  Funnels are a new natural subclass of DAGs. Intuitively, a DAG is a funnel if
every source-sink path can be uniquely identified by one of its arcs. Funnels
are an analog to trees for directed graphs that is more restrictive than DAGs
but more expressive than in-/out-trees. Computational problems such as finding
vertex-disjoint paths or tracking the origin of memes remain NP-hard on DAGs
while on funnels they become solvable in polynomial time. Our main focus is the
algorithmic complexity of finding out how funnel-like a given DAG is. To this
end, we study the NP-hard problem of computing the arc-deletion distance to a
funnel of a given DAG. We develop efficient exact and approximation algorithms
for the problem and test them on synthetic random graphs and real-world graphs.
