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Efficient algorithms for measuring the funnel-likeness of DAGs

Author

Listed:
  • Marcelo Garlet Millani

    (TU Berlin)

  • Hendrik Molter

    (TU Berlin)

  • Rolf Niedermeier

    (TU Berlin)

  • Manuel Sorge

    (TU Berlin
    University of Warsaw
    Ben-Gurion University of the Negev)

Abstract

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.

Suggested Citation

  • Marcelo Garlet Millani & Hendrik Molter & Rolf Niedermeier & Manuel Sorge, 2020. "Efficient algorithms for measuring the funnel-likeness of DAGs," Journal of Combinatorial Optimization, Springer, vol. 39(1), pages 216-245, January.
    • Handle: RePEc:spr:jcomop:v:39:y:2020:i:1:d:10.1007_s10878-019-00464-4
    DOI: 10.1007/s10878-019-00464-4
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    Cited by:

    1. Alain Quilliot & Djamal Rebaine, 2022. "Linear time algorithms on mirror trees," Journal of Combinatorial Optimization, Springer, vol. 44(5), pages 3495-3519, December.

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