Determination of maximum likelihood tree T^* given cascade c on graph G.
To me, the main insight to solve this problem is to realize that T^* identification given c, G can be efficiently performed by a node-wise optimization of the active nodes in c (i.e. any active node has exactly one infection source). On the other hand, I am not entirely certain whether w(i,j) = \log(P'(i,j))-\log(\epsilon) (preprint on arXiv) or w(i,j) = \log(P'(i,j))-\log(\epsilon P(i,j)) (KDD '12) is actually the right weight to use. It seems to me that we ought to use w(i,j)=\log(P'(i,j)) directly, and that we don't necessarily have to make the approximation of Eq. 11 (i.e. assuming all unactivated edges are \epsilon-edges). Let me try out my idea first.
