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DOI: 10.4230/LIPIcs.ISAAC.2016.20
URN: urn:nbn:de:0030-drops-67898
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6789/
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Bodlaender, Hans L. ; Ono, Hirotaka ; Otachi, Yota

Degree-Constrained Orientation of Maximum Satisfaction: Graph Classes and Parameterized Complexity

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Abstract

The problem Max W-Light (Max W-Heavy) for an undirected graph is to assign a direction to each edge so that the number of vertices of outdegree at most W (resp. at least W) is maximized. It is known that these problems are NP-hard even for fixed W. For example, Max 0-Light is equivalent to the problem of finding a maximum independent set. In this paper, we show that for any fixed constant W, Max W-Heavy can be solved in linear time for hereditary graph classes for which treewidth is bounded by a function of degeneracy. We show that such graph classes include chordal graphs, circular-arc graphs, d-trapezoid graphs, chordal bipartite graphs, and graphs of bounded clique-width. To have a polynomial-time algorithm for Max W-Light, we need an additional condition of a polynomial upper bound on the number of potential maximal cliques to apply the metatheorem by Fomin, Todinca, and Villanger [SIAM J. Comput., 44(1):57-87, 2015]. The aforementioned graph classes, except bounded clique-width graphs, satisfy such a condition. For graphs of bounded clique-width, we present a dynamic programming approach not using the metatheorem to show that it is actually polynomial-time solvable for this graph class too. We also study the parameterized complexity of the problems and show some tractability and intractability results.

BibTeX - Entry

@InProceedings{bodlaender_et_al:LIPIcs:2016:6789,
  author =	{Hans L. Bodlaender and Hirotaka Ono and Yota Otachi},
  title =	{{Degree-Constrained Orientation of Maximum Satisfaction: Graph Classes and Parameterized Complexity}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{20:1--20:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Seok-Hee Hong},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6789},
  URN =		{urn:nbn:de:0030-drops-67898},
  doi =		{10.4230/LIPIcs.ISAAC.2016.20},
  annote =	{Keywords: orientation, graph class, width parameter, parameterized complexity}
}

Keywords: orientation, graph class, width parameter, parameterized complexity
Seminar: 27th International Symposium on Algorithms and Computation (ISAAC 2016)
Issue Date: 2016
Date of publication: 02.12.2016


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