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 mem...

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Veröffentlicht in:Algorithmica Jg. 82; H. 4; S. 1006 - 1032
Hauptverfasser: Huang, Chien-Chung, Kakimura, Naonori, Yoshida, Yuichi
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.04.2020
Springer Nature B.V
Schlagworte:
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
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Zusammenfassung: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 .
Bibliographie:ObjectType-Article-1
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-019-00628-y