eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-12-06
18:1
18:13
10.4230/LIPIcs.ISAAC.2018.18
article
Target Set Selection in Dense Graph Classes
Dvorák, Pavel
1
Knop, Dusan
2
Toufar, Tomás
1
Computer Science Institute, Charles University, Prague, Czech Republic
Algorithmics and Computational Complexity, Faculty IV, TU Berlin, Berlin, Germany and Faculty of Information Technology, Czech Technical University in Prague, Czech Republic
In this paper we study the Target Set Selection problem from a parameterized complexity perspective. Here for a given graph and a threshold for each vertex the task is to find a set of vertices (called a target set) to activate at the beginning which activates the whole graph during the following iterative process. A vertex outside the active set becomes active if the number of so far activated vertices in its neighborhood is at least its threshold.
We give two parameterized algorithms for a special case where each vertex has the threshold set to the half of its neighbors (the so called Majority Target Set Selection problem) for parameterizations by the neighborhood diversity and the twin cover number of the input graph.
We complement these results from the negative side. We give a hardness proof for the Majority Target Set Selection problem when parameterized by (a restriction of) the modular-width - a natural generalization of both previous structural parameters. We show that the Target Set Selection problem parameterized by the neighborhood diversity when there is no restriction on the thresholds is W[1]-hard.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol123-isaac2018/LIPIcs.ISAAC.2018.18/LIPIcs.ISAAC.2018.18.pdf
parameterized complexity
target set selection
dense graphs