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

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

Published in: LIPIcs, Volume 63, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)


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, 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.

Cite as

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)


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@InProceedings{bredereck_et_al:LIPIcs.IPEC.2016.10,
  author =	{Bredereck, Robert and Froese, Vincent and Koseler, Marcel and Millani, Marcelo Garlet and Nichterlein, Andr\'{e} and Niedermeier, Rolf},
  title =	{{A Parameterized Algorithmics Framework for Degree Sequence Completion Problems in Directed Graphs}},
  booktitle =	{11th International Symposium on Parameterized and Exact Computation (IPEC 2016)},
  pages =	{10:1--10:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-023-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{63},
  editor =	{Guo, Jiong and Hermelin, Danny},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2016.10},
  URN =		{urn:nbn:de:0030-drops-69353},
  doi =		{10.4230/LIPIcs.IPEC.2016.10},
  annote =	{Keywords: NP-hard graph problem, graph realizability, graph modification, arc insertion, fixed-parameter tractability, kernelization}
}
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