The objective of a two-stage submodular maximization problem is to reduce the ground set using provided training functions that are submodular, with the aim of ensuring that optimizing new objective functions over the reduced ground set yields results comparable to those obtained over the original ground set. This problem has applications in various domains including data summarization. Existing studies often assume the monotonicity of the objective function, whereas our work pioneers the extension of this research to accommodate non-monotone submodular functions. We have introduced the first constant-factor approximation algorithms for this more general case.

翻译：摘要：两阶段子模最大化问题的目标是通过利用提供的训练函数（这些函数具有子模性）来缩减原始数据集，以确保在新目标函数上对缩减后的数据集进行优化所得到的结果，与在原始数据集上优化所得到的结果具有可比性。该问题在数据摘要等多个领域具有应用价值。现有研究通常假设目标函数具有单调性，而我们的工作率先将这一研究拓展至非单调子模函数的情景。针对这一更一般的情况，我们提出了首个常数因子近似算法。