Fractals for kernelization lower bounds, with an application to length-bounded cut problems

Till Fluschnik, Dan Hermelin, André Nichterlein, Rolf Niedermeier

Research output: Contribution to journalConference articlepeer-review

3 Scopus citations


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.

Original languageEnglish GB
JournalLeibniz International Proceedings in Informatics, LIPIcs
StatePublished - 1 Aug 2016
Event43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016 - Rome, Italy
Duration: 12 Jul 201615 Jul 2016


  • Cross-compositions
  • Graph modification problems
  • Interdiction problems
  • Lower bounds
  • Parameterized complexity
  • Polynomial-time data reduction

ASJC Scopus subject areas

  • Software


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