A fully dynamic algorithm to test the upward planarity of single-source embedded digraphs

Abstract

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. Let G Øφ be an upward planar single-source embedded digraph and let G?Øφ? Ø be a single-source embedded digraph obtained by updating G Øφ. We show that the upward planarity of G? Øφ?can be checked in O(logn) amortized time when the external face is fixed. © 2009 Springer Berlin Heidelberg.