Основные понятия
Determining the minimum number of initially infected individuals required to infect the entire population in a dynamic network is a computationally hard problem, with hardness results depending on the specific temporal constraints.
Аннотация
The paper studies the Temporal Reachability Dominating Set (TaRDiS) problem on temporal graphs, which asks whether there exists a small set of k initially infected individuals that can indirectly infect the entire population. The authors provide a comprehensive analysis of the computational complexity of TaRDiS and its variants, considering different temporal constraints.
Key highlights:
- TaRDiS is shown to be NP-complete, even when the lifetime of the temporal graph is bounded or the footprint graph is planar.
- The authors identify the maximum lifetime τ for which each variant of TaRDiS is tractable, demonstrating that the problem becomes intractable for larger lifetimes.
- Parameterized complexity results are provided, showing that TaRDiS is fixed-parameter tractable with respect to the treewidth of the footprint graph and the lifetime.
- The authors also introduce and study the MaxMinTaRDiS problem, which aims to schedule connections between individuals to maximize the minimum size of any TaRDiS. They show this problem to be computationally hard in various settings.
- Interestingly, the authors establish a connection between Nonstrict MaxMinTaRDiS and the well-studied Distance-3 Independent Set problem.
Статистика
The paper does not contain any explicit numerical data or statistics to support the key arguments.
Цитаты
"Given a population with dynamic pairwise connections, we ask if the entire population could be (indirectly) infected by a small group of k initially infected individuals."
"We formalise this problem as the Temporal Reachability Dominating Set (TaRDiS) problem on temporal graphs."
"We show these to be coNP-complete, NP-hard, and ΣP2-complete, respectively."