Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.IPEC.2020.13
URN: urn:nbn:de:0030-drops-133163
URL: https://drops.dagstuhl.de/opus/volltexte/2020/13316/
Garlet Milani, Marcelo
A Polynomial Kernel for Funnel Arc Deletion Set
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Abstract
In Directed Feedback Arc Set (DFAS) we search for a set of at most k arcs which intersect every cycle in the input digraph. It is a well-known open problem in parameterized complexity to decide if DFAS admits a kernel of polynomial size. We consider π-Arc Deletion Set (π-ADS), a variant of DFAS where we want to remove at most k arcs from the input digraph in order to turn it into a digraph of a class π. In this work, we choose π to be the class of funnels. Funnel-ADS is NP-hard even if the input is a DAG, but is fixed-parameter tractable with respect to k. So far no polynomial kernel for this problem was known. Our main result is a kernel for Funnel-ADS with πͺ(kβΆ) many vertices and πͺ(kβ·) many arcs, computable in πͺ(nm) time, where n is the number of vertices and m the number of arcs of the input digraph.
BibTeX - Entry
@InProceedings{garletmilani:LIPIcs:2020:13316,
author = {Marcelo Garlet Milani},
title = {{A Polynomial Kernel for Funnel Arc Deletion Set}},
booktitle = {15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
pages = {13:1--13:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-172-6},
ISSN = {1868-8969},
year = {2020},
volume = {180},
editor = {Yixin Cao and Marcin Pilipczuk},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/13316},
URN = {urn:nbn:de:0030-drops-133163},
doi = {10.4230/LIPIcs.IPEC.2020.13},
annote = {Keywords: graph editing, directed feedback arc set, parameterized algorithm, kernels, funnels}
}
| Keywords: | graph editing, directed feedback arc set, parameterized algorithm, kernels, funnels | |
| Seminar: | 15th International Symposium on Parameterized and Exact Computation (IPEC 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 04.12.2020 |
