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DOI: 10.4230/LIPIcs.ICALP.2016.25
URN: urn:nbn:de:0030-drops-63049
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6304/
Fluschnik, Till ; Hermelin, Danny ; Nichterlein, André ; Niedermeier, Rolf
Fractals for Kernelization Lower Bounds, With an Application to Length-Bounded Cut Problems
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Abstract
Bodlaender et al.'s [Bodlaender/Jansen/Kratsch,2014] cross-composition technique is a popular method for excluding polynomial-size problem kernels for NP-hard parameterized problems. We present a new technique exploiting triangle-based fractal structures for extending the range of applicability of cross-compositions. Our technique makes it possible to prove new no-polynomial-kernel results for a number of problems dealing with length-bounded cuts. Roughly speaking, our new technique combines the advantages of serial and parallel composition. In particular, answering an open question of Golovach and Thilikos [Golovach/Thilikos,2011], we show that, unless NP subseteq coNP/poly, the NP-hard Length-Bounded Edge-Cut problem (delete at most k edges such that the resulting graph has no s-t path of length shorter than l) parameterized by the combination of k and l has no polynomial-size problem kernel. Our framework applies to planar as well as directed variants of the basic problems and also applies to both edge and vertex deletion problems.
BibTeX - Entry
@InProceedings{fluschnik_et_al:LIPIcs:2016:6304,
author = {Till Fluschnik and Danny Hermelin and Andr{\'e} Nichterlein and Rolf Niedermeier},
title = {{Fractals for Kernelization Lower Bounds, With an Application to Length-Bounded Cut Problems}},
booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
pages = {25:1--25:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-013-2},
ISSN = {1868-8969},
year = {2016},
volume = {55},
editor = {Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6304},
URN = {urn:nbn:de:0030-drops-63049},
doi = {10.4230/LIPIcs.ICALP.2016.25},
annote = {Keywords: Parameterized complexity, polynomial-time data reduction, cross-compositions, lower bounds, graph modification problems, interdiction problems}
}
| Keywords: | Parameterized complexity, polynomial-time data reduction, cross-compositions, lower bounds, graph modification problems, interdiction problems | |
| Seminar: | 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) | |
| Issue date: | 2016 | |
| Date of publication: | 23.08.2016 |
