We study random order semi-streaming algorithms for submodular maximization under a wide range of combinatorial constraint classes, including matroids, matroid $p$-parity, $p$-exchange systems and $p$-systems. For most of these classes of constraints, our results are the first improvement over what is known to be achievable for adversarial order. For matroids, matching and $p$-matchoids, previous random order results were known, and we improve over some of these as well. In the case of matroids, our improved results show a separation between adversarial and random order semi-streaming algorithms, and exponentially improve the number of passes necessary for getting $1 - 1/e - \varepsilon$ approximation for maximizing a monotone submodular function subject to a matroid constraint. We also prove a new hardness result showing a similar separation for $p$-systems. Our results are based on two new technical tools. One tool provides a general way to translate offline algorithms for many classes of constraints into random order semi-streaming algorithms. The other tool is a semi-streaming variant of a recently proposed offline algorithm for matroid constraints.

翻译：我们研究了在广泛组合约束类别（包括拟阵、拟阵$p$-配对、$p$-交换系统和$p$-系统）下，子模最大化的随机顺序半流式算法。对于大多数约束类别，我们的结果是首次在对抗顺序已知结果基础上实现的改进。对于拟阵、匹配和$p$-拟阵匹配，已有随机顺序结果，我们在其中部分结果上也有所提升。在拟阵情形中，我们的改进结果揭示了对抗顺序与随机顺序半流式算法之间的差异，并将获取单调子模函数在拟阵约束下$1 - 1/e - \varepsilon$近似所需的轮次数量呈指数级改善。我们还证明了一个新的硬度结果，显示$p$-系统也存在类似的分离现象。我们的结果基于两项新技术工具：一项工具提供了将多种约束类别的离线算法通用转化为随机顺序半流式算法的方法；另一项工具是针对拟阵约束的近期提出的离线算法的半流式变体。