License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SWAT.2018.24
URN: urn:nbn:de:0030-drops-88506
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8850/
Hanaka, Tesshu ;
Katsikarelis, Ioannis ;
Lampis, Michael ;
Otachi, Yota ;
Sikora, Florian
Parameterized Orientable Deletion
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: |
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Graph orientations, FPT algorithms, Treewidth, SETH |
Collection: |
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16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018) |
Issue Date: |
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2018 |
Date of publication: |
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04.06.2018 |