Detecting monomials with k distinct variables

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Detecting monomials with k distinct variables

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Publication Article, peer reviewed scientific
Title Detecting monomials with k distinct variables
Author Floderus, Peter ; Lingas, Andrzej ; Persson, Mia ; Sledneu, Dzmitry
Date 2015
English abstract
We study the complexity of detecting monomials with special properties in the sum-product expansion of a polynomial represented by an arithmetic circuit of size polynomial in the number of input variables and using only multiplication and addition. We focus on monomial properties expressed in terms of the number of distinct variables occurring in a monomial. Our first result is a randomized FPT algorithm for detection of a monomial having at least k distinct variables, parametrized with respect to k. For a more restricted class of circuits, we can also provide a deterministic FPT algorithm for detection of a monomial having at most k distinct variables parametrized by the degree of the polynomial represented by the input circuit. Furthermore, we derive several hardness results on detection of monomials with such properties within exact, parametrized and approximation complexity. In particular, we observe that the detection of a monomial having at most k distinct variables is W[2]-hard for the parameter k. (C) 2014 Elsevier B.V. All rights reserved.
DOI http://dx.doi.org/10.1016/j.ipl.2014.07.003 (link to publisher's fulltext)
Publisher Elsevier
Host/Issue Information Processing Letters;2
Volume 115
ISSN 0020-0190
Pages 82-86
Language eng (iso)
Subject Algorithms
Polynomial
Monomial
Arithmetic circuit
Parametrized
complexity
Approximation hardness
Technology
Research Subject Categories::TECHNOLOGY
Handle http://hdl.handle.net/2043/19729 Permalink to this page
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