Streaming Algorithms for Maximizing Monotone Submodular Functions Under a Knapsack Constraint

• Published in: Algorithmica Vol. 82; no. 4; pp. 1006 - 1032
• Main Authors: Huang, Chien-Chung, Kakimura, Naonori, Yoshida, Yuichi
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2020; Springer Nature B.V
• Subjects: Algorithm Analysis and Problem Complexity; Algorithms; Approximation; Computer Science; Computer Systems Organization and Communication Networks; Data Structures and Information Theory; Mathematical analysis; Mathematics of Computing; Maximization; Optimization; Theory of Computation; Multiple-pass streaming; Submodular functions; Single-pass streaming; Constant approximation
• ISSN: 0178-4617; 1432-0541
• DOI: 10.1007/s00453-019-00628-y

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 - ε ) -approximation algorithm, requiring only a single pass through the data; moreover, we propose a ( 0.4 - ε ) -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 ε .