Kernelization lower bound for Permutation Pattern Matching
نویسندگان
چکیده
منابع مشابه
Kernelization lower bound for Permutation Pattern Matching
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 NP 6⊆ co-NP/poly) by introducing a new polynomial reduction...
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Given permutations T and P of length n and m, respectively, the Permutation Pattern Matching problem asks to find allm-length subsequences of T that are order-isomorphic to P . This problem has a wide range of applications but is known to be NP-hard. In this paper, we study the special case, where the goal is to only find the boxed subsequences of T that are order-isomorphic to P . This problem...
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Definition 2.1. Let f : X × Y → V . A subset R of X × Y is a rectangle1 if it is of the form A × B for some A ⊆ X and B ⊆ Y . The rectangle R is said to be monochromatic (wrt. f) if f is constant on R. A monochromatic rectangle R is a 0-rectangle if f(R) = {0}; it is a 1-rectangle if f(R) = {1}. Observation 2.2. A subset S of X × Y is a rectangle iff for all x, x′ ∈ X and y, y′ ∈ Y (x, x′) ∈ S ...
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Permutation Pattern Matching (or PPM) is a decision problem whose input is a pair of permutations π and τ , represented as sequences of integers, and the task is to determine whether τ contains a subsequence order-isomorphic to π. Bose, Buss and Lubiw proved that PPM is NP-complete on general inputs. We show that PPM is NP-complete even when π has no decreasing subsequence of length 3 and τ has...
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ژورنال
عنوان ژورنال: Information Processing Letters
سال: 2015
ISSN: 0020-0190
DOI: 10.1016/j.ipl.2015.01.001