New performance guarantees for the greedy maximization of submodular set functions

被引:0
|
作者
Jussi Laitila
Atte Moilanen
机构
[1] University of Helsinki,Department of Mathematics and Statistics
[2] University of Helsinki,Department of Biosciences
来源
Optimization Letters | 2017年 / 11卷
关键词
Approximation; Cardinality; Convex optimization ; Greedy algorithm; Maximization; Steepest ascent;
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学科分类号
摘要
We present new tight performance guarantees for the greedy maximization of monotone submodular set functions. Our main result first provides a performance guarantee in terms of the overlap of the optimal and greedy solutions. As a consequence we improve performance guarantees of Nemhauser et al. (Math Program 14:265–294, 1978) and Conforti and Cornuéjols (Discr Appl Math 7:251–274, 1984) for maximization over subsets, which are at least half the size of the problem domain. As a further application, we obtain a new tight approximation guarantee in terms of the cardinality of the problem domain.
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页码:655 / 665
页数:10
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