  Several classical combinatorial problems have been considered and analysed on
temporal graphs. Recently, a variant of Vertex Cover on temporal graphs, called
MinTimelineCover, has been introduced to summarize timeline activities in
social networks. The problem asks to cover every temporal edge while minimizing
the total span of the vertices (where the span of a vertex is the length of the
timestamp interval it must remain active in, minus one). While the problem has
been shown to be NP-hard even in very restricted cases, its parameterized
complexity has not been fully understood. The problem is known to be in FPT
under the span parameter only for graphs with two timestamps, but the
parameterized complexity for the general case is open. We settle this open
problem by giving an FPT algorithm that is based on a combination of iterative
compression and a reduction to the Digraph Pair Cut problem, a powerful problem
that has received significant attention recently.
