  Constrained $k$-submodular maximization is a general framework that captures
many discrete optimization problems such as ad allocation, influence
maximization, personalized recommendation, and many others. In many of these
applications, datasets are large or decisions need to be made in an online
manner, which motivates the development of efficient streaming and online
algorithms. In this work, we develop single-pass streaming and online
algorithms for constrained $k$-submodular maximization with both monotone and
general (possibly non-monotone) objectives subject to cardinality and knapsack
constraints. Our algorithms achieve provable constant-factor approximation
guarantees which improve upon the state of the art in almost all settings.
Moreover, they are combinatorial and very efficient, and have optimal space and
running time. We experimentally evaluate our algorithms on instances for ad
allocation and other applications, where we observe that our algorithms are
efficient and scalable, and construct solutions that are comparable in value to
offline greedy algorithms.
