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Efficient Algorithms for Measuring the Funnel-Likeness of DAGs

  • Marcelo Garlet Millani
  • Hendrik Molter
  • Rolf Niedermeier
  • Manuel Sorge
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10856)

Abstract

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.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Marcelo Garlet Millani
    • 1
  • Hendrik Molter
    • 1
  • Rolf Niedermeier
    • 1
  • Manuel Sorge
    • 1
    • 2
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany
  2. 2.Department of Industrial Engineering and ManagementBen-Gurion University of the NegevBeer ShevaIsrael

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