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Detecting monomials with k distinct variables

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Author

Summary, in English

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.

Department/s

Publishing year

2015

Language

English

Pages

82-86

Publication/Series

Information Processing Letters

Volume

115

Issue

2

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics
  • Computer Science

Keywords

  • Algorithms
  • Polynomial
  • Monomial
  • Arithmetic circuit
  • Parametrized
  • complexity
  • Approximation hardness

Status

Published

ISBN/ISSN/Other

  • ISSN: 0020-0190