One‐pass streaming algorithm for monotone lattice submodular maximization subject to a cardinality constraint

Summary In the article, we devise streaming algorithms for maximization of a monotone submodular function subject to a cardinality constraint on the integer lattice. Based on the observation that lattice submodularity is not equivalent to diminishing return submodularity on the integer lattice but r...

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Bibliographic Details
Published in:Concurrency and computation Vol. 35; no. 17
Main Authors: Zhang, Zhenning, Guo, Longkun, Wang, Linyang, Zou, Juan
Format: Journal Article
Language:English
Published: Hoboken Wiley Subscription Services, Inc 01.08.2023
Subjects:
Algorithms
cardinality
Complexity
integer lattice
Integers
lattice submodular
Maximization
memory complexity
Optimization
streaming algorithm
ISSN:1532-0626, 1532-0634
Online Access:Get full text
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Summary:Summary In the article, we devise streaming algorithms for maximization of a monotone submodular function subject to a cardinality constraint on the integer lattice. Based on the observation that lattice submodularity is not equivalent to diminishing return submodularity on the integer lattice but rather a weaker condition, we propose a one‐pass streaming algorithm with a modified binary search as subroutine of each step. Finally, we show that the algorithm is with approximation ratio 1/2−ε, memory complexity O(ε−1klogk), and per‐element query complexity O(ε−2log2k).
Bibliography:Funding information
Science and Technology Program of Beijing Education Commission, KM201810005006; Beijing Natural Science Foundation Project, Z200002; National Natural Science Foundation of China, 12001025, 61772005, 11871081, 11801310; Outstanding Youth Innovation Team Project for Universities of Shandong Province, 2020KJN008
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ISSN:1532-0626
1532-0634
DOI:10.1002/cpe.6645