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 $\mbox{NP} \not\subseteq \mbox{co-NP}/\mbox{poly}$) by introducing a new polynomial reduction from the clique problem to permutation pattern matching.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2014
- DOI:
- 10.48550/arXiv.1406.1158
- arXiv:
- arXiv:1406.1158
- Bibcode:
- 2014arXiv1406.1158B
- Keywords:
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- Computer Science - Data Structures and Algorithms;
- Computer Science - Computational Complexity