Single-source shortest paths and strong connectivity in dynamic planar graphs

We give a fully dynamic single-source shortest paths data structure for planar weighted digraphs with O˜(n4/5) worst-case update time and O(log2⁡n) query time. Here, single can either change the graph by inserting or deleting an edge, reset source s of interest. All known non-trivial planarity-exploiting exact algorithms to date had polynomial then extend our approach, obtaining that maintain digraph under edge insertions deletions, is capable returning identifier strongly connected component any vertex. The bounds are same as distance oracle. To best knowledge, this first strong-connectivity algorithm achieving both sublinear polylogarithmic important class digraphs.