We consider the problem of maximizing a non-negative submodular function under the $b$-matching constraint, in the semi-streaming model. When the function is linear, monotone, and non-monotone, we obtain the approximation ratios of $2+\varepsilon$, $3 + 2 \sqrt{2} \approx 5.828$, and $4 + 2 \sqrt{3} \approx 7.464$, respectively. We also consider a generalized problem, where a $k$-uniform hypergraph is given, along with an extra matroid or a $k'$-matchoid constraint imposed on the edges, with the same goal of finding a $b$-matching that maximizes a submodular function. When the extra constraint is a matroid, we obtain the approximation ratios of $k + 1 + \varepsilon$, $k + 2\sqrt{k+1} + 2$, and $k + 2\sqrt{k + 2} + 3$ for linear, monotone and non-monotone submodular functions, respectively. When the extra constraint is a $k'$-matchoid, we attain the approximation ratio $\frac{8}{3}k+ \frac{64}{9}k' + O(1)$ for general submodular functions.

翻译：我们分别考虑在半流模式中将非负值子模块功能在 $b$- 匹配限制下最大化的问题。 当函数是线性、 单调和不单调时, 我们得到的近似比率为 2 ⁇ varepsilon$, 3 + 2\ sqrt{2}\ approx 5. 828美元, 和 4 + 2 + 2\ sqrt{ 3}\ approx 7.464美元。 我们还考虑一个普遍的问题, 提供美元- 单制超标, 以及给边缘强加的超配机或 $k$- 美元- 配成质限制, 相同的目标是找到美元- 匹配, 使亚调函数最大化 。 当额外的制约是 ⁇ + 1 + + ⁇ + ⁇ crqrt{k} + $ 2k_k+ 美元, 当普通软质 3\\ mror_ 的 软质 函数分别达到 0. 3\ moral=x pral pral press press 。