The following paper is important. The authors develop a streaming algorithm for maximizing a submodular function.
Streaming Algorithms for News and Scientific Literature Recommendation: Submodular Maximization with a d-Knapsack Constraint by Qilian Yu, Easton Li Xu, Shuguang Cui
Submodular maximization problems belong to the family of combinatorial optimization problems and enjoy wide applications. In this paper, we focus on the problem of maximizing a monotone submodular function subject to a
d-knapsack constraint, for which we propose a streaming algorithm that achieves a (11+d−ϵ)-approximation of the optimal value, while it only needs one single pass through the dataset without storing all the data in the memory. In our experiments, we extensively evaluate the effectiveness of our proposed algorithm via two applications: news recommendation and scientific literature recommendation. It is observed that the proposed streaming algorithm achieves both execution speedup and memory saving by several orders of magnitude, compared with existing approaches.
- Learning with Submodular Functions: A Convex Optimization Perspective (demo ). - implementation- ( more recent pdf version is here)
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