Kernelization lower bound for Permutation Pattern Matching
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 $\mbox{NP} \not\subseteq \mbox{coNP}/\mbox{poly}$) by introducing a new polynomial reduction from the clique problem to permutation pattern matching.
 Publication:

arXiv eprints
 Pub Date:
 June 2014
 DOI:
 10.48550/arXiv.1406.1158
 arXiv:
 arXiv:1406.1158
 Bibcode:
 2014arXiv1406.1158B
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Computational Complexity