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Multilinear Monomial Detection

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  • First Online:
Encyclopedia of Algorithms

  • 89 Accesses

Years and Authors of Summarized Original Work

  • 2008; Koutis

  • 2009; Williams

Problem Definition

The topic of this article is the parameterized multilinear monomial detection problem:

k-MlD::

Given an arithmetic circuit C representing a polynomial P(X) over \(\mathbb{Z}_{+}\), decide whether P(X) construed as a sum of monomials contains a multilinear monomial of degree k.

An arithmetic circuit is a directed acyclic graph with nodes corresponding to addition and multiplication gates, sources labeled with variables from a set X or positive integers, and one special terminal corresponding to the output gate. A monomial of degree k is a product of exactly k variables from X, and it is called multilinear if these k variables are distinct.

The k-MlD problem is arguably a fundamental problem, encompassing as special cases many natural and well-studied parameterized problems. Along with the algorithm for its solution, k-MlD provides a general framework for designing parameterized algorithms [11, 15...

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Author information

Authors and Affiliations

  1. Computer Science Department, University of Puerto Rico-Rio Piedras, San Juan, PR, USA

    Ioannis Koutis

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  1. Ioannis Koutis
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Correspondence to Ioannis Koutis .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Koutis, I. (2016). Multilinear Monomial Detection. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_784

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