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.

翻译：约束$k$-子模最大化是一个通用框架，涵盖了众多离散优化问题，如广告分配、影响力最大化、个性化推荐等。在这些应用的许多场景中，数据集规模庞大或需以在线方式做出决策，这推动了高效流式算法与在线算法的发展。本文针对基数约束和背包约束下的单调与一般（可能非单调）目标函数，提出了单遍流式算法与在线算法，用于解决约束$k$-子模最大化问题。我们的算法具有可证明的常数因子近似保证，在几乎所有场景中均超越了现有最优结果。此外，这些算法具有组合特性、极高的效率，并达到了空间与运行时间的最优性。我们通过广告分配及其他应用的实例对算法进行了实验评估，结果表明算法高效且可扩展，所构造的解在价值上与离线贪心算法相当。