Fully Dynamic Submodular Maximization over Matroids

Maximizing monotone submodular functions under a matroid constraint is a classic algorithmic problem with multiple applications in data mining and machine learning. We study this significant problem in the fully dynamic setting, where elements can be both inserted and deleted in real-time. Our main...

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Bibliographic Details
Published inACM transactions on algorithms Vol. 21; no. 1; pp. 1 - 23
Main Authors Dütting, Paul, Fusco, Federico, Lattanzi, Silvio, Norouzi-Fard, Ashkan, Zadimoghaddam, Morteza
Format Journal Article
LanguageEnglish
Published New York, NY ACM 30.11.2024
Subjects
Approximation algorithms analysis
Combinatorial algorithms
Mathematics of computing
Theory of computation
Matroids
Fully Dynamic Algorithms
Submodular Maximization
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Summary:Maximizing monotone submodular functions under a matroid constraint is a classic algorithmic problem with multiple applications in data mining and machine learning. We study this significant problem in the fully dynamic setting, where elements can be both inserted and deleted in real-time. Our main result is a randomized algorithm that maintains an efficient data structure with an \({\tilde{O}(\frac{{k^{2}}}{{\varepsilon}})}\) amortized update time (in the number of insertions and deletions) and yields a \({(4+O(\varepsilon))}\) -approximate solution with respect to the dynamic optimum, where \(k\) is the rank of the matroid.
ISSN:1549-6325
1549-6333
DOI:10.1145/3698397