I have the following problem. I would like to know if this reduces to some standard problem in Graph theory. Any suggestions are much appreciated.
I have a multi-cast network with 1 source (denoted in black in the figure http://s22.postimage.org/7a32mikc1/Graph.jpg) and $N$ destination nodes (red). The network also has $R$ relay nodes (green). The network has an associated edge set $E$ which describes the connections between all the nodes. The constraint for the network is that there should be at-least $k$-edge connectivity between source and each of the destinations. Can we find the minimum number of relays (and which relays) to meet this constraint. Note that in some cases $R$ relays may not be sufficient to meet the $k$-edge connectivity requirement and in other cases a subset of $R$ may be sufficient.
http://s22.postimage.org/7a32mikc1/Graph.jpg has an example network. From the figure, this network has 5 destination nodes and 14 relay nodes. But it is clear that even if we remove the three relay nodes circled in blue, the source still has 2-edge connectivity to each destination nodes. How to determine the relay nodes that are not necessary but still maintain the edge connectivity.