  In this paper, we study the \underline{R}obust \underline{o}ptimization for
\underline{se}quence \underline{Net}worked \underline{s}ubmodular maximization
(RoseNets) problem. We interweave the robust optimization with the sequence
networked submodular maximization. The elements are connected by a directed
acyclic graph and the objective function is not submodular on the elements but
on the edges in the graph. Under such networked submodular scenario, the impact
of removing an element from a sequence depends both on its position in the
sequence and in the network. This makes the existing robust algorithms
inapplicable. In this paper, we take the first step to study the RoseNets
problem. We design a robust greedy algorithm, which is robust against the
removal of an arbitrary subset of the selected elements. The approximation
ratio of the algorithm depends both on the number of the removed elements and
the network topology. We further conduct experiments on real applications of
recommendation and link prediction. The experimental results demonstrate the
effectiveness of the proposed algorithm.
