4,701 research outputs found
Monomial Testing and Applications
In this paper, we devise two algorithms for the problem of testing
-monomials of degree in any multivariate polynomial represented by a
circuit, regardless of the primality of . One is an time
randomized algorithm. The other is an time deterministic
algorithm for the same -monomial testing problem but requiring the
polynomials to be represented by tree-like circuits. Several applications of
-monomial testing are also given, including a deterministic
upper bound for the -set -packing problem.Comment: 17 pages, 4 figures, submitted FAW-AAIM 2013. arXiv admin note:
substantial text overlap with arXiv:1302.5898; and text overlap with
arXiv:1007.2675, arXiv:1007.2678, arXiv:1007.2673 by other author
The Complexity of Testing Monomials in Multivariate Polynomials
The work in this paper is to initiate a theory of testing monomials in
multivariate polynomials. The central question is to ask whether a polynomial
represented by certain economically compact structure has a multilinear
monomial in its sum-product expansion. The complexity aspects of this problem
and its variants are investigated with two folds of objectives. One is to
understand how this problem relates to critical problems in complexity, and if
so to what extent. The other is to exploit possibilities of applying algebraic
properties of polynomials to the study of those problems. A series of results
about and polynomials are obtained in this paper,
laying a basis for further study along this line
Faster Deterministic Algorithms for Packing, Matching and -Dominating Set Problems
In this paper, we devise three deterministic algorithms for solving the
-set -packing, -dimensional -matching, and -dominating set
problems in time , and ,
respectively. Although recently there has been remarkable progress on
randomized solutions to those problems, our bounds make good improvements on
the best known bounds for deterministic solutions to those problems.Comment: ISAAC13 Submission. arXiv admin note: substantial text overlap with
arXiv:1303.047
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