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

Authors Robert Bredereck, Vincent Froese, Marcel Koseler, Marcelo Garlet Millani, André Nichterlein, Rolf Niedermeier

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

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Robert Bredereck, Vincent Froese, Marcel Koseler, Marcelo Garlet Millani, André Nichterlein, and Rolf Niedermeier. A Parameterized Algorithmics Framework for Degree Sequence Completion Problems in Directed Graphs. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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, our general two-stage framework consists of efficiently solving a problem-specific number problem 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.
  • NP-hard graph problem
  • graph realizability
  • graph modification
  • arc insertion
  • fixed-parameter tractability
  • kernelization


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