ehard, Stefan, Penso, Lucia D., Rautenbach, Dieter
Format: Artikel
Sprache:eng
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Zusammenfassung:For a graph G and a non-negative integer-valued function τ on its vertex set, a dynamic monopoly is a set of vertices of G such that iteratively adding to it vertices u of G that have at least τ(u) neighbors in it eventually yields the vertex set of G. We study the problem of maximizing the minimum order of a dynamic monopoly by increasing the threshold values of individual vertices subject to vertex-dependent lower and upper bounds, and fixing the total increase. We solve this problem efficiently for trees, which extends a result of Khoshkhah and Zaker (2015).
ISSN:1572-5286
1873-636X
DOI:10.1016/j.disopt.2020.100568