A baby steps/giant steps probabilistic algorithm for computing roadmaps in smooth bounded real hypersurface (Q629823)

A probabilitstic algorithm of complexity \((nD)^{O(n^{1.5})}\) for the problem of computing a roadmap of a closed and bounded hypersurface \(V\) of degree \(D\) in \(n\) variables with finitely many singular points is given. The concept of a roadmap is slightly modified considering algebraic sets \(V\subseteq \mathbb{C}^n\). An algebraic set \(\mathfrak{R}\subseteq V\) is a roadmap if each semi--algebraic component of \(V\cap \mathbb{R}^n\) has a nonempty and semi--algebraically connected intersection with \(\mathfrak {R}\cap \mathbb{R}^n\).