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.

本文提出了单遍流式和在线算法的受约束k-次模最大化，其中包含基数和背包约束限制,该算法可以提供不错的近似解和高效的解决方案，并在广告分配等应用实例上得到了验证。

约束k次模最大化的在线和流式算法