an:07161781
Zbl 1434.05148
Garlet Millani, Marcelo; Molter, Hendrik; Niedermeier, Rolf; Sorge, Manuel
Efficient algorithms for measuring the funnel-likeness of DAGs
EN
J. Comb. Optim. 39, No. 1, 216-245 (2020).
00445182
2020
j
05C85 68Q25 05C20 68W25
directed graphs; acyclic digraph; NP-hard problems; approximation hardness; fixed-parameter tractability; approximation algorithms; graph parameters; experiments
Summary: We propose funnels as 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 analogue to trees for directed graphs, being more restrictive than DAGs but more expressive than mere 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 identify the NP-hard problem of computing the arc-deletion distance of a given DAG to a funnel. We develop efficient exact and approximation algorithms for the problem and test them on synthetic random graphs and real-world graphs.