I have a non-weighted directed graph G with edges E and vertices G. Edges can be added or removed, and therefore vertices can be added.
For instance, if I have a graph with 4 nodes: 0, 1, 2, 3 and if I add the edge 3 -> 4, it means the node 4 will be added. Nodes cannot be removed.
I am studying the problem of determining the shortest distance (just distance, not path) in this dynamic graph. I am very newbie in this problem, but as I know it would be still an open problem.
What is the fastest algorithm for this problem so far?
Thank you very much