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Algorithmica

pp 1–31 | Cite as

A Parameterized Algorithmics Framework for Degree Sequence Completion Problems in Directed Graphs

  • Robert Bredereck
  • Vincent Froese
  • Marcel Koseler
  • Marcelo Garlet Millani
  • André Nichterlein
  • Rolf Niedermeier
Article

Abstract

There has been intensive work on the parameterized complexity of the typically NP-hard task to edit undirected graphs into graphs fulfilling certain given vertex degree constraints. In this work, we lift the investigations to the case of directed graphs; herein, we focus on arc insertions. To this end, we develop a general two-stage framework which consists of efficiently solving a problem-specific number problem and transferring its solution to a solution for the graph problem by applying flow computations. In this way, we obtain fixed-parameter tractability and polynomial kernelizability results, with the central parameter being the maximum vertex in- or outdegree of the output digraph. Although there are certain similarities with the much better studied undirected case, the flow computation used in the directed case seems not to work for the undirected case while f-factor computations as used in the undirected case seem not to work for the directed case.

Keywords

NP-hard graph problem Graph realizability k-anonymity Graph modification Arc insertion Fixed-parameter tractability Kernelization 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Robert Bredereck
    • 1
  • Vincent Froese
    • 1
  • Marcel Koseler
    • 1
  • Marcelo Garlet Millani
    • 1
  • André Nichterlein
    • 1
  • Rolf Niedermeier
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany

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