TY - GEN
T1 - Fractals for kernelization lower bounds, with an application to length-bounded cut problems
AU - Fluschnik, Till
AU - Hermelin, Danny
AU - Nichterlein, André
AU - Niedermeier, Rolf
PY - 2016/8/1
Y1 - 2016/8/1
N2 - Bodlaender et al.'s [6] cross-composition technique is a popular method for excluding polynomialsize 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 [13], we show that, unless NP ⊆ 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 polynomialsize 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.
AB - Bodlaender et al.'s [6] cross-composition technique is a popular method for excluding polynomialsize 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 [13], we show that, unless NP ⊆ 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 polynomialsize 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.
KW - Cross-compositions
KW - Graph modification problems
KW - Interdiction problems
KW - Lower bounds
KW - Parameterized complexity
KW - Polynomial-time data reduction
UR - http://www.scopus.com/inward/record.url?scp=85012901973&partnerID=8YFLogxK
U2 - https://doi.org/10.4230/LIPIcs.ICALP.2016.25
DO - https://doi.org/10.4230/LIPIcs.ICALP.2016.25
M3 - Conference contribution
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016
A2 - Rabani, Yuval
A2 - Chatzigiannakis, Ioannis
A2 - Sangiorgi, Davide
A2 - Mitzenmacher, Michael
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016
Y2 - 12 July 2016 through 15 July 2016
ER -