Online and Streaming Algorithms for Constrained $k$-Submodular Maximization
This work addresses the need for efficient algorithms in applications like ad allocation and influence maximization where data is large or decisions must be made online, representing an incremental advancement with specific performance gains.
The paper tackled the problem of constrained k-submodular maximization in large-scale or real-time settings by developing single-pass streaming and online algorithms for monotone and non-monotone objectives under cardinality and knapsack constraints, achieving provable constant-factor approximation guarantees that improve upon state-of-the-art results in most cases.
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.