Before revision:  An edge e from the complement of G can be inserted {\em  into D(G) if there exists a simple drawing of G ' = (V, E\cup \{e \ D(G) as a subdrawing. We show that it is NP-complete to decide whether a given edge can be inserted into a simple drawing , by this solving an open question by Arroyo, Derka, and Parada and a pseudosegment \sigma, it can be decided in polynomial time whether there exists a pseudocircle \Phi_\sigma extending \sigma for which \mathcal{A}\cup\{\Phi_\sigma\} is again an arrangement of pseudocircles} .
After revision:  An edge e from the complement of G can be inserted {\em into D(G) if there exists a simple drawing of G ' = (V, E\cup \{e \ D(G) . As a result of Levi's Enlargement Lemma, if a drawing is rectilinear (pseudolinear), that is, the edges can be extended into an arrangement of lines (pseudolines), then any edge in the complement of G can be inserted. In contrast, we show that it is NP-complete to decide whether a given edge can be inserted into a simple drawing , by this solving an open question by Arroyo, Derka, and Parada and a pseudosegment \sigma, it can be decided in polynomial time whether there exists a pseudocircle \Phi_\sigma extending \sigma for which \mathcal{A}\cup\{\Phi_\sigma\} is again an arrangement of pseudocircles} .