Streaming Algorithms for Maximizing Monotone Submodular Functions Under a Knapsack Constraint

Chien-Chung Huang, Naonori Kakimura, Yuichi Yoshida

Abstract: 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 \((0.363-\varepsilon )\)-approximation algorithm, requiring only a single pass through the data; moreover, we propose a \((0.4-\varepsilon )\)-approximation algorithm requiring a constant number of passes through the data. The required memory space of both algorithms depends only on the size of the knapsack capacity and \(\varepsilon \).