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In this paper, we devise three deterministic algorithms for solving the m-set k-packing, m-dimensional k-matching, and t-dominating set problems in time O * (5.44 mk), O * (5.44 (m−1)k) and O * (5.44 t), respectively. Although recently there have been remarkable progresses on ran-domized solutions to those problems, yet our bounds make good improvements on… (More)

Given any fixed integer q ≥ 2, a q-monomial is of the format x s 1 i 1 x s 2 i 2 · · · x st it such that 1 ≤ s j ≤ q − 1, 1 ≤ j ≤ t. q-monomials are natural generalizations of multilinear monomials. Recent research on testing multilinear monomials and q-monomials for prime q in multivariate polynomials relies on the property that Zq is a field when q ≥ 2 is… (More)

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 determinis-tic algorithm for the same q-monomial testing problem but requiring the polynomials… (More)

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