Improved Streaming Algorithms for Maximizing Monotone Submodular Functions Under a Knapsack Constraint

In this paper, we consider the problem of maximizing a monotone submodular function subject to a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access only to a small fraction of the data stored in primary memory. For this problem, we propose a \((0.4-\varepsilon )\)-approximation algorithm requiring only a single pass through the data. This improves on the currently best \((0.363-\varepsilon )\)-approximation algorithm. The required memory space depends only on the size of the knapsack capacity and \(\varepsilon \).

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