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ESA
2009
Springer

Kernel Bounds for Disjoint Cycles and Disjoint Paths

13 years 9 months ago
Kernel Bounds for Disjoint Cycles and Disjoint Paths
In this paper, we give evidence for the problems Disjoint Cycles and Disjoint Paths that they cannot be preprocessed in polynomial time such that resulting instances always have a size bounded by a polynomial in a specified parameter (or, in short: do not have a polynomial kernel); these results are assuming the validity of certain complexity theoretic assumptions. We build upon recent results by Bodlaender et al. [3] and Fortnow and Santhanam [13], that show that NPcomplete problems that are or-compositional do not have polynomial kernels, unless NP ⊆ coNP/poly. To this machinery, we add a notion of transformation, and thus obtain that Disjoint Cycles and Disjoint Paths do not have polynomial kernels, unless NP ⊆ coNP/poly. We also show that the related Disjoint Cycles Packing problem has a kernel of size O(k log k).
Hans L. Bodlaender, Stéphan Thomassé
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where ESA
Authors Hans L. Bodlaender, Stéphan Thomassé, Anders Yeo
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