Fixed-parameter tractability by treewidth and lifespan

Establish that the Temporal Zero Forcing Set problem on temporal graphs can be solved in fixed-parameter tractable time when parameterized by the treewidth and lifespan of the input temporal graph.

Background

The paper studies the Temporal Zero Forcing Set problem, which asks for a minimum initial set of corrupted vertices whose corruption propagates through a temporal graph according to the zero forcing rule, with one corruption step performed in each snapshot. The authors prove polynomial-time solvability when the underlying graph is a bounded-degree tree and fixed-parameter tractability when the parameters are the lifespan and maximum degree for temporal trees.

Motivated by these tractability results and by corresponding static zero forcing results parameterized by treewidth, the authors conjecture that bounded treewidth, together with bounded lifespan, is sufficient for fixed-parameter tractability even when the underlying temporal graph is not a tree. They note that the conjecture is known when all snapshots are identical, but remains to be established for general temporal graphs.