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DOI: 10.4230/LIPIcs.IPEC.2015.30
URN: urn:nbn:de:0030-drops-55697
URL: https://drops.dagstuhl.de/opus/volltexte/2015/5569/
Golovach, Petr A. ; Requilé, Clément ; Thilikos, Dimitrios M.
Variants of Plane Diameter Completion
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Abstract
The Plane Diameter Completion problem asks, given a plane graph G and a positive integer d, if it is a spanning subgraph of a plane graph H that has diameter at most d. We examine two variants of this problem where the input comes with another parameter k. In the first variant, called BPDC, k upper bounds the total number of edges to be added and in the second, called BFPDC, k upper bounds the number of additional edges per face. We prove that both problems are NP-complete, the first even for 3-connected graphs of face-degree at most 4 and the second even when k=1 on 3-connected graphs of face-degree at most 5. In this paper we give parameterized algorithms for both problems that run in O(n^{3})+2^{2^{O((kd)^2\log d)}} * n steps.
BibTeX - Entry
@InProceedings{golovach_et_al:LIPIcs:2015:5569,
author = {Petr A. Golovach and Cl{\'e}ment Requil{\'e} and Dimitrios M. Thilikos},
title = {{Variants of Plane Diameter Completion}},
booktitle = {10th International Symposium on Parameterized and Exact Computation (IPEC 2015)},
pages = {30--42},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-92-7},
ISSN = {1868-8969},
year = {2015},
volume = {43},
editor = {Thore Husfeldt and Iyad Kanj},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2015/5569},
URN = {urn:nbn:de:0030-drops-55697},
doi = {10.4230/LIPIcs.IPEC.2015.30},
annote = {Keywords: Planar graphs, graph modification problems, parameterized algorithms, dynamic programming, branchwidth}
}
| Keywords: | Planar graphs, graph modification problems, parameterized algorithms, dynamic programming, branchwidth | |
| Seminar: | 10th International Symposium on Parameterized and Exact Computation (IPEC 2015) | |
| Issue date: | 2015 | |
| Date of publication: | 19.11.2015 |
