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We show that detecting real roots for honestly <i>n</i>-variate (<i>n</i>+2)-nomials with integer exponents and coefficients) can be done in time polynomial in the sparse encoding for any fixed n<i>n</i>. The best previous complexity bounds were exponential in the sparse encoding, even for <i>n</i> fixed. We then give a characterization of those functions… (More)

Let FEAS R denote the problem of deciding whether a given system of real polynomial equations has a real root or not. We give a new, nearly tight threshold for when m is large enough to make FEAS R be NP-hard for input a single n-variate polynomial with exactly m monomial terms. We also outline a connection between the complexity of FEAS R , the topology of… (More)

Fewnomial theory began with explicit bounds — solely in terms of the number of variables and monomial terms — on the number of real roots of systems of polynomial equations. Here we take the next logical step of investigating the corresponding existence problem: Let FEAS R denote the problem of deciding whether a given system of multivariate polynomial… (More)

Cloud computing and big data are two core services in many organizations. Combining a big data platform, such as Hadoop, into the cloud architecture using virtualization technique will result in losing the performance benefit of MapReduce. Unique for the existing virtualized big data cloud, this work introduces an innovative cloud architecture called the… (More)

- Casey E. Stella
- 2005

Let FEAS R denote the problem of deciding whether a given system of polynomial equations has a real root or not. We give a new, nearly tight threshold for when m is large enough to make FEAS R be NP-hard for input a single n-variate polynomial with exactly m mono-mial terms. We also outline a connection between the complexity of FEAS R , the topology of A A… (More)

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