We study submodular maximization problems with matroid constraints, in particular, problems where the objective can be expressed via compositions of analytic and multilinear functions. We show that for functions of this form, the so-called continuous greedy algorithm attains a ratio arbitrarily close to $(1-1/e) \approx 0.63$ using a deterministic estimation via Taylor series approximation. This drastically reduces execution time over prior art that uses sampling.

翻译：我们研究的亚模式最大化问题与机器人限制有关,特别是目标可以通过分析和多线函数的构成来表达的问题。我们表明,对于这种形式的功能,所谓的持续贪婪算法在使用泰勒系列近似法的确定性估计方法中任意得出接近于$(1-1/e)\approx 0.63美元的比例。这大大缩短了使用抽样的先前艺术的处决时间。