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.ICALP.2017.58
URN: urn:nbn:de:0030-drops-73788
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7378/
Gutin, Gregory ;
Reidl, Felix ;
Wahlström, Magnus
k-Distinct In- and Out-Branchings in Digraphs
Abstract
An out-branching and an in-branching of a digraph D are called k-distinct if each of them has k arcs absent in the other. Bang-Jensen, Saurabh and Simonsen (2016) proved that the problem of deciding whether a strongly connected digraph D has k-distinct out-branching and in-branching is fixed-parameter tractable (FPT) when parameterized by k. They asked whether the problem remains FPT when extended to arbitrary digraphs. Bang-Jensen and Yeo (2008) asked whether the same problem is FPT when the out-branching and in-branching have the same root.
By linking the two problems with the problem of whether a digraph has an out-branching with at least k leaves (a leaf is a vertex of out-degree zero), we first solve the problem of Bang-Jensen and Yeo (2008). We then develop a new digraph decomposition called the rooted cut decomposition and using it we prove that the problem of Bang-Jensen et al. (2016) is FPT for all digraphs. We believe that the rooted cut decomposition will be useful for obtaining other results on digraphs.
BibTeX - Entry
@InProceedings{gutin_et_al:LIPIcs:2017:7378,
author = {Gregory Gutin and Felix Reidl and Magnus Wahlstr{\"o}m},
title = {{k-Distinct In- and Out-Branchings in Digraphs}},
booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
pages = {58:1--58:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-041-5},
ISSN = {1868-8969},
year = {2017},
volume = {80},
editor = {Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7378},
URN = {urn:nbn:de:0030-drops-73788},
doi = {10.4230/LIPIcs.ICALP.2017.58},
annote = {Keywords: Digraphs, Branchings, Decompositions, FPT algorithms}
}
Keywords: |
|
Digraphs, Branchings, Decompositions, FPT algorithms |
Collection: |
|
44th International Colloquium on Automata, Languages, and Programming (ICALP 2017) |
Issue Date: |
|
2017 |
Date of publication: |
|
07.07.2017 |