DeepAI AI Chat
Log In Sign Up

Target Set Selection Parameterized by Clique-Width and Maximum Threshold

by   Tim A. Hartmann, et al.
RWTH Aachen University

The Target Set Selection problem takes as an input a graph G and a non-negative integer threshold thr(v) for every vertex v. A vertex v can get active as soon as at least 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.


page 1

page 2

page 3

page 4


Maximizing Happiness in Graphs of Bounded Clique-Width

Clique-width is one of the most important parameters that describes stru...

Target set selection with maximum activation time

A target set selection model is a graph G with a threshold function τ:V→...

Improved Parameterized Complexity of Happy Set Problems

We present fixed-parameter tractable (FPT) algorithms for two problems, ...

Solving Target Set Selection with Bounded Thresholds Faster than 2^n

In this paper we consider the Target Set Selection problem. The problem ...

XNLP-completeness for Parameterized Problems on Graphs with a Linear Structure

In this paper, we show several parameterized problems to be complete for...

Computing L(p,1)-Labeling with Combined Parameters

Given a graph, an L(p,1)-labeling of the graph is an assignment f from t...

On some tractable and hard instances for partial incentives and target set selection

A widely studied model for influence diffusion in social networks are t...