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Documents authored by Bredereck, Robert

Document
DOI: 10.4230/LIPIcs.ISAAC.2019.44
Parameterized Complexity of Stable Roommates with Ties and Incomplete Lists Through the Lens of Graph Parameters

Authors: Robert Bredereck, Klaus Heeger, Dušan Knop, and Rolf Niedermeier

Published in: LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Abstract
We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well as on the side of fixed-parameter tractability. Other than for its famous sister problem Stable Marriage which focuses on a bipartite scenario, Stable Roommates with Incomplete Lists allows for arbitrary acceptability graphs whose edges specify the possible matchings of each two agents (agents are represented by graph vertices). Herein, incomplete lists and ties reflect the fact that in realistic application scenarios the agents cannot bring all other agents into a linear order. Among our main contributions is to show that it is W[1]-hard to compute a maximum-cardinality stable matching for acceptability graphs of bounded treedepth, bounded tree-cut width, and bounded feedback vertex number (these are each time the respective parameters). However, if we "only" ask for perfect stable matchings or the mere existence of a stable matching, then we obtain fixed-parameter tractability with respect to tree-cut width but not with respect to treedepth. On the positive side, we also provide fixed-parameter tractability results for the parameter feedback edge set number.
Cite as

Robert Bredereck, Klaus Heeger, Dušan Knop, and Rolf Niedermeier. Parameterized Complexity of Stable Roommates with Ties and Incomplete Lists Through the Lens of Graph Parameters. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bredereck_et_al:LIPIcs.ISAAC.2019.44,
  author =	{Bredereck, Robert and Heeger, Klaus and Knop, Du\v{s}an and Niedermeier, Rolf},
  title =	{{Parameterized Complexity of Stable Roommates with Ties and Incomplete Lists Through the Lens of Graph Parameters}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{44:1--44:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Lu, Pinyan and Zhang, Guochuan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.44},
  URN =		{urn:nbn:de:0030-drops-115406},
  doi =		{10.4230/LIPIcs.ISAAC.2019.44},
  annote =	{Keywords: Stable matching, acceptability graph, fixed-parameter tractability, W\lbrack1\rbrack-hardness, treewidth, treedepth, tree-cut width, feedback set numbers}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2016.10
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-dev.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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