I have a problem that is reducible to (efficiently) determining the reachability of a node in a fully dynamic planar digraph.
I'm aware of "A fully dynamic data structure for reachability in planar digraphs" which provides O(n^(2/3) log n) query with a O(n)-space data structure.
Can this be / has this been bettered?
If all my queries have the same source node, is there a more efficient (in time/space/both) way?
Are there any other related literature that deals with more efficient queries albeit with more restrictions imposed on the digraph?