  Maximizing submodular functions have been studied extensively for a wide
range of subset-selection problems. However, much less attention has been given
to the role of submodularity in sequence-selection and ranking problems. A
recently-introduced framework, named \emph{maximum submodular ranking} (MSR),
tackles a family of ranking problems that arise naturally when resources are
shared among multiple demands with different budgets. For example, the MSR
framework can be used to rank web pages for multiple user intents. In this
paper, we extend the MSR framework in the streaming setting. In particular, we
consider two different streaming models and we propose practical approximation
algorithms. In the first streaming model, called \emph{function arriving}, we
assume that submodular functions (demands) arrive continuously in a stream,
while in the second model, called \emph{item arriving}, we assume that items
(resources) arrive continuously. Furthermore, we study the MSR problem with
additional constraints on the output sequence, such as a matroid constraint
that can ensure fair exposure among items from different groups. These
extensions significantly broaden the range of problems that can be captured by
the MSR framework. On the practical side, we develop several novel applications
based on the MSR formulation, and empirically evaluate the performance of the
proposed~methods.
