Abstract
Let F 1,..., F s ∈ Z[X 1,...,X n ] be quasiconvex polynomials of degree bounded by d≥2. Let L be an upper bound for the binary length of their coefficients. We show that the system F 1≤0,..., F s ≤0 admits an integer solution if and only if there exists such a solution with binary length bounded by (sd)cn · L. (Here c>0 is a constant independent on s, d, n and L). We obtain a similar geometric bound for the corresponding minimization problem. The simply exponential feature of our bound is intrinsic to this problem.
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© 1991 Springer-Verlag Berlin Heidelberg
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Bank, B., Krick, T., Mandel, R., Solernó, P. (1991). A geometrical bound for integer programming with polynomial constraints. In: Budach, L. (eds) Fundamentals of Computation Theory. FCT 1991. Lecture Notes in Computer Science, vol 529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54458-5_56
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DOI: https://doi.org/10.1007/3-540-54458-5_56
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