Monomial testing and applications

Abstract

In this paper, we devise two algorithms for the problem of testing q-monomials of degree k in any multivariate polynomial represented by a circuit, regardless of the primality of q. One is an O(2 k ) time randomized algorithm. The other is an O(12.8 k ) time deterministic algorithm for the same q-monomial testing problem but requiring the polynomials to be represented by tree-like circuits. Several applications of q-monomial testing are also given, including a deterministic O(12.8 mk ) upper bound for the m-set k-packing problem. © 2013 Springer-Verlag Berlin Heidelberg.