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DOI: 10.4230/LIPIcs.STACS.2019.28
URN: urn:nbn:de:0030-drops-102677
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10267/
Fomin, Fedor V. ; Golovach, Petr A. ; Thilikos, Dimitrios M.
Modification to Planarity is Fixed Parameter Tractable
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Abstract
A replacement action is a function L that maps each k-vertex labeled graph to another k-vertex graph. We consider a general family of graph modification problems, called L-Replacement to C, where the input is a graph G and the question is whether it is possible to replace in G some k-vertex subgraph H of it by L(H) so that the new graph belongs to the graph class C. L-Replacement to C can simulate several modification operations such as edge addition, edge removal, edge editing, and diverse completion and superposition operations. In this paper, we prove that for any action L, if C is the class of planar graphs, there is an algorithm that solves L-Replacement to C in O(|G|^{2}) steps. We also present several applications of our approach to related problems.
BibTeX - Entry
@InProceedings{fomin_et_al:LIPIcs:2019:10267,
author = {Fedor V. Fomin and Petr A. Golovach and Dimitrios M. Thilikos},
title = {{Modification to Planarity is Fixed Parameter Tractable}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {28:1--28:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Rolf Niedermeier and Christophe Paul},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10267},
doi = {10.4230/LIPIcs.STACS.2019.28},
annote = {Keywords: Modification problems, Planar graphs, Irrelevant vertex technique}
}
| Keywords: | Modification problems, Planar graphs, Irrelevant vertex technique | |
| Seminar: | 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 12.03.2019 |
