On the Complexity of Computing the Topology of Real Algebraic Space Curves.

In this paper, we present a deterministic algorithm to find a strong generic position for an algebraic space curve. We modify our existing algorithm for computing the topology of an algebraic space curve and analyze the bit complexity of the algorithm. It is $\tilde{\mathcal {O}} (N^{20})$, where $N=\max\{d,\tau\}$, $d, \tau$ are the degree bound and the bit size bound of the coefficients of the defining polynomials of the algebraic space curve. To our knowledge, this is the best bound among the existing work. It gains the existing results at least $N^2$.