Dynamic Upward Planarity Testing of Single Source Embedded Digraphs.

In this paper, we present a dynamic algorithm that checks if a single-source embedded digraph is upward planar in the presence of edge insertions and edge deletions without changing the embedding of the digraph. We show that it can be checked in $O\ (log\ n)$ amortized time whether the updated graph is a single-source upward planar digraph with a fixed external face.