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Kernelization Lower Bounds for Finding Constant-Size Subgraphs

  • Till FluschnikEmail author
  • George B. Mertzios
  • André Nichterlein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10936)

Abstract

Kernelization is an important tool in parameterized algorithmics. Given an input instance accompanied by a parameter, the goal is to compute in polynomial time an equivalent instance of the same problem such that the size of the reduced instance only depends on the parameter and not on the size of the original instance. In this paper, we provide a first conceptual study on limits of kernelization for several polynomial-time solvable problems. For instance, we consider the problem of finding a triangle with negative sum of edge weights parameterized by the maximum degree of the input graph. We prove that a linear-time computable strict kernel of truly subcubic size for this problem violates the popular APSP-conjecture.

Notes

Acknowledgement

We thank Holger Dell (Saarland University) for fruitful discussion on Sect. 2 and Rolf Niedermeier for discussions leading to this work.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Till Fluschnik
    • 1
    Email author
  • George B. Mertzios
    • 2
  • André Nichterlein
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische Informatik, TU BerlinBerlinGermany
  2. 2.Department of Computer ScienceDurham UniversityDurhamUK

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