Efficient algorithms for measuring the funnel-likeness of DAGs

  • Marcelo Garlet Millani
  • Hendrik MolterEmail author
  • Rolf Niedermeier
  • Manuel Sorge


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.


Directed graphs Acyclic digraph NP-hard problems Approximation hardness Fixed-parameter tractability Approximation algorithms Graph parameters Experiments 



We are grateful to anonymous reviewers of Journal of Combinatorial Optimization whose constructive feedback helped to improve the presentation and remove some bugs from this paper.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Marcelo Garlet Millani
    • 1
  • Hendrik Molter
    • 1
    Email author
  • Rolf Niedermeier
    • 1
  • Manuel Sorge
    • 1
    • 2
    • 3
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany
  2. 2.Faculty of Mathematics, Informatics and MechanicsUniversity of WarsawWarsawPoland
  3. 3.Department of Industrial Engineering and ManagementBen-Gurion University of the Negev Beer ShevaIsrael

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