Two-stage submodular maximization problem beyond nonnegative and monotone
We consider a two-stage submodular maximization problem subject to a cardinality constraint and k matroid constraints, where the objective function is the expected difference of a nonnegative monotone submodular function and a nonnegative monotone modular function. We give two bi-factor approximatio...
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| Published in: | Mathematical structures in computer science Vol. 34; no. 3; pp. 211 - 226 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
01.03.2024
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| ISSN: | 0960-1295, 1469-8072 |
| Online Access: | Get full text |
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| Summary: | We consider a two-stage submodular maximization problem subject to a cardinality constraint and
k
matroid constraints, where the objective function is the expected difference of a nonnegative monotone submodular function and a nonnegative monotone modular function. We give two bi-factor approximation algorithms for this problem. The first is a deterministic
$\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}} \right),1} \right)$
-approximation algorithm, and the second is a randomized
$\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}} \right) - \varepsilon ,1} \right)$
-approximation algorithm with improved time efficiency. |
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| ISSN: | 0960-1295 1469-8072 |
| DOI: | 10.1017/S0960129521000372 |