Work

Kernelization lower bound for Permutation Pattern Matching

Year: 2014

Type: preprint

Abstract: A permutation $π$ contains a permutation $σ$ as a pattern if it contains a subsequence of length $|σ|$ whose elements are in the same relative order as in the permutation $σ$. 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1406.1158

Authors: Bliznets, Ivan, Cygan, Marek, Komosa, Pawel, Mach, Lukas

Institutions: Russian Academy of Sciences, St. Petersburg Department of Steklov Institute of Mathematics, Steklov Mathematical Institute, University of Warsaw, University of Warwick

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, FP7 Ideas: European Research Council

Awards: G3207356259, G3423300469, G393177772, G5702163051, Classes of combinatorial objects: from structure to algorithms

OpenAlex ID: W2950342364

Cites: 10

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Related to: 20