Submodular Maximization Subject to a Knapsack Constraint Under Noise Models

Dung K. T. Ha, Canh V. Pham, Huan X. Hoang
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引用次数: 1

Abstract

The field of Submodular Maximization subject to a Knapsack constraint has recently expanded to a variety of application domains, which is facing some challenges such as data explosions or additional conditions. There exist plenty of objective functions that cannot be evaluated exactly in many real cases unless they are estimated with errors. It leads to solving the problem under noise models. Somewhat surprisingly, Submodular Maximization subject to a Knapsack constraint under Noise models ([Formula: see text]) has never been discussed a lot before. Hence, in this paper, we consider the problem with two kinds of noise models which are addition and multiplication. Inspired by the traditional Greedy algorithm, we first propose a Greedy algorithm under Noises with provable theoretical bounds. In order to find the solution when input data are extremely large, we then devise an efficient streaming algorithm that scans only a single pass over the data and guarantees theoretical approximations. Finally, we conduct some experiments on Influence Maximization problem under knapsack constraint, an instance of [Formula: see text] to show the performances of the proposed algorithms.
噪声模型下背包约束下的子模最大化
受背包约束的子模块最大化领域最近已经扩展到各种应用领域,这些领域面临着一些挑战,例如数据爆炸或附加条件。在许多实际情况下,存在大量的目标函数,除非对它们进行误差估计,否则无法准确地求值。从而解决了噪声模型下的问题。令人惊讶的是,噪声模型下背包约束下的次模最大化([公式:见文本])以前从未被大量讨论过。因此,在本文中,我们考虑了两种噪声模型:加法和乘法。在传统贪心算法的启发下,我们首先提出了一种具有可证明理论边界的噪声下的贪心算法。为了在输入数据非常大的情况下找到解决方案,我们设计了一种高效的流算法,该算法只扫描一次数据并保证理论近似值。最后,我们对背包约束下的影响最大化问题进行了一些实验,以[公式:见文本]为例,展示了所提出算法的性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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