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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2014.288
URN: urn:nbn:de:0030-drops-44659
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2014/4465/
Drange, Pal Gronas ;
Fomin, Fedor V. ;
Pilipczuk, Michal ;
Villanger, Yngve
Exploring Subexponential Parameterized Complexity of Completion Problems
Abstract
Let F be a family of graphs. In the F-Completion problem, we are given an n-vertex graph G and an integer k as input, and asked whether at most k edges can be added to G so that the resulting graph does not contain a graph from F as an induced subgraph. It appeared recently that special cases of F-Completion, the problem of completing into a chordal graph known as "Minimum Fill-in", corresponding to the case of F={C_4,C_5,C_6,...}, and the problem of completing into a split graph, i.e., the case of F={C_4,2K_2,C_5}, are solvable in parameterized subexponential time. The exploration of this phenomenon is the main motivation for our research on F-Completion.
In this paper we prove that completions into several well studied classes of graphs without long induced cycles also admit parameterized subexponential time algorithms by showing that:
- The problem Trivially Perfect Completion is solvable in parameterized subexponential time, that is F-Completion for F={C_4,P_4}, a cycle and a path on four vertices.
- The problems known in the literature as Pseudosplit Completion, the case where F={2K_2,C_4}, and Threshold Completion, where F={2K_2,P_4,C_4}, are also solvable in subexponential time.
We complement our algorithms for $F$-Completion with the following lower bounds:
- For F={2K_2}, F={C_4}, F={P_4}, and F={2K_2,P_4}, F-Completion cannot be solved in time 2^o(k).n^O(1) unless the Exponential Time Hypothesis (ETH) fails.
Our upper and lower bounds provide a complete picture of the subexponential parameterized complexity of F-Completion problems for F contained inside {2K_2,C_4,P_4}.
BibTeX - Entry
@InProceedings{drange_et_al:LIPIcs:2014:4465,
author = {Pal Gronas Drange and Fedor V. Fomin and Michal Pilipczuk and Yngve Villanger},
title = {{Exploring Subexponential Parameterized Complexity of Completion Problems}},
booktitle = {31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
pages = {288--299},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-65-1},
ISSN = {1868-8969},
year = {2014},
volume = {25},
editor = {Ernst W. Mayr and Natacha Portier},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2014/4465},
URN = {urn:nbn:de:0030-drops-44659},
doi = {10.4230/LIPIcs.STACS.2014.288},
annote = {Keywords: edge completion, modification, subexponential parameterized complexity}
}
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Keywords: |
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edge completion, modification, subexponential parameterized complexity |
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Collection: |
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31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014) |
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Issue Date: |
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2014 |
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Date of publication: |
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05.03.2014 |
