Shenshi Chen

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In this paper, we devise three deterministic algorithms for solving them-set k-packing,m-dimensional k-matching, and t-dominating set problems in time O(5.44), O(5.44) and O(5.44), respectively. Although recently there have been remarkable progresses on randomized solutions to those problems, yet our bounds make good improvements on the best known bounds(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) time randomized algorithm. The other is an O(12.8) time deterministic algorithm for the same q-monomial testing problem but requiring the polynomials to be(More)
Given any fixed integer q ≥ 2, a q-monomial is of the format x1 i1 x s2 i2 · · · x st it such that 1 ≤ sj ≤ 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 prime.(More)
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