Approximation Algorithms for Size-Constrained Non-Monotone Submodular Maximization in Deterministic Linear Time
In this work, we study the problem of finding the maximum value of a non-negative submodular function subject to a limit on the number of items selected, a ubiquitous problem that appears in many applications, such as data summarization and nonlinear regression. We provide the first deterministic, l...
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| Published in: | arXiv.org |
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| Main Authors: | , |
| Format: | Paper |
| Language: | English |
| Published: |
Ithaca
Cornell University Library, arXiv.org
04.08.2023
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| Subjects: | |
| ISSN: | 2331-8422 |
| Online Access: | Get full text |
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| Summary: | In this work, we study the problem of finding the maximum value of a non-negative submodular function subject to a limit on the number of items selected, a ubiquitous problem that appears in many applications, such as data summarization and nonlinear regression. We provide the first deterministic, linear-time approximation algorithms for this problem that do not assume the objective is monotone. We present three deterministic, linear-time algorithms: a single-pass streaming algorithm with a ratio of \(23.313 + \epsilon\), which is the first linear-time streaming algorithm; a simpler deterministic linear-time algorithm with a ratio of \(11.657\); and a \((4 + O(\epsilon ))\)-approximation algorithm. Finally, we present a deterministic algorithm that obtains ratio of \(e + \epsilon\) in \(O_{\epsilon}(n \log(n))\) time, close to the best known expected ratio of \(e - 0.121\) in polynomial time. |
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| Bibliography: | SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50 |
| ISSN: | 2331-8422 |
| DOI: | 10.48550/arxiv.2104.06873 |