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arXiv · 1406.1158

Kernelization lower bound for Permutation Pattern Matching

Ivan Bliznets·Marek Cygan·Pawel Komosa·Lukas Mach
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Abstract

A permutation $\pi$ contains a permutation $\sigma$ as a pattern if it contains a subsequence of length $|\sigma|$ whose elements are in the same relative order as in the permutation $\sigma$. This notion plays a major role in enumerative combinatorics. We prove that the problem does not have a polynomial kernel (under the widely believed complexity assumption $\mbox{NP} \not\subseteq \mbox{co-NP}/\mbox{poly}$) by introducing a new polynomial reduction from the clique problem to permutation pattern matching.

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Ivan Bliznets, Marek Cygan, Pawel Komosa, Lukas Mach. 2014-06-04. Kernelization lower bound for Permutation Pattern Matching. https://arxiv.org/abs/1406.1158

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