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DOI: 10.4230/LIPIcs.SWAT.2018.24
URN: urn:nbn:de:0030-drops-88506
URL: http://drops.dagstuhl.de/opus/volltexte/2018/8850/
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Hanaka, Tesshu ; Katsikarelis, Ioannis ; Lampis, Michael ; Otachi, Yota ; Sikora, Florian

Parameterized Orientable Deletion

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LIPIcs-SWAT-2018-24.pdf (0.6 MB)


Abstract

A graph is d-orientable if its edges can be oriented so that the maximum in-degree of the resulting digraph is at most d. d-orientability is a well-studied concept with close connections to fundamental graph-theoretic notions and applications as a load balancing problem. In this paper we consider the d-Orientable Deletion problem: given a graph G=(V,E), delete the minimum number of vertices to make G d-orientable. We contribute a number of results that improve the state of the art on this problem. Specifically: - We show that the problem is W[2]-hard and log n-inapproximable with respect to k, the number of deleted vertices. This closes the gap in the problem's approximability. - We completely characterize the parameterized complexity of the problem on chordal graphs: it is FPT parameterized by d+k, but W-hard for each of the parameters d,k separately. - We show that, under the SETH, for all d,epsilon, the problem does not admit a (d+2-epsilon)^{tw}, algorithm where tw is the graph's treewidth, resolving as a special case an open problem on the complexity of PseudoForest Deletion. - We show that the problem is W-hard parameterized by the input graph's clique-width. Complementing this, we provide an algorithm running in time d^{O(d * cw)}, showing that the problem is FPT by d+cw, and improving the previously best know algorithm for this case.

BibTeX - Entry

@InProceedings{hanaka_et_al:LIPIcs:2018:8850,
  author =	{Tesshu Hanaka and Ioannis Katsikarelis and Michael Lampis and Yota Otachi and Florian Sikora},
  title =	{{Parameterized Orientable Deletion}},
  booktitle =	{16th Scandinavian Symposium and Workshops on Algorithm  Theory (SWAT 2018)},
  pages =	{24:1--24:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-068-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{101},
  editor =	{David Eppstein},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8850},
  URN =		{urn:nbn:de:0030-drops-88506},
  doi =		{10.4230/LIPIcs.SWAT.2018.24},
  annote =	{Keywords: Graph orientations, FPT algorithms, Treewidth, SETH}
}

Keywords: Graph orientations, FPT algorithms, Treewidth, SETH
Seminar: 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)
Issue Date: 2018
Date of publication: 30.05.2018


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