Solving systems of polynomial inequalities in subexponential time

extensions of some polynomial inequalities to the polar derivative

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Solving Systems of Polynomial

Current geometric and solid modeling systems use semi-algebraic sets for deening the boundaries of solid objects, curves and surfaces, geometric constraints with mating relationship in a mechanical assembly, physical contacts between objects, collision detection. It turns out that performing many of the geometric operations on the solid boundaries or interacting with geometric constraints is re...

Planar k-Path in Subexponential Time and Polynomial Space

In the k-Path problem we are given an n-vertex graph G together with an integer k and asked whether G contains a path of length k as a subgraph. We give the first subexponential time, polynomial space parameterized algorithm for k-Path on planar graphs, and more generally, on H-minor-free graphs. The running time of our algorithm is O(2 √ k log2 n).

Solving parametric polynomial systems

We present a new algorithm for solving basic parametric constructible or semi-algebraic systems like C = {x ∈ C, p1(x) = 0, , ps(x) = 0, f1(x) 0, , fl(x) 0} or S = {x ∈ R, p1(x) = 0, , ps(x) = 0, f1(x)> 0, , fl(x)> 0}, where pi, fi ∈Q[U , X], U = [U1, , Ud] is the set of parameters and X = [Xd+1, , Xn] the set of unknowns. If ΠU denotes the canonical projection onto the parameter’s space, solvi...

Solving Systems of Polynomial Equations