We consider the problem of maximizing submodular functions in single-pass streaming and secretaries-with-shortlists models, both with random arrival order. For cardinality constrained monotone functions, Agrawal, Shadravan, and Stein gave a single-pass $(1-1/e-\varepsilon)$-approximation algorithm using only linear memory, but their exponential dependence on $\varepsilon$ makes it impractical even for $\varepsilon=0.1$. We simplify both the algorithm and the analysis, obtaining an exponential improvement in the $\varepsilon$-dependence (in particular, $O(k/\varepsilon)$ memory). Extending these techniques, we also give a simple $(1/e-\varepsilon)$-approximation for non-monotone functions in $O(k/\varepsilon)$ memory. For the monotone case, we also give a corresponding unconditional hardness barrier of $1-1/e+\varepsilon$ for single-pass algorithms in randomly ordered streams, even assuming unlimited computation. Finally, we show that the algorithms are simple to implement and work well on real world datasets.

翻译：我们考虑在单流流中最大限度地增加子模块功能的问题,在单流中和秘书与分流中最大限度地增加子模块功能的问题,这两种模式都具有随机抵达顺序。对于受限制的单质功能,Agrawal、Shadravan和Stein提供了单流(1-1/e-varepsilon)$-ogymogymation 算法,仅使用线性内存,但是它们对美元(varepsilon)的指数依赖使得对美元(varepsilon=0.1美元)的记忆也变得不切实际。我们简化了算法和分析,使美元(varepsilon)的依赖性(特别是美元//craepsilon)得到指数性改进。为了扩大这些技术,我们还在美元(k/k/\varepsilon)的记忆中为非分子函数提供了简单的($(1/e-e- varepsilon) 美元支持。对于单行算算法中,我们给出了相应的无条件的硬度障碍屏障屏障屏障屏障屏障屏障1-1/euu-ureepsluslonlonlonon 用于随机流中,甚至假设地计算。